76

O'3 0D. - cs.umd.edu

  • Upload
    others

  • View
    6

  • Download
    0

Embed Size (px)

Citation preview

Page 1: O'3 0D. - cs.umd.edu

�������������� �������������������

� � � ���������������� � �"!$#�%'&�#�( �������

)+*-,/.10�243�57698;:�.<0>=@?$3"?$A�BC?'0D?'*E*-F$*�GIHJ?$3�2-?'*LKMHNF$0D?$3�2-.JOP8QR#TSVUXW;Y$Z[��]\_^ZC&�`'&�` � &�ab�"ced

^]f d � [�abg$%$c��"# �ih S-�"` h �kjC�"g'&�#�c�ak�"`�cd ��`'l�cTSVcm%$c��Cno[�# �qp�r &�` h � ps� [�akg$%$cm�"# �ih S-�"` h ��l

^]f d � �"`�c��"#�nt[�# � %$c�[�a>&�cTSV[�` � ��l���&�# hmuv�`�S r �"#elwS-c�(+[�n�xX&�#�(�\4&y` p� [�\z\-�"{��k|R&�#�U<}~xXj �� ������

)+�N8"3�0D?'��3Q�� h S-�"`ic p &�ce& � g'&y#e&D\z\-�]\&D\-{�[�#TSVc u a>lCnt[�#�c u #��"� h [�akab[�`�l�g'&�cTS4&�\ p &�ce&+lTc�#�% h c�%$#���lM��c u �k!$% h U��"c;|�x �

� %'& p c�#��"��} �� c�#��"��}�&�` p���N� c�#m�"���q&�#��@g$#���l��"`�c�� p Y ��u � p [�a>&�SV` h [�`'lwS_l�c]l;[�ng�\_&�`'&�#�\zSV`$�Xl��"{�ak�"`�c p &�ce&�tS�Y���Y-}N��%$#���&�%9[�n�c u � � �"`'lT%'l � �mWqQ �q��� S-`$�@�$\-��l]�eY>|R&y#e&D\z\-�]\&D\-{�[�#TSVc u a>l�no[�#�!$%�Sz\ p SV`${sc u � p &�ce& � g'&�#e&D\z\-�]\l�g'&�cTS4&�\l�c�#m% h c�%$#���l"}R&�lL���]\z\&�l p �"c��"#ma;S-`�SV`${sc u � h \-[il�� p g/[�\-(i{�[�`'l�nt[�#�ab� p !i(Xc u �b\zS-`$��l��"{�ak�"`�cel"}Ja>&�gS-`icm�"#el�� h c�S-[�`I}'&y` p &kl�g'&�c�S_&D\I#e&y`${�� � %$�"#�(+&�#�� p ��l h #�S-!'� p Y �u ��g'�"#�nt[�#�a>&y` h ��[�n p &�ce& � g'&�#e&D\z\-�]\�&D\-{�[�#TSVc u a>lnt[�#kl�g'&�c�S_&D\[�g/�"#e&�c�S-[�`'l�S_l@&D\_l�[ h [�akg'&�#m� p Y �u ��&D\-{�[�#�S-c u a>lb&�#��bSVabg�\V�"ab�"`ic�� p %'lwS-`${9c u ��l h &�`�ak[ p �]\[�n�g'&�#]&D\z\V�]\ h [�akg$%$c]&�c�S-[�`X[�`�c u � u (ig/�"# h %$!'�>&y# h�u S-c�� h cm%$#���[�n�c u � � [�`$`$� h cTSV[�`�xX& hmu S-`$��Y ��u �;#���lT%�\Vc]l[�n�]�$g'�"#�S-ak�"`�cel�#�� r ��&D\Ic u &�c�c u ��!$% h U��"c|�x � � %'& p c�#��"�C[�%$c�g/�"#�nt[�#�a>l�!'[�c u c u � ��� c�#��"��&�` p+� � � c�#m�"��Y �u S4lS_lkg$#TSVa@&�#�Sz\-(�!'� h &�%'l���c u ��!$% h U��"c>|�x � � %'& p c�#��"�+(�SV�]\ p l+&X#m�"{�%�\_&�# p S_lE��[�S-`ic p � h [�akg/[ilwS-c�S-[�`�[�n�l�g'& h �� u Sz\-�>c u � ��� c�#��"�+&�` p9� � � c�#��"� p [+`$[�cDY ��u �k#m�"{�%�\_&�# p S_lE��[�S-`ic p � h [�akg/[ilwS-c�S-[�`�S-` h #���&�l���lLc u �kg/[�c��"`�c�S_&D\nt[�#CS-`ic��"#mg$#�[ h ��lml�[�# h [�aka;%$`�S h &�c�S-[�`�&�` p g'&�#e&�\�\-�]\zS_l�a�S-`9c u �k!$% h U��"c�|�x � � %'& p c�#��"��}Jc u �"#��"!�(��"`'&�!�\zS-`${c u ���]�$� h %$c�S-[�`Xc�S-ak��l�c�[ p � h #���&�l���#��]\_&�cTS r ��c�[kc u [il��C`$�"� p � p !�(@c u � ��� c�#��"�;&�` p+� � � c�#m�"��Y

�I�"� �N¡<¢e£t¤¡I¥m�I�t¦�§D§�¢e£t¨t©�ªC� «�§�¥m£t¨I¬"­C¨t��©�®N¥�¨E� ¢]«�¥T¯'°"±w� ©�«�±�©²�¢]¦�«Dª�¥m¨E� ¢e«�¦�«Dª�©�£�³N£�¥m«"¨I´tµ<´4¶o·e¸T¶�¹�ºe·]»]¼"½

Page 2: O'3 0D. - cs.umd.edu

� � O'3�0D.����P��3�24.IO

|R&�#e&�\�\-�]\ p &�ce&�!'&�l�� l�($l�c��"a@l u & r ��!'�"�"` c u �9l�%$! � � h c@[�n�S-` h #���&�lwS-`${�&�c�c��"`�c�S-[�`IY �u S4lbS_l p %$��}�S-`�g'&�#�c�}c�[9c u ��& p�r �"`icb[�n u S-{ u \-( g'&�#e&�\�\-�]\ &�# h�u S-c�� h c�%$#m��l"}& p [�g$c�S-[�` [�n�c u ��#��]\_&�c�S-[�`'&D\�ak[ p �]\ }C&�` p�h�u &�\�\-�"`${���lg'[�l�� p !�(9[�! � � h c � [�#�S-�"`ic�� p l�($l�c��"a>l�� jC�� S �� }��S-a �� � YXx�% hmu [�nc u �>g'&y#e&D\z\-�]\ p &yce&�!'&�l��b#���l���&�# hmu�u &�lnt[ h %'l�� p [�`9a;%�\-c�S � &�c�cm#�S-!$%$c�� p � h \-%'l�cm�"#�S-`${9c�� hmu `�S � %$��l@� lT% h�u &�l���%$!$!'&�� lL�]�~c��"` p � p #e&�`${�� p � h \-%'l�c��"#�S-`${� ��[�#e& �� �� &�` p a;%�\-c�S � &�c�c�#�S-!$%$c��s{�#�S p p � h \-%'l�c��"#�S-`${��zW u &�` ����� �e} p &�ce&�g�\_& h �"ab�"`ic�� � [�g/����� � }�&�` p S-`icm#e& �[�g/�"#e&�c�[�#�g'&�#e&D\z\-�]\zS���&�c�S-[�`�� jC�� S�� ��� Y � [�g�S h llT% h�u &�l�&D\-{�[�#�S-c u a@lRnt[�#�a>&�`�S-g$%�\_&�c�S-`${>#m�]\4&yc�S-[�`'l h [�`ic]&DS-`�SV`${u S-{ u \-( l�U��"��� p &yc�c�#�S-!$%$c�� r &D\-%$��l"}1&y` p g'&�#e&D\z\-�]\ lTg'&�c�S_&D\ p &�c]& lTc�#�% h c�%$#���l�&�` p &D\-{�[�#�S-c u a@l"}$#��"a>&�SV`�[�g'�"`IY

����� B�0�2-.<0��bF$8"F�?'0���5�2tO�3�5<F�BC?'0D?'*E*-F$*�GPHJ?$3�24?'* [email protected] ?'2 O

|R#TSV[�#�#���l���&y# h�u S-`�c u �>l�g'&�c�S_&D\ p [�a>&DS-` u &�l�!'�"�"`s\zSVaMSVcm� p c�[ � %'& p c�#��"��l } � ��p c�#��"��l }�&y` p9��� c�#��"��l }R��S-c up S"!I�"#��"`ick&�g$g$#m[i& hmu ��l;�tS�Y���Y-}JS-a>&�{�� � l�g'& h �@[�#�[�! � � h c � lTg'& h �#� �$[�\-� �� �� ��&�` p {�[i&D\_l"Y ��u �b[�!$��� h c � l�g'& h �+&�g �g$#�[i& h�u ��lC&�l�lwS-{�`�[�`$��g$#m[ h ��l�lT[�#g'�"#�lTg'&�c�S_&D\7[�! � � h c�} � u Sz\V�;c u �LS-a>&�{�� � l�g'& h �M&yg$g$#�[i& hmu &�l�lwS-{�`'l�[�`$��g$#�[ �h ��l�l�[�#g'�"#C#��"{�S-[�`+[�n�l�g'& h ��Y

�u � � %'& p c�#��"�#���lT��&�# hmuku &�lNg$#�S-a>&�#TS�\-(bno[ h %'l�l�� p [�`>&�#���&M��#e&�lTc��"#"� p &�ce&�&�` p #m�"{�S-[�` � %'& p c�#m�"��l"YRx�% hmu#���l���&y# h�u�u &�l h [�` h �"`�c�#e&yc�� p [�` &D\-{�[�#TSVc u a>l;nt[�#;!$%�Sz\ p SV`${ ���]S-c u �"#MSV` &Xcm[�g ��p [��`�[�#k!/[�c�c�[�a � %$g�a>&�` �`$�"#"��!/[�c u g'[�S-`�c��"# � !'&�l�� p &�` p \zS-`$��&�#C#��"{�S-[�` � %'& p cm#��"��l$� Z�%$`${%� � }'jC� u ` �$� }$��!'&�# ��� � Y'&c u �"#�(!I[�#�cel u & r �nt[ h %'l�lT� p [�` p � r �]\-[�g�S-`${ `$�]S-{ u !'[�#+�'` p S-`${�c�� hmu `�S � %$��l)�+* &�` p �,�i}�Z�%$`${%� � � &�lb���]\z\ &�lb�]�$c�#e& h c�S-`${�#�� �{�S-[�`Xg$#�[�g/�"#�c�S-��l�&y` p g/�"#�nt[�#�a;S-`${�l��"cCc u �"[�#��"cTS h � %$�"#�S-��l-� � u &�l.����}��&�lwS����$}<Z%$`${/� � }<jC� u ` �$�� Y � [�ak��[�nc u �@��[�#�U u &�l��"akg�\-[�(�� p g$#�[�g$#�S-�"ce&y#�(Xg'&�#e&D\z\-�]\q&�# hmu S-c�� h c�%$#���lb����Y {'Y-}Nc���[ ��p SVab�"`'lwS-[�`'&D\l u %/0>�+�]� hmu &�`${��`$�"c���[�#�U1� x��]S�� � � }i[�#$2-3�465 78� xX&�#�c9� �� �e}�ak��l u$��h [�`$`$� h c�� p�h [�akg$%$c��"#el:� Z�%$`${%� ��� }$[�# p S"!I�"#��"`�c g$#�[�{�#e&�a �a;S-`${�\_&�`${�%'&�{���lb����Y {'Y-} � [�` h %$#m#��"`ic;|R#�[y\V[�{;� Q p �]\<�,= � �]}I� u Sz\-�+c u �ka>&y� [�#�S-c ( u &�l p ��&D\-c;��S-c u9u (ig/�"# h %$!'�&�# hmu S-c�� h c�%$#���l Y9����lTc�%�\>� ����l�c ����� �]�~cm�"` p � p c u � � %'& p c�#m�"�>#���lT��&�# hmu %$` p �"#kc u � p &�ce& � g'&�#]&D\z\V�]\ ��� x �tnt[�#�ih &�` �t� ` p�� x�[�`$[�c�[�`�S h]� a>&yg$g�SV`${ � ak[ p �]\�[�n�g'&�#e&�\�\-�]\ h [�abg$%$ce&�c�S-[�`IYC��`9& p$p S-c�S-[�`sc�[ p ��&�\�S-`${���S-c u \�S-`$��&�##��"{�S-[�` � %'& p c�#��"��lJS-`�c u � p &�c]& � g'&�#e&D\z\-�]\�� Z�Sz\z\�� �,�~h [�`�c��]�$c�}�&D\-{�[�#�S-c u a>lJ���"#�� p � r �]\V[�g'� p !i(�����l�cm%�\int[�#N!$%�S�\ p��S-`${�&�` p a>&�`�S-g$%�\_&�c�S-`${9�w��Y�{'Y-}'lT�"c c u �"[�#��"c�S h l�g'&�c�S_&D\ � %$�"#TSV��l � | � � %'& p c�#��"��l?�"&#m�"`�� � } � ` p ��� � } � [�l���� ���&�` p |�x � %'& p c�#m�"��l$�@�9�"!$!�� � } � &�ak����=y! � Y

�u �A� ��p c�#��"�B� ���"`ic � = � #m��l���&�# hmu �&�lq\zSVaMSVcm� p !$%$c;#���l�%�\-c�� p S-` & p ��l h #�S-g$c�S-[�`�[�n�&�`9S-akg/[�#�ce&y`ic;&D\ �{�[�#TSVc u a nt[�#;!$%�Sz\ p SV`${�c u � p &�c]&�l�c�#m% h c�%$#��bno[�#k& h [�\z\-� h c�S-[�` [yn g'[�S-`�cel;%'lwS-`${�� \-�]\z\-[ hmu � l@l h &�`�ak[ p �]\[�nh [�akg$%$c]&�c�S-[�`)� � \-�]\�� � ! � Y

� [�ak� [yn�c u ��g'&y#e&D\z\-�]\ ��� c�#��"��#m��l���&�# hmu+u &�l�nt[ h %'lml�� p [�`�&D\-{�[�#TSVc u a>l�nt[�#lwS-`${�\-� h g$% � a;%�\-c�S-g�\V�;g'&�#]&D\z\V�]\�

Page 3: O'3 0D. - cs.umd.edu

p S_l�U�l�($l�c��"a@l?� �&�ak� ��� � Y &%$# ��� c�#��"�@#���l���&�# h�u9u &�l h [�` h �"`�c�#e&�cm� p [�`9c u � p � r �]\-[�g$ak�"`�c�[�n &D\-{�[�#TSVc u a>lnt[�#;!$%�S�\ p S-`${ p &�ce& � g'&�#e&D\z\-�]\ ��� c�#m�"��lk&�` p g'[y\V(�{�[�`�S���&�cTSV[�` � Z�[i�]\ ��� � }�&�l����]\z\q&�l;l�g'&�c�S_&D\�� [�S-`'l � Z[��]\ ��� &�}Z�[i�]\ ��� ! � YN��c p S"!I�"#el�lwS-{�`�Sz� h &�`icT\V(@nt#�[�a c u ��nt[�#�ak�"#�&�g$g$#�[i& hmu SV`+c u &�c����Ca>&�U��%'l���[�n7a@&�`i(;g$#�[ h ��l�l�[�#elc�[@�]�~� h %$cm�kc u �kl�g'&�c�S_&D\ � %$�"#�S-��l�#e&�c u �"# c u &y` ab�"#��]\-( l�c�[�#��;c u � p &�c]&@[�`�g'&�#]&D\z\V�]\ p S_l�U~lC� u S�\-�@[�g'�"#]&�c�S-`${��S-c u &>lwS-`${�\-� h g$%9�w��Y�{'Y-}��+�&�ak� ����� �eY���`�c��"#���lTc�S-`${�\-(�}<c u ��g'&�#mc�S-c�S-[�`�S-`${+[�n p &yce&>& h #�[il�l�g'&y#e&D\z\-�]\ p S_l�U$l h &�`!'� h [�`'lwS p �"#�� p &�`+S-a>&�{�� � l�g'& h ��&�g$g$#�[�& h�u � u �"#���[�`$��g$#m[ h ��l�lT[�#���[�# p S_l�U/��S_lC&�l�lwS-{�`$� p cm[k��& hmu #��"{�S-[�`IY

����� � 5I2_8 �kF$8"F�?'0���5

&%$#�"akg u &�lwS_l�S_l�[�`+c u ��g'�"#�nt[�#�a>&y` h ��[�n�l�g'&�cTS4&�\P[�g'�"#e&�cTSV[�`'l�S-` & p &�c]& � g'&�#e&D\z\-�]\I�"` r S-#�[�`$ak�"`�cC� u �"`+c u �p &�ce&MS_l�#��"g$#m��l��"`icm� p %'l SV`${ u S-�"#e&�# hmu S h &D\�l�g'&�c�S_&D\ p &yce&>lTc�#�% h c�%$#���l:� � &�ab� �� &�} � &�ak� �� ! � Y:&%$#�&�g$g$#�[i& hmuS_llwS-a;Sz\_&�#CS-`�l�g�S-#�S-c cm[M&y`+��&�#�\zS-�"#ql�cm% p (#� Z�[��]\ ��� � S-`+c u &�cc u ��l�&�ak� p &�ce&;l�c�#m% h c�%$#���l&�#m���]� &�aMSV`$� p �tS�Y���Y-}c u � �� c�#��"��}Nc u � � � � c�#��"��}R&�` p c u �>|�x � � %'& p c�#��"���]Y ��u � p S"!I�"#��"` h �bS_l�c u &�c u �"#��k���kc���lTc�[�g'�"#e&yc�S-[�`'l#�� � %�S-#�S-`${ &@lwS-{�`�Sz� h &�`ic�&yak[�%$`�c [�n h [�akg$%$ce&�c�S-[�`Xl�[@c u &�cC%'lwS-`${+g'&�#e&D\z\-�]\zS4lTa a@&�(+!/�k&�c�c�#e& h c�S r ��Y ��u %'l"}��� p [;`$[�c�lTc�% p (;g'[�S-`�c�[�g'�"#e&�cTSV[�`'l�lT% h�u &�lN�'` p S-`${kc u �C`$��&�#���l�c \zSV`$��cm[ &�g/[�S-`ic&�l�S-`#� Z�[��]\ ��� � YN��`'l�cm��& p }�����]�'&�a;S-`$�;ak[�#�� h [�akg�\-�]� [�g/�"#e&�c�S-[�`'lCl�% hmu &�l p &�ce&klTc�#�% h c�%$#�� h #���&�c�S-[�`I}/g'[y\V(�{�[�`�S���&�cTSV[�`I}I&�` p l�g'&yc�S_&D\��[�S-`IY7�wc�l u [�%�\ p !'�`$[�cm� p c u &�cRc u � p &�c]& � g'&�#e&D\z\-�]\P&�\V{�[�#�S-c u a>lR&�#m�&�l�l�%$ak� p cm[�!'�a>&�SV`bak�"ak[�#�(�#���lwS p �"`�c�Y&%$#�&yg$g�\�S h &�cTSV[�`+�"` r S-#�[�`$ak�"`�c�}i&La;S-`�S-a>&D\z\-( h [�`��'{�%$#�� pk��u S-`$U�SV`${kxX& hmu S-`$��l � x � =C�SVc u>��� g$#m[ h ��l�lT[�#el"}h [�`�ce&DS-`'l � Wq� [�n�a>&�SV`Xak�"ab[�#�(�Y ��u �k& p &yg$ce&�c�S-[�`X[�n�c u ��l��;a>&DS-`Xak�"ak[�#m(�&D\-{�[�#�S-c u a>lCcm[ p S4lTU � !'&�lT� pr &y#�S_&�`ic]l�S_l &klT%$!$� � h c�[�n�[�%$#�[�`${�[�S-`${>#m��l���&�# hmu Y

�w`+c u S_l�g'&�g/�"#[�%$#l�&�akg�\-�;l�g'&�c�S_&D\ p &�ce&y!'&�l���S4l[�`$��c u &�c h [�`�ce&DS-`'l h [�\z\-� h c�S-[�`'l�[�nI\zS-`$� l��"{�ak�"`ic]lC�tS�Y���Y-}a>&�g'l � h [�#�#���lTg'[�` p S-`${@c�[�no��&�cm%$#���ll�% hmu &�l�#�[�& p l"}�#e&DSz\-�&�(b\zS-`$��l"}'!/[�%$` p &�#�S-��lC[�nNg'[�\zS-c�S h &D\�&�` p � h [�`$[�a;S h%$`�S-cel"}J%$c�Sz\�S-c�( p &�ce&$}<�"c h Y j�&�c]&>l�cm#�% h c�%$#�� h #���&�cTSV[�`XS_lCc u �kc�S-ak�;`$� h ��l�l�&y#�(Xc�[>!$%�Sz\ p c u � p &�ce&@l�c�#m% h c�%$#��nt[�# &;g'&�#mc�S h %�\4&y# a>&ygIY ��u S_lS_l�&�`@S-akg'[�#mce&�`�c�S_l�l�%$��}/!'� h &�%'l��;� u �"`�c u � p &yce&kl�c�#m% h c�%$#��CS_l%'lT� p nt[�#R��%'l�c[�`$� � %$�"#�(�}/S-c�a>&D(+`$[�c !/�;��[�#�c u � u Sz\V�;c�[@�]�$g'�"` p a;% hmu �(!I[�#mc�S-`XS-cel h [�`'l�c�#m% h c�S-[�`IY�|N[�\-(i{�[�`�S ��&yc�S-[�`�S4lc u ��g$#�[ h ��lml[�n p �"c��"#�aMSV`�S-`${�&D\z\ h \-[il�� p g'[�\-(�{�[�`'lno[�#�ak� p !�(�& h [�\z\-� h c�S-[�`9[�nRg�\_&�`'&�#�\�S-`$�>lT�"{�ak�"`�cel"Y��$[�#�]�'&�akg�\-��}�S-c h &y`k!'�%'lT� p c�[��'` p c u �!/[�%$` p &�#�S-��lR[ynP&D\z\1c u � h [�%$`ic�#TSV��l�S-`kc u ����[�#�\ p YR��[�c ukp &�ce&�l�c�#m% h c�%$#��h #���&�cTSV[�`�&�` p g/[�\-(i{�[�`'&D\zS ��&yc�S-[�`�SV` r [�\ r ����%'l�c[�`$� p &�ce&;l��"cDY

�w` h [�`�c�#e&�lTc�}'c u �>l�g'&�c�S_&D\I��[�S-`sSV` r [�\ r ��lLc���[ p &�ce&+lT�"cel"Y;��cLS_l�[�`$�k[yn�c u �kab[il�c h [�akab[�`X[�g'�"#e&yc�S-[�`'lS-`�l�g'&�cTS4&�\ p &�c]&�!'&�l���l:� � [�cm� �$� }IW��%$`ic ����� Y �u S4lLc��"#�a S_lC%'l�%'&D\z\-( %'lT� p S-` h [�`�� %$` h c�S-[�`s��S-c u &k#��]\_&�cTSV[�`'&D\p &�ce&y!'&�l��ka>&y`'&�{��"ak�"`�c l�($l�c��"a � QN\-a>&,� ��� Y+��`�c u &�c h [�`�c��]�~cD}7&b� [ySV`sS_l;l�&DS p cm[ h [�a;!�S-`$�>�"`�c�S-c�S-��l�nt#�[�ac���[ p &�c]&+l��"cel�S-`icm[ &+lwS-`${�\-�+l��"cCno[�#�� r �"#�(�g'&�SV#�[�n��]\-�"ak�"`�celLS-`9c u �kc���[+l��"celCc u &�c�lm&�c�S_lwnt( &@g'&�#�cTS h %�\_&�#h [�` p S-c�S-[�`IY �u ��l�� h [�` p S-c�S-[�`'l�%'l�%'&�\�\-(�S-` r [�\ r �kl�g'� h Sz�'� p &�cmc�#�S-!$%$c���lCc u &�c�&�#�� h [�akak[�`�c�[@c u ��c���[+l��"cel"Y

Page 4: O'3 0D. - cs.umd.edu

��`�c u � lTg'&�c�S_&D\ r &�#�S_&�`�cC[�n�c u ���[�S-`I}'c u � h [�` p S-c�S-[�`�S_l�SV`�c��"#�g$#m�"c�� p &�l�!'�]S-`${�l�&yc�S_lw�'� p �tS�Y���Y4}'c���[;�]\V�"ab�"`icel&�#��L� [�S-`$� p ��� u �"`�c u �b�]\V�"ab�"`icelM[�nc u �kg'&DS-# h [ r �"# l�[�ak�>g'&y#�c�[�nc u �+l�g'& h �@c u &�cCS_l�S p �"`�c�S h &D\�YX��`�c u �l�� � %$�"`icTS4&�\ p [�a>&DS-`I}Rc u S_l�g$#�[�!�\-�"a u &�l�!'�"�"` l�cm% p SV� p �SVc u g/[�\-(i{�[�`'&D\ p &�c]&+!'[�c u &�\V{�[�#�S-c u a;S h &D\z\-( &�` p�"akg�S-#�S h &D\z\-(�no[�#�c u � �� c�#��"��� ��#TSV` ��� � }�� u Sz\-��S-`+c u � p &�ce& � g'&y#e&D\z\-�]\ p [�a>&DS-`@S-c u &�l�!'�"�"`9l�c�% p S-� p �SVc u \�S-`$�l��"{�ab�"`ic p &yce&�!'[�c u &D\-{�[�#�S-c u aMS h &�\�\-(X&�` p �"akg�S-#�S h &D\z\-( � Z[��]\ ��� &�}'Z�[i�]\ ��� ! � Y

�s� �]�'&�a;S-`$�>& r &�#�S_&�`�c�[�n�c u �>l�g'&�c�S_&D\I��[�S-`Xc u &�c�l��"�"U$l�cm[k�'` p &�\�\�\zSV`$�+l��"{�ab�"`icel�c u &�cC\zS-�@��S-c u S-`�&{�S r �"` p S_l�ce&y` h � [�nJ\�S-`$�;l��"{�ak�"`�celR[yn�&�`$[�c u �"#�c�(ig/����c u �\zS-`$� l��"{�ak�"`ic]lR`$�"� p `$[�c�!'� h [�`ic�S-{�%$[�%'l]�eY ��u S_l S4lc u ��l�g'&�c�S_&D\I&�`'&D\-[�{�[�n�&�#]&�`${�� � %$�"#�(+� &�\4lT[ cm�"#�ak� p &���S-` p [����IS-`�& h [�` r �"`ic�S-[�`'&�\ p &�ce&y!'&�l���� u [���� r �"#�}yS-`[�%$# &y`'&D\-[�{;c u � � %$�"#m(>#��"{ySV[�`@S4l�`$[�c�\zS-a;S-c�� p c�[k&;#�� h ce&�`${y\V��Y ��c�S_l&D\_l�[bUi`$[��`+&�l& h [�#�#TS p [�#[�#&;!$%/!I�"#�"[�`$��S-`XW � � }�[�#�S-a>&�{�� p Sz\_&�c�S-[�` SV`@S-a>&y{�� g$#m[ h ��l�l SV`${/Y � l�&�`@�]�'&�akg�\-��}'l�%$g$g/[il���c u &�c���� u & r �C[�`$�Ca>&�gh [�#�#m��l�g'[�` p S-`${�c�[kc u �;#�[i& p l�S-`Xc u �kv`�S-c�� ps� ce&yc���l &y` p &y`$[�c u �"#Ca>&�g h [�#�#���lTg'[�` p S-`${+c�[@c u �;!'[�# p �"# [�nxX&�#�(�\_&�` p &�` p �����&�`�c�c�[ p �"c��"#�a;S-`$� &�\�\R#�[i& p l�c u &�c�\zS-����S-c u S-` �� a;Sz\-��lC[�n7c u ��!'[�# p �"#�[�n xX&�#m(�\_&�` p Y

����� GPHJ?$3�2-?'*C=@F$��.I69HN.18D2-3�24.IOI8

��`�c u S_lbg'&�g'�"#+��� no[ h %'lk[�` #��"g$#���lT�"`ice&yc�S-[�`'lkc u &�c>l�[�#mc>c u � p &�ce&X�SVc u #m��l�g'� h c@c�[�c u � l�g'& h ��c u &�cbS-c[ h"h %$g�SV��l Y ��u S_l@#���l�%�\-celMS-` l�g/�"� p S-`${ %$g [�g'�"#e&�cTSV[�`'l;S-` r [�\ r S-`${ l���&y# h�u Y �u ���(!I� h ck[�n�c u ��lT[�#�c;S_l@c�[p � h [�akg/[il���c u ��l�g'& h ��nt#�[�a � u S h�u c u � p &�c]&CS_l p #e&D�`�����Y�{'Y4}�c u ��c���[ ��p SVab�"`'lwS-[�`'&D\7l�g'& h � h [�`�ce&DS-`�S-`${kc u �\zS-`$��l]��S-`�c�[9#��"{ySV[�`'l h &D\z\-� p��������� �� Y�&`$�X&�g$g$#�[i& hmu Ui`$[��`�&�lk&�` ��� c�#m�"�)�zW %$c�c(� � � !$% h U��"celMc u � p &�ce&!'&�l�� p [�` c u � h [�` h �"g$c+[�n &9aMSV`�S-a;%$a !'[�%$` p SV`${ ��[�#k�"` h \-[il SV`${ �>#�� h ce&y`${�\-��Y ��`�c u S_l h &�lT��}�\�S-`$��l�&�#��{�#�[�%$g'� p � u [�g/�]no%�\z\-(X!i(+g$#�[D��S-a;S-c (/��SV`�c�[ u S-�"#e&�# hmu S-��l"}I&�` p c u �"` lTc�[�#�� p SV`9&�`$[�c u �"#qlTc�#�% h c�%$#��;l�% hmu &�lC&� � c�#��"�$� � [�ak� ���� Y �u � p #e&D�!'& h U�[�n'c u � ��� cm#��"��S4lNc u &�c<S-c p [i��lN`$[�c7#���lT%�\VcNS-`k& p S4lo� [�S-`�c p � h [�abg'[ilwS-c�S-[�`;[�nl�g'& h ��� c u &�c�S4l }ic u ��!'[�%$` p S-`${k#�� h c]&�`${�\-��l h [�#�#���l�g/[�` p S-`${kc�[ p S"!I�"#��"`ic�\zS-`$��la@&�(;[ r �"#�\_&�gIYRQ � %�S r &�\V�"`�c�\-(�}&L\zSV`$�;a>&D(k!/��l�g'&�c�S_&D\z\-( h [�`�ce&DS-`$� p S-`�l�� r �"#e&D\I!'[�%$` p S-`${+#�� h c]&�`${�\-��l"}$(��"c�S-c�S_l�[�`�\-(�&�lml�[ h S_&�cm� p ��S-c u [�`$�!'[�%$` p SV`${;#�� h c]&�`${�\-��Y ��u S_lRab��&�`'lRc u &yc�&�l�g'&�cTS4&�\ � %$�"#�(;a>&D(�[�nocm�"`k#�� � %�SV#m� l�� r �"#e&�\'!'[�%$` p S-`${k#�� h c]&�`${�\-��lc�[k!/� h�u � h U�� p !'�]nt[�#�� &�l h �"#�ce&DS-`�S-`${kc u ��g$#���l��"` h ��[�# &�!'l��"` h ��[�n�&;g'&y#�c�S h %�\_&�#\zS-`$��Y

�u ��`$[�` ��p S4lo� [�S-`�c�`$��l�l [�n1c u � ��� cm#��"��S_lN[ r �"# h [�ak��!i(;& p � h [�akg/[ilwS-c�S-[�`k[�nIl�g'& h ��S-`icm[ p S4lo� [�S-`�c h �]\z\_l"YR�w`c u S_l h &�lT��}i��& h�u \zSV`$�LS_l p � h [�akg/[il�� p S-`icm[ p S_lE��[�S-`�c l�%$!�\zS-`$��l�l�% h�u c u &�c���& hmu [�n7c u ��l�%$!�\zS-`$��lS4l�&�l�l�[ h S_&�c�� p��S-c u & p S"!I�"#��"`�c h �]\z\�Y ��u �"#���&�#���&M`i%$a;!'�"#�[�n r &�#�S_&�`�cel�[�nNc u S_l &�g$g$#m[i& hmu Y �u �"( p S !I�"#�S-`�c u � p �"{�#��"��[�n#��"{�%�\_&�#TSVc�(@S-akg/[il�� p !�(+c u �]S-# %$` p �"#T\V(�S-`${ p � h [�akg'[�lwS-c�S-[�`X#�%�\-��l�&�` p !i(+c u ���&�(bS-`X� u S h�u c u � h �]\z\_l�&�#��&�{�{�#��"{i&�c�� p Y ��u �bg$#�S h �kg'&DS p nt[�# c u � p S_lE��[�S-`�c�`$��l�lCS_lLc u &�c�SV`s[�# p �"#�c�[ p �"c��"#�a;S-`$�kc u �>&�#���& h [ r �"#�� p !i(&bg'&�#�c�S h %�\_&�#�\zS-`$��}I��� u & r � cm[>#��"cm#�S-� r �k&D\z\�c u � h �]\z\_l�c u &ycS-c�[ h"h %$g�SV��l Y ��u �;#���&�l�[�`+S_lCc u &yc ��& hmu \zSV`$�MS4l

Page 5: O'3 0D. - cs.umd.edu

p � h [�akg/[il�� p SV`�c�[+&�l�a>&y`i(@g�S-� h ��l���cm�"#�ak� p���� ��������� ��&�l�c u �"#m��&�#�� h �]\z\_lCc u #�[�%${ u � u S hmu S-cg'&�l�l���l Y�Z��"#������l�c�% p (@c���[;ak�"c u [ p l�� c u � ��N� c�#��"�-� �'&D\-[%� ��� &y` p & r &�#�S_&�`�c[�nRc u ��|�x � � %'& p c�#��"�-�+*�]\_l � � � Y

�u � � � � c�#m�"��g'&�#�cTSVcTSV[�`'lkc u � \zSV`$��lbS-`�c�[�&�#�!�S-c�#e&�#m( l�%$!�\zS-`$��l u & r S-`${ p S4lo� [�S-`�c>!/[�%$` p S-`${ #�� h c]&�`${�\-��l� u S hmu &�#���{�#�[�%$g'� p SV`X&�`$[�c u �"#l�cm#�% h c�%$#���l�% hmu &�l�& � � c�#m�"��Y ��u ��g'&�#�cTSVcTSV[�`�&�` p c u ��l�%$!'l�� � %$�"`ic{�#�[�%$g �S-`${il�&y#�� l�% hmu c u &�cRc u �!'[�%$` p S-`${k#m� h ce&�`${�\-��l�&y#�� p S4lo� [�S-`�c&�cR��& hmu \-� r �]\1[�nIc u �Cl�c�#�% h c�%$#m��Y �u � p #e&D�!'& h U[�n�c u � � � � c�#m�"�@S4lMc u &�ckc u � p � h [�akg'[il SVcTSV[�`�S_l p &yce& ��p �"g'�"` p �"`�c�Y �u S4lba>&�U���l�S-c p Sz� h %�\-c+c�[Xg/�"#�no[�#�ace&�lTU~l�c u &�c#m� � %�S-#�� h [�akg'[il SVcTSV[�` [yn p S !I�"#��"`�c�[�g/�"#e&�c�S-[�`'lC&�` pXp &�ce&@l��"celL����Y�{'Y4}'l��"c � c u �"[�#��"c�S h [�g'�"#e&yc�S-[�`'ll�% hmu &�l[ r �"#T\4&D(/�eY���` h [�`�c�#e&�l�c�}$c u �k|�x � � %'& p c�#��"��S_lC!'&�l�� p [�`9&k#��"{�%�\4&y# p � h [�abg'[ilwS-c�S-[�`IY ��u �kl�g'& h �h [�`�ce&DS-`�S-`${�c u ��\zSV`$��l�S_lR#�� h %$#el S r �]\V( p � h [�abg'[il�� p S-`�c�[Cno[�%$#7� � %'&D\1&�#���&�!�\-[ h U$lN[�`;c u ��!'&�l S4l [�n'c u ��`�%$a !/�"#[�n�\zS-`$��lkc u &yc�S-c h [�`ic]&DS-`'l"YB�9�@%'l�� & r &�#TS4&y`ic;c��"#�ab� p & �������� ��� ��������� �� ��� c u &�c p � h [�akg'[ilT��l;c u �l�g'& h ��� u �"`$� r �"#�S-c h [�`�ce&DS-`'l�ak[�#��Cc u &�`��\zS-`$��l����S_l�c��"#�ab� p c u � � � � � ����������� �� �eY ��u � p � h [�akg'[il SVcTSV[�`g$#�[ h ��l�l h &�`�!'�@S-akg�\-�"ak�"`�c�� p !�(9&�cm#��"� lTc�#�% h c�%$#���Y���c�S_l�%'l��]nt%�\�nt[�#;l��"c � c u �"[�#m�"c�S h [�g'�"#e&yc�S-[�`'l"}R&�l�c u �g'&�#�cTSVcTSV[�`'l�[�nRc u ��c���[ p &�c]&kl��"cel�[ h"h %$#�S-`�c u � l�&�ab��g'[ilwS-c�S-[�`'l Y

� l�ak�"`�c�S-[�`$� p &�!'[ r ��} ��� cm#��"��l&�` p+� � � cm#��"��l�&�#�� h \V[�l��]\-(+#��]\_&�c�� p c�[k� � c�#��"��l"Y � ` ��� c�#��"��[�# � � � c�#��"�[�n'[�# p �"#�������� � u &�lNc u ��g$#�[�g'�"#�c�(�c u &�cN��& hmu `$[ p ��S-`;c u ��c�#��"��}��SVc u c u ���]� h �"g$c�S-[�`k[yn1c u ��#�[�[�c�} h [�`�ce&DS-`'l!'�"c����"�"`�� �"!#�%$ ��& &�` p � �"`ic�#TSV��l Y ��u ��#m[i[�c�`$[ p � u &�l&�c�\-��&�l�c�c ��[��"`ic�#TSV��l%$`�\V��lml�S-c�S-cel��]\znRS_l&�\-��&Dn`$[ p ��Y ��u %'l�����l��"��c u &�c�c u ��`$[ p � h &�g'& h S-c�('� S-`+c u � ��� c�#m�"��&�` p+� � � c�#��"��g�\_&D($l�c u ��l�&�ab� #�[y\V��&�l�c u �!$% h U��"c h &yg'& h S-c ( S-` c u ��!$% h U��"c�|�x � � %'& p cm#��"��Y �9�;��Sz\z\�a>&�U���%'l���[�n�c u S_l�&�`'&D\-[�{�(@S-`X[�%$# p S_l h %'l�lwS-[�`� u �"#���}/&�cc�S-ak��l"} c u ��c��"#�a>l��Sz\�\N!'��%'lT� p S-`icm�"# h�u &y`${���&�!�\-(�Y

���)( GPHJ?$3�2-?'*+*<.12 OP8

��u �"#��@&�#��k&@`i%$a;!/�"#�[�n�g'[il�l SV!�\-�@�&�($l�c�[@S-akg�\-�"ak�"`ick&+l�g'&yc�S_&D\I� [ySV`IY;�w`9[�# p �"#�cm[ h [�akg'&�#��;c u �bc u #��"�#��"g$#���lT�"`ice&yc�S-[�`'l����%'l��k&D\-{�[�#�S-c u a>l�c u &�c�ce&�U�� h [�akg'&�#e&y!�\V�k& p�r &�`�ce&�{���[�n�c u � p S"!I�"#��"`ic�lTg'&�c�S_&D\ p � h [�a �g'[�lwS-c�S-[�`'l"Y��9� u & r � hmu [il��"` &�!'[�c�c�[�a � %$g�&�g$g$#�[�& h�u ��S-c u c u � p &yce& � g'&�#e&�\�\-�]\ |�x � � %'& p c�#m�"��}�&�l�c u �

� %'& p c�#��"�>lTc�#�% h c�%$#��;`'&�cm%$#e&D\z\-(�\-�"` p lLS-cel��]\znc�[+c u S_l�lTc (�\-�k[�n�SVabg�\V�"ab�"`ice&yc�S-[�` � S Y ��Y-}<`$[�` � [ r �"#�\_&�g$g�S-`${X#�� �{�S-[�`'l@��S-c u l�g�\zS-c &��~��lMS-` #��"{�S_l�c�#]&�c�S-[�`<�eY ��` h [�`�c�#e&�l�cD}�no[�#@c u � p &�ce& � g'&�#e&D\z\-�]\ �� c�#��"��&�` p � � � c�#��"��}C&c�[�g ��p [��`�&D\-{�[�#�S-c u a � lT�"�1� ��#�S-` ��� � no[�#�&�lwS-a;Sz\_&�#k&D\-{�[�#�S-c u a SV`�c u �>lT� � %$�"`�c�S_&D\ p [�a>&DS-`<�S_l�g$#m�]no�"#e&y!�\V��}&�lLS-c h &�`�ce&�U��@& p�r &�`�ce&�{��>[�nCc u � lTg'&�c�S_&D\ p � h [�akg/[ilwS-c�S-[�`�!�( p �"c��"#�a;S-`�S-`${���&�#�\-(9� u S hmu `$[ p ��l h &y`$`$[�cg'[�l�lwS-!�\-(�SV`�c��"#elT� h c�Y���`�c u �@S-`�c��"#���l�ck[yn g$#�[ r S p S-`${�& h [�akg'&�#�S_l�[�`�����&D\_l�[�S-akg�\-�"ak�"`�c�� p &�!'[�c�cm[�a � %$g&D\-{�[�#TSVc u a nt[�#�c u � �� c�#��"��}$&�lR���]\z\7&�l�& r �"#m(>lwS-akg�\-� p &�ce& � g'&y#e&D\z\-�]\J&�\V{�[�#�S-c u a c u &�c p [i��l�`$[�c��"akg�\-[�(@&�`i(l�g'&�cTS4&�\JlT[�#�c�S-`${k&�` p c u %'l h�u � h U~l� r �"#�(;\zS-`$� l��"{�ak�"`ic&�{�&DS-`'l�c�� r �"#�(@[�c u �"#�\zSV`$�;l��"{�ak�"`�c�no[�#lm&�c�S_lwn�& h c�S-[�`[�nRc u ����[�S-` h [�` p S-c�S-[�`IY

Page 6: O'3 0D. - cs.umd.edu

� p ��&D\z\-(�}���>��[�%�\ p \�S-U���c�[9ce&yU�� & p�r &�`�ce&�{��+[ynqc u � p � h [�akg'[il SVcTSV[�` [�n�c u �+%$` p �"#�\-(�SV`${ lTg'& h �+nt#�[�a� u S hmu c u ��\zS-`$��l�&�#�� p #e&D�` &y` p & r [�S p�h [�akg'&�#�S-`${@\zS-`$��lCc u &�c h &�`$`$[�cCg'[il�l SV!�\-(�S-`icm�"#el�� h c�Y ��u S_l�S4l � %�SVcm���&�l�(s� u �"`�%'lwS-`${9c u � p &�c]& � g'&�#e&D\z\-�]\!$% h U��"c>|�x � � %'& p c�#��"�+&�lLSVcbg$#�[ r S p ��lk&Xl�[�#mc [yn c u �@%$` p �"#�\-(�S-`${l�g'& h ��&y` p &;g'&�#�c�S-c�S-[�`@S-`�c�[ p S_lE��[�S-`ic�!�\V[ h U~l"Y�x�[�#��"[ r �"#�}�lwS-` h ��c u � p &yce& � g'&�#e&�\�\-�]\7!$% h U��"c |�x � � %'& p c�#��"�S_l!'&�l�� p [�`X&;#��"{�%�\_&�# p � h [�akg/[ilwS-c�S-[�`I}/S-c�S4l���&�l�(+cm[;S p �"`ic�Sznt(�!�\-[ h U$l�S-`Xc u ��c ��[;a>&�g'l�c u &�c h [�#�#���l�g/[�` pc�[;c u �;l�&�ak�Cg'&�#�cel[�n7c u ��%$` p �"#�\-(�S-`${�l�g'& h ��}$c u �"#m�"!i(+& r [�S p S-`${ u & r SV`${bc�[ hmu � h Ubno[�#�c u �CSV`�c��"#elT� h c�S-[�`�[�n\zS-`$��l�c u &�c h &�`$`$[�cCg'[il�l SV!�\-(�S-`icm�"#el�� h c�YCZ[���� r �"#�}$c u S4lS_lC`$[�cg/[il�lwS-!�\-�;nt[�# c u � p &�ce& � g'&�#e&D\z\-�]\ �� c�#��"�k&�` pc u � � � � c�#��"�@&�l�c u �"( p [�`$[�c;a>&�U��k%'l��@[�n#��"{�%�\_&�# p � h [�akg'[il SVcTSV[�`IY9�$%$#�c u �"#mak[�#���}PSV`�c u � h &�l��@[�nc u �p &�ce& � g'&�#e&D\z\-�]\ ��� c�#m�"��}$c u ��!'[�%$` p SV`${+#m� h ce&�`${�\-��l&�#m��`$[�c p S_lE��[�S-`ic�Y ��u %'lc u ��!/��l�c��� h &�` u [�g/��nt[�#�S4l�c�[%'l��@c u �;n�& h c�c u &�c l�[�ak�k[�nc u �k!/[�%$` p S-`${9#�� h ce&y`${�\-��l p [�`$[�c�S-`�c��"#el�� h c;c u �"#m�"!i(9& r [�S p S-`${Xc u �k`$�"� p c�[c���l�c�c u �]S-# h [�`'l�c�S-c�%$�"`�cC!'[�%$` p S-`${@#�� h ce&�`${�\-��l�[�#�\zS-`$�kl��"{�ak�"`�cel no[�#g'[ilmlwS-!�\V��S-`�c��"#el�� h c�S-[�`IY

�u �g$#�[�!�\-�"a �SVc u %'lwS-`${�c u � ��� c�#m�"�q&�` pb��N� c�#��"� p &yce&�l�c�#�% h cm%$#���lRc�[�g/�"#�nt[�#�a &�lTg'&�c�S_&D\i��[�S-`;S_l�c u &�cc u �"( p [+`$[�c h [�`�ce&DS-`9&�`i( S-`�no[�#ma>&�c�S-[�`Xc�[ u �]\-g9%'l�S-` p �"c��"#ma;S-`�SV`${X� u S hmu !'[�%$` p SV`${�#�� h ce&�`${y\V��lqS-`9[�`$�a>&�g@[ r �"#�\_&�gk�SVc u !'[�%$` p S-`${k#�� h c]&�`${�\-��l�S-`>c u � [�c u �"#�a@&�gIY ��u S_l�ak��&�`'l�c u &�c \zSVcmc�\-��[�n7c u ��l���&�# hmu l�g'& h �h &�`+!/��g$#�%$`$� p � u Sz\-��g/�"#�no[�#�a;S-`${>c u ��[�g'�"#e&yc�S-[�`'l"Y ��u � p Sz� h %�\-c (@S_l�c u &�c &�\Vc u [�%${ u c u ��a>&�SV`�%$c�Sz\zSVc�(+[�nc u � �� c�#��"��&�` p>� � c�#��"��S_l�c�[��"`'&�!�\-� c u �C%'l��"#�c�[ p S_l�c�S-`${�%�S_l u ��&�lwSz\-(k!'�"c����"�"`@[ h"h %$g�S-� p &�` p %$`$[ h"h %$g�S-� p#��"{�S-[�`'lqS-`�&@g'&�#�c�S h %�\_&�#�a>&�gI}<c u �"( p [+`$[�c�g$#�[ r S p �>&@ak��&�`'lL[�n h [�#m#��]\_&�c�S-`${+c u � h [�`�c��"`�celC[�n�[�`$�;a>&�g��S-c u c u [ilT��[�n�&�`$[�c u �"#Ca>&�gIYCv`�nt[�#�cm%$`'&�c��]\-(�}'c u S4l�S_l��]� & h c�\-(�c u �;&�!�Sz\�S-c�(�c u &�cS_lC`$�"� p � p c�[bS-akg�\-�"ak�"`icl�g'&�cTS4&�\�� [�S-`>&�\V{�[�#�S-c u a>lN�]� h S-�"`�c�\-(�Y � lN������Sz\�\Il��"��}�c u S4l g�\_& h ��lRc u � p &�c]& � g'&�#e&D\z\-�]\ �� c�#��"� &�` p;��N� cm#��"� &�c& h [�`'lwS p �"#e&�!�\-� p S4lm& p�r &�`�ce&�{��CSV` h [�akg'&�#�S_l�[�`@c�[;c u � p &�ce& � g'&y#e&D\z\-�]\7!$% h U��"c|�x � � %'& p c�#m�"��&�l SVc�#�� p % h ��lc u �;g'[�c��"`icTS4&�\�nt[�#S-`�c��"#�g$#�[ h ��l�l h [�aka;%$`�S h &�c�S-[�`9c u �"#m�"!i(X#���l�%�\-c�S-`${ SV`�{�#���&yc��"# �]�$� h %$c�S-[�`9cTSVab��lCnt[�#�c u �p &�ce& � g'&�#e&D\z\-�]\ ��� c�#m�"� &�` p+� � � cm#��"��Y

�u �9#���l�c+[�n;c u S_l�g'&�g'�"# S4l [�#�{i&y`�S �"� p &�l@nt[�\z\-[��Cl"Y � � h c�S-[�` � p ��l h #�S-!/��l�c u #��"�9%'l��]nt%�\ ak[ p �]\_l+[�ng'&�#e&�\�\-�]\ h [�akg$%$ce&yc�S-[�` � | ��� x�} �ih &�`I}&�` p���� x�Y � � h cTSV[�` � {�S r ��lbc u � h [�`'l�c�#�% h cTSV[�` &D\-{�[�#TSVc u a>l;nt[�#c u � p &�ce& � g'&�#]&D\z\V�]\�!$% h U��"c |�x � � %'& p c�#��"��} ��� c�#m�"��}&�` p � � � cm#��"��Y � � h c�S-[�` ��h [�`�ce&DS-`'l@& p ��l h #�S-g$c�S-[�`[�n�c u �kg'[y\V(�{�[�`'&�\�S���&�cTSV[�` &�` p l�g'&�cTS4&�\7��[�S-`�&D\-{�[�#�S-c u a@lCnt[�#���& hmu [�nc u �kc u #m�"� p &�ce& � g'&y#e&D\z\-�]\l�c�#m% h c�%$#���l"Y� � h c�S-[�`8= h [�akg'&�#���lLc u �@c u #��"� p &�ce& � g'&�#]&D\z\V�]\ p &�c]&�l�c�#m% h c�%$#���lCS-`�c��"#ma>l�[�ng/�"#�no[�#�a>&�` h � p &�ce& no[�#�c u �l�g/� h S��'� p [�g'�"#e&yc�S-[�`'lI[�` & ��u S-`$U�S-`${�xX& hmu SV`$��l � x � =g'&�#e&D\z\-�]\ h [�akg$%$c��"#DY � � h c�S-[�` �Ch [�`ic]&DS-`'l h [�` h \-% p S-`${#��"a>&y#�U~l�&�l���]\z\�&�l & p S4l h %'l�lwS-[�`9[�nRc�[�g�S h l�nt[�#�nt%$c�%$#���#���l���&�# hmu Y���`X[�%$# p S_l h %'l�lwS-[�`X[�n�c u � r &y#�S-[�%'l p &�ce&l�c�#m% h c�%$#���l"} S-`9c u ��S-`�c��"#���l�c�[yn�!$#�� r S-c�(�}<������Sz\z\ p #m[�g�c u � � %'&D\zSz�'�"# ���� �� � ��� ������� ��� %$`�\-��l�lCc u � p S_l�c�S-` h c�S-[�``$�"� p l�c�[k!'���"abg u &�lwS��"� p SV`X& h &�l���� u �"#���c u �"#m�CS4lC&;g/[�c��"`�c�S_&D\<no[�#�a;S_l�%$` p �"#el�ce&y` p SV`${�& h \4&�SVa�Y

=

Page 7: O'3 0D. - cs.umd.edu

� � .��JF~*E8k./:qBC?'0D?'*E*-F$*���.I69H��13"?$3�24.IO

��`Xc u S_l�l�� h cTSV[�` ��� p ��l h #�S-!'�kc u #��"��ak[ p �]\_lC[�n�g'&�#e&�\�\-�]\ h [�abg$%$ce&�c�S-[�` �| ��� x�} �ih &�`I}I&�` p���� x�Y/��`Xc u �g$#�[ h ��l�l������]\_&�!'[�#]&�c���[�`�c u �]S-#�l�%�S-ce&�!�Sz\zS-c�(+nt[�# [�g'�"#e&�cTSV[�`'l[�`Xl�g'&�c�S_&D\ p &�ce&@l�c�#�% h c�%$#m��l"Y � l�������Sz\z\�l��"��}c u ��l h &�`@ak[ p �]\'S_l�c u �Cak[il�c�&�g$g$#�[�g$#TS4&yc���YR�$[�#�c u �ql h &�`>ab[ p �]\I��� &D\_l�[ p ��l h #�S-!/��c u �c�(�g'��l�[�n7g$#TSVaMSVcTS r �[�g/�"#e&�c�S-[�`'l"}/&�l�c u �"(@��Sz\z\�!/��%'l�� p SV`�c u � p ��l h #�S-g$c�S-[�`X[�nNc u � r &�#�S-[�%'l&D\-{�[�#�S-c u a>l"Y

� ��� B>�@) � 8

� `�� g$#�[ h ��lml�[�#|R&�#e&D\z\-�]\ � &�` p [�a ��h"h ��l�lxX& hmu S-`$�;��[�#�| ��� x9� h [�`'l S4lTcel�[�n�& h [�\z\-� h c�S-[�`�[�nIg$#�[ h ��l�l�[�#el� ^ ��� d ����� ���� &y` p &�{y\V[�!'&D\7l u &�#�� p ak�"ak[�#m(1� C% h U ��� } � �]SV{ ��� � YR�JS-{�%$#�� ��h [�`�ce&DS-`'l�&;lwS-akg�\-��#��"g$#���lT�"` �ce&�cTSV[�`9[�n &�`�� g$#�[ h ��l�l�[�# | �� x�Y7Q�& hmu [�nc u � � g$#�[ h ��l�l�[�#el h &�`9#���& p [�#��#TSVcm�knt#�[�a &�`�(�\-[ h &�cTSV[�`��S-c u S-`�c u � l u &�#m� p ak�"ak[�#�(+&�c���& hmu l�c��"g�[�n7c u � h [�akg$%$ce&�cTSV[�`IY

P1 P2 PN

global shared memory

...

��� �����������������! �" �$#������������% &���(')�%*,+-�.*%� � ���/�01�(')')/2�3'401/�*2*%�01+5�67+5/ 8�01/��9�:/�*;'�<�8%�3�6���%�:/��>=?��*?+@<%�!ACB�D:EF�G/�6%�%"IH

| ��� x lR&y#�� h [�akab[�`�\-( h \_&�lmlwSz�'� p & h"h [�# p S-`${�c�[ h [�` h %$#m#��"`ic�& h"h ��l�l h &�g'&�!�Sz\zSVcTSV��l[�nIc u ��{�\-[�!'&D\Pl u &�#�� pak�"ak[�#�(�Y ��u �ak[ilTc�#���l�cm#�S h c�S r � [yn1c u �Cak[ p �]\4l S_l�c u ��]� h \-%'lwS r � � #���& p }$�]� h \-%'lwS r � � �#�S-c��b� Q � Q6� �7| ��� x�Y� c�&�`�( lTce&�{��;[�n�c u � h [�akg$%$ce&�cTSV[�`I}I[�`�\-(X[�`$�kg$#�[ h ��l�l�[�#CS4l�&D\z\-[���� p cm[+�]SVc u �"#�#���& p nt#�[�a [�#���#�S-c��;c�[�&l�g/� h S�� h ab�"ak[�#�(�\-[ h &yc�S-[�`9S-`�c u �@{�\-[�!'&D\l u &�#�� p ak�"ab[�#�(�Y@�tn ���k#m�]\4&���c u �k�]� h \-%'lwS r �+#���& p9h [�`'l�c�#e&DS-`�c&�` p &D\z\-[�� a;%�\-c�S-g�\V�@g$#�[ h ��l�l�[�#]lCc�[ l SVa;%�\-ce&�`$�"[�%'lw\-(9#���& p nt#�[�a &+l�g'� h Sz� h ak�"ak[�#�( \-[ h &�cTSV[�`I}I���;[�!$ce&DS-`c u � h [�` h %$#�#m�"`ic � #m��& p }I�]� h \-%'lwS r �>��#�S-c��+� ��� Q6� �| ��� x�YI�JS-`'&D\z\-(�}NSznc u �;�]� h \-%'lwS r �@�#�S-c�� h [�`'l�c�#e&�SV`�c�S4llwS-a;Sz\_&�#�\-(�#m�]\4&��~� p }/��� [�!$c]&DS-`�c u � h [�` h %$#m#��"`ic � #���& p } h [�` h %$#m#��"`ic � �#�S-c��k� ����� � � | ��� x�Y

�u �>| ��� x ak[ p �]\�[�ng'&�#]&D\z\V�]\ h [�akg$%$ce&yc�S-[�`9nt#��"��lLc u �k%'l��"#Lno#�[�a c u �>cm� p SV[�%'l p �"ce&DSz\_l�[�n & h c�%'&D\z\-(S-akg�\-�"ak�"`�c�S-`${ &;g'&y#e&D\z\-�]\�&D\-{�[�#�S-c u a [�`+&;g'&�#]&D\z\V�]\Na>& hmu SV`$��Y ��u ��g$#�[�{�#]&�akak�"# p [i��l�`$[�c�`$�"� p cm[ ��[�#m#�(&�!/[�%$c�c u �@g$#�[ h ��l�l�[�#LS-`ic��"# h [�`$`$� h c�S-[�`�c�[�g/[�\-[�{�(9&�` p�h [�aka;%$`�S h &�c�S-[�` h [�`�J$S h cel"YXv`�nt[�#�cm%$`'&�c��]\-(�}J\4&y#�{��l u &�#m� p ak�"ab[�#�(;g'&�#e&D\z\-�]\ h [�akg$%$c��"#]l�&y#�� p Sz� h %�\-cc�[LSVabg�\V�"ab�"`ic�}/&�` p l u &�#�� p�� `$[�c u S-`${;a>& hmu S-`$��l&�g$g/��&�#c�[C!'��ak[�#m��l h &D\_&�!�\-� &�` p ���]\z\ � l�%�S-c�� p c�[ p � r �]\-[�g�S-`${�g'&�#e&D\z\-�]\'a>& hmu S-`$��lN��S-c u \4&y#�{���`�%$a;!'�"#elJ[�n'g$#�[ h ��l�l�[�#el� jC�� S ����� Y �wckS_l@g/[il�lwS-!�\-��} u [���� r �"#D}�c�[9�"a;%�\_&�c��9| ��� xXlk[�`�\_&�#�{��Xl u &�#�� p�� `$[�c u S-`${ a>& hmu S-`$��l�����Y�{'Y4}u (ig/�"# h %$!'��l?� � �]SV{ ��� � ��l�% hmu &�lc u � � x � =$}�!$%$c��S-c u %$`$Ui`$[��`+g/�"#�no[�#�a>&�` h ��g'�"`'&D\-c�S-��l"Y

Page 8: O'3 0D. - cs.umd.edu

� ��� GP��?<O � .��JF~*

��u �9l h &�` ak[ p �]\�[�n�g'&�#e&D\z\-�]\ h [�akg$%$c]&�c�S-[�` � �R\-�]\����/}�� \-�]\�� � & � S_l p �]�'`$� p S-`�c��"#�a@lk[�n & h [�\z\-� h c�S-[�` [�ng$#�S-a;S-c�S r �X[�g/�"#e&�c�S-[�`'lbc u &�c h &�` [�g'�"#e&�cm�+[�` &�#m!�SVcm#e&�#�Sz\-(�\-[�`${ r � h c�[�#]l@� lwS-`${�\-� p S-ak�"`'lwS-[�`'&D\ &�#m#e&D(~l]��[�np &�ce& Y ��u #��"�kc�(�g'��lC[�n�g$#�S-a;S-c�S r ��lb���]\-�"ak�"`�c �S4lT��}Ig'�"#ma %$c]&�c�S-[�`I}I&�` p l h &�`<� &�#��;%'l�� p cm[>g$#�[ p % h �@#���l�%�\-cr � h c�[�#elk[yn�� � %'&D\C\-�"`${�c u Y � � ����� [�g'�"#e&yc�S-[�`�� �ih�u � � �� ce&�U���l@&�` &�l�lT[ h S_&�c�S r �X[�g/�"#e&�c�[�#�� }& r � h c�[�#����� ��� ^ ����� ����� ^ � }$&�` p #��"c�%$#�`'lc u � r � h c�[�#$�������"������� � ^ ������� �"������� � ^ ������������� ^ � � Y � % h�u &bl h &�`bS4ll�&DS p cm[+!'�;S-`9c u �;%$g��&�# pXp S-#�� h c�S-[�`IY �u �>l h &�`Xak[ p �]\ h [�`'l S p �"#]l�&D\z\�g$#�S-a;S-c�S r �@[�g'�"#]&�c�S-[�`'l;� SV` h \-% p S-`${l h &�`'l �>&�l@ce&�U�S-`${�%$`�SVc�c�S-ak�9[�` & u (ig/�"# h %$!'��&�# hmu S-c�� h c�%$#���Y ��u S_l�&�\�\-[�� l+l�[�#�c�S-`${�[�g'�"#]&�c�S-[�`'l+cm[�!/�g'�"#Tno[�#mak� p S-`��;� \V[�{��J��c�S-ak��Y

� ��� ��� GI��?<O��>2E8"FsKMHNF$0D?$3�2-.JOP8

��`9& p$p S-c�S-[�`Xc�[@!'�]S-`${ h \_&�l�l S��'� p &�l�]S-c u �"#C%$g��&y# p [�# p [��`��&y# p }'l h &�`�[�g'�"#]&�c�S-[�`'l�a>&D(>!/�MlT�"{�ak�"`�c�� p Y� l��"{�ak�"`�c�� p l h &�`ka@&�(;!/� c u [�%${ u cR[ynJ&�lRa;%�\-c�S-g�\V��g'&�#e&D\z\-�]\Pl h &�`'l"}�� u �"#����& h�u [�g'�"#]&�c���lNS-` p �"g/�"` p �"`ic�\-([�`�&;l��"{�ab�"`ic�[�n h [�`ic�S-{�%$[�%'l�g$#�[ h ��l�l�[�#el Y � �"{�ak�"`ic�{�#�[�%$g'l�&�#�� h [�akab[�`�\-( p �]\zS-a;S-c�� p !i(@&kl��"{�ak�"`�c�!�S-c�}� u �"#��;& r &D\-%$�;[�n�� p �"`$[�c���lCc u ���'#]l�cg$#�[ h ��l�l�[�#�S-`Xc u � l��"{�ak�"`icDY�$[�#�]�'&�akg�\-��}/S-` �JS-{�%$#m� � }$c u �"#��;&�#��nt[�%$# l��"{�ab�"`ic{�#�[�%$g'l"} h [�#�#m��l�g'[�` p S-`${@c�[>l��"{�ak�"`ic]l�[yn lwS��"� � } � } � }'&y` p+� Y

3 1 2 1 0 1 2 2 1 0 3 31 0 0 1 0 0 0 1 0 1 0 0

3 4 6 1 1 2 4 2 3 0 3 60 3 4 0 1 1 2 0 2 0 0 3

6 3 2 4 3 3 2 3 1 6 6 33 2 0 3 3 2 0 1 0 6 3 0

datasf:segment flag

up-scan(data,sf,+,in)up-scan(data,sf,+,ex)

down-scan(data,sf,+,in)down-scan(data,sf,+,ex)

��� �������������! 8&�9 �" � ')�(�����%*,+ �6?'@0(8&*%'#" /��#$�/�+-<?+@<%���� �% 8%� 6G8&*�6 6&/&%�*&% 8 � 6 6������01+@� /�*%'' 8�'(% �%"."�8';��* 0�"��,'1� )��?8&* 6��� �0�".�%'1� )�+*1H

�JS-`'&D\z\-(�}l h &�`�[�g/�"#e&�c�S-[�`'l;a@&�(s!'�@nt%$#�c u �"# h \_&�l�l S��'� p &�l�!'�]S-`${��]SVc u �"#kS-` h \-%'lwS r �X[�#;�]� h \-%'lwS r ��Y �$[�#�]�'&�akg�\-��}�&y`�%$gi�&�# p �,� � � �����.- � l h &�`�[�g'�"#]&�c�S-[�`�%'lwS-`${�c u ��&�l�l�[ h S_&�c�S r �+[�g/�"#e&�c�[�# � #��"c�%$#�`'lMc u � r � h]�c�[�# ����� � ����� � � ^ ������� � ����� � � ^ � ����� � ��� ^ � � }I� u Sz\-��&�`9%$g��&�# p �]� h \-%'lwS r ��l h &�`�#��"c�%$#�`'lLc u � r � h c�[�#� ����������� �"�/��� � � ^ � ����� � ��� d � � Y10�&�#TSV[�%'l h [�a !�S-`'&�cTSV[�`'l�[ynJlT�"{�ak�"`�c�� p l h &�`'l"}�� u �"#�� � S_l�!/[�%$` p c�[c u ��& p$p S-c�S-[�`X[�g/�"#e&�c�[�#�}$&�#���l u [��`@S-` �JS-{�%$#�� � Y

Page 9: O'3 0D. - cs.umd.edu

� ��� ��� � *-F/6 F/O'3��>2E8"F9KkHNF$0�?$3�24.IOI8

� ` � � ��� ��� �� ����� g$#�S-a;S-c�S r ��S4l+&y` [�g/�"#e&�c�S-[�`�c u &�c@ce&�U���l;c���[ r � h c�[�#elb[�n�� � %'&D\C\V�"`${�c u &�` p g$#�[ p % h ��l&�`�&y`'l����"# r � h c�[�#�}N&D\_l�[�[yn�� � %'&D\�\-�"`${�c u Y ��u ������ �]\-�"ak�"`�c�SV`�c u �>&y`'l����"# r � h c�[�#CS_l�c u �k#���lT%�\Vc�[�nc u �&�g$g�\zS h &�c�S-[�`k[ynP&�`;&�#�S-c u ak�"c�S h [�#I\-[�{�S h &D\'g$#TSVaMSVcTS r �c�[Cc u �� �� �]\-�"ak�"`ic]lN[�n1c u ��S-`$g$%$c r � h c�[�#el"YI�w`>�JS-{�%$#�� � }&�`@�]� &yakg�\-���]\V�"ab�"`ic���S_l���& p$p S-c�S-[�`+[�g'�"#e&�cTSV[�`kS_ll u [��`IY��>&y` p� >h [�#�#���l�g/[�` p c�[�c u � c���[�S-`$g$%$c r � h cm[�#el"}&�` p���������� � �� ���p �"`$[�cm��lc u ��&y`'l����"# r � h c�[�#DY

0 1 2 1 4 3 6 2 9 54 7 2 0 3 6 1 5 0 4

4 8 4 1 7 9 7 7 9 9

AB

ew(+,A,B)

� � �������������! 8&�9 �" � <2� ��<2"�� ��<%+@��*,�?8&*?�%" �%�G�%*%+ %4� ')�:8%626 � +-� /�* /� ��%� 8+-� /�*�H

� ��� ��� BCF$0�6 �13"?$3�24.IOI8

�"� � ��� � ��� ������ g$#�S-a;S-c�S r �+ce&yU���lCc���[ r � h c�[�#]l"}Ic u � p &�ce& r � h c�[�# &y` p &�`�SV` p �]� r � h c�[�#�}7&�` p #���&�#m#e&�`${���l��g/�"#�a;%$c���l]�7��& h�u �]\-�"ak�"`ic�[�nIc u � p &�ce& r � h c�[�#�c�[�c u �g'[il SVcTSV[�`�l�g'� h Sz�'� p !�(;c u ��SV` p �]� r � h c�[�#�Y�*�[�c��Cc u &�cc u �@g'�"#�a;%$ce&yc�S-[�`�a;%'l�c;!/�>[�`$� � cm[ � [�`$����c ��[�[�#�ak[�#�� p &yce&+�]\-�"ak�"`�cel;a>&D(X`$[�ckl u &�#m�>c u �+l�&�ab�kS-` p �]�r � h c�[�# r &D\-%$��Y��JS-{�%$#�� � g$#�[ r S p ��l�&�`��]� &yakg�\-��g'�"#ma %$c]&�c�S-[�`�[�g'�"#e&�cTSV[�`IY�bS4lCc u � p &�ce& r � h c�[�#�}! #"%$ ��& S4lc u �CS-` p �]� r � h c�[�#�}$&�` p('��*)�+-,/.0�1� � � 2"-$ ��&3��p �"`$[�c���l�c u ��&�`'lT���"# r � h c�[�#�Y

0 1 2 3 4 5 6 7 8 9a b c d e f g h i j3 2 6 0 1 8 7 4 5 9

0 1 2 3 4 5 6 7 8 9d e b a h i c g f j

positionA

index

position permute(A,index)

� � �������54 � �! 8&�9 2" ��/!" 87 ��%�5�7�,+)8+-� /�*�H

� ��� GP) � � .��IF$*

� lwS-a;Sz\_&�#�!$%$c@ak[�#m��#���l�cm#�S h c�S r �Xak[ p �]\�[�n�g'&�#]&D\z\V�]\ h [�akg$%$ce&�c�S-[�`I}�c u � ��� x � �ih &y` �t� ` p�� x�[�`$[�cm[�`�S h]�a>&�g$g�S-`${$��ak[ p �]\7[�n7g'&y#e&D\z\-�]\ h [�abg$%$ce&�c�S-[�`)� ����l�c ����� }$a>&D(k!/� p �]�'`$� p !i(@[�`$��[�#�ak[�#��C\zS-`$��&�#�\-(�[�# p �"#�� pl��"cel�[�n�g$#�[ h ��l�l�[�#el� u S hmu &D\z\-[�� �]\-�"ak�"`�c � ��S_l��@&�` p l h &�` � ��S_l��;[�g/�"#e&�c�S-[�`'lCc�[@!'�;g/�"#�no[�#�ak� p YC��`'l�cm��& p [�nc u �kg/�"#�a;%$ce&�c�S-[�`X[�g/�"#e&�c�S-[�`I}Nc u � ��� x ak[ p �]\�[�`�\-(9&D\z\-[��Cl�c u �kg/�"#�nt[�#�a>&�` h �;[�n �6���0�� ���� ����� � ��� �,� ���

Page 10: O'3 0D. - cs.umd.edu

!'[�c u ��S-c u S-`X&�` p !/�"c ���"�"`���& h�u \zS-`$��&�#�\-(X[�# p �"#m� p l��"c [yn�g$#�[ h ��l�l�[�#el"Y � ak[�`$[�c�[�`�S h a>&�g$g�S-`${@S_l p �]�'`$� p&�l�[�`$��S-`X� u S hmu c u � p ��l�c�S-`'&�cTSV[�` g$#m[ h ��l�lT[�#S-` p S h ��l�&y#���&kab[�`$[�c�[�`�S h &D\z\-(+S-` h #���&�lwS-`${+[�# ab[�`$[�c�[�`�S h &D\z\-(p � h #���&�l SV`${�nt%$` h c�S-[�`+[�nIc u � lT[�%$# h �Cg$#�[ h ��lml�[�#RS-` p S h ��l"Y� [�#��]�'&�akg�\-��} h [�`'lwS p �"#�c u ��lwS-c�%'&�c�S-[�` p �"g�S h c�� p S-`�JS-{�%$#�� =�� u �"#���c u �lT[�%$# h ��g$#m[ h ��l�lT[�#elN&�#�� h [�`ice&�SV`$� p S-`kg$#�[ h ��l�l�[�#�l��"c��<}�&�` p c u � p ��l�c�S-`'&�c�S-[�`;g$#�[ h ��l�l�[�#el&�#�� \-[ h &�cm� p S-`�g$#�[ h ��l�l�[�#�lT�"c Y��JS-{�%$#m�#=�&�S_l+& r &D\zS p ak[�`$[�c�[�`�S h a>&�g$g�S-`${'}C� u Sz\-�9c u ��a>&�g$g�S-`${�S-`�JS-{�%$#��>=�! S_l�`$[�c &;ab[�`$[�c�[�`�S h a>&yg$g�SV`${�� &�l�� h [�ab��l�!'�]nt[�#�����S-`�c u �C\zS-`$��&�#�[�# p �"#TSV`${ �eY

B

A

a b c d e f i j

1 2 3 4

g h B

A

a b c d e f i j

1 2 3 4

g h

(a) (b)

��� ����������� ' 8�* D *?�� �8��9 �" �:��/�*/&+5/�*�� 0 � 8& � ��.*� $��(+ % �(�%* + % /G')�(+ '4/+" ��3/ 01�(')')/���'�� 8&*�6' $ * 8?'1���!��" 8%� � 8& 2 ���*,��%�<2� 0�< � ';*%/�+4��/�*/&+5/�*�� 0%H

���]S-`${kak[�#�� #m��l�c�#�S h c�S r ��c u &y`+c u ��l h &�` � ak[ p �]\7!�(k#�� � %�S-#�S-`${>ak[�`$[�c�[�`�S h a>&�g$g�S-`${il }$c u � ��� x�ak[ p �]\&D\_l�[ h [�`'lwS p �"#el+l h &y` [�g/�"#e&�c�S-[�`'l+&�lMce&�U�SV`${�%$`�S-c+c�S-ak��}c u %'l@&D\z\-[��SV`${ lT[�#�c�S-`${�[�g'�"#e&yc�S-[�`'lkcm[�!/��g'�"# �nt[�#�ak� p S-` �;�t\-[�{(�J�eY ��u � ��� x ab[ p �]\7�&�l p �"�"ak� p SV`'&yg$g$#�[�g$#�S_&�c��Lno[�#[�%$##���lT��&�# hmu &�l�S-c�S_l%$`'&�!�\-�;c�[�]� h S-�"`�c�\-(Xn & h S�\zS-ce&�cm�>c u �ba>&�`�S-g$%�\_&�c�S-[�`�[�n ��� c�#��"��l"Y ��u S_lLS4l p %$�>cm[+c u � p Sz� h %�\-c�S-��l�S-` r [�\ r � p S-`9a@&DS-` �ce&DS-`�S-`${Xak[�`$[�cm[�`�S h a>&�g$g�S-`${il�!'�"c����"�"`9c���[ p S"!P�"#m�"`ic ��� c�#��"��l�� u �"`9g/�"#�nt[�#�a;S-`${9l�g'&�c�S_&D\ � %$�"#TSV��l;l�% hmu&�lLa>&�gsSV`�c��"#elT� h c�S-[�` ��l��"�#� Z[��]\ ��� &�}7Z�[i�]\ ��� ! � nt[�#�ak[�#�� p �"c]&DSz\4l �eY#*�[�c�� u [���� r �"#�c u &�c�[�%$# &D\-{�[�#�S-c u ant[�# !$%�Sz\ p S-`${ p &�ce& � g'&�#]&D\z\V�]\ ��� c�#m�"��l�&�l p ��l h #�S-!'� p SV` � � h c�S-[�` � Y �kp [���lC`$[�c r S-[�\_&�c��;c u ��ak[�#��;#���lTc�#�S h c�S r ���� x ak[ p �]\�Y@��% h U��"c;|�x � � %'& p c�#��"��l }I��S-c u c u �]SV#�#��"{�%�\_&�# p S4lo� [�S-`�c p � h [�abg'[ilwS-c�S-[�`'l }�&y#��>&+l�c�#m% h c�%$#��nt[�#� u S hmu c u � ��� x�ak[ p �]\JS4l����]\z\ � lT%�SVcm� p Y

��� h &�%'lT�>[�nCc u �>!$% h U��"c>|�x � � %'& p c�#m�"��� l�#��"{�%�\_&�# p � h [�akg/[ilwS-c�S-[�`I}�&�%$`�S � %$�+\zS-`$��&�#k[�# p �"#�S-`${9a>&D(#���& p Sz\-(@!'�C[�!$ce&DS-`$� p {�S r �"`>&�g'&y#�c�S h %�\_&�#�\�S-`$��&�#�[�# p �"#�S-`${;ak�"c u [ p [�\-[�{�(kl�% hmu &�lR&�|N��&�`$[ h %$# r �?� |N��&�` �� �� Y� l���Sz\z\�!/� l u [��`@\_&�c��"#D}ic u � ��� c�#m�"��}$��S-c u S-celSV#m#��"{�%�\_&�# p � h [�abg'[ilwS-c�S-[�`I} p [���l`$[�c u & r �q&;%$`�S � %$��\�S-`$��&�#[�# p �"#TSV`${/Y?� u �"`Xg/�"#�no[�#�a;S-`${�[�g/�"#e&�c�S-[�`'lC[�`9c���[@a>&�g'lC�SVc u `$[�` � %$`�S � %$�@\zS-`$��&�#�[�# p �"#�S-`${il"}Ic u � a@&DS-` �c��"`'&�` h ��[�n7c u ��ak[�`$[�cm[�`�S h a>&�g$g�S-`${il�!'� h [�ak��l��]�$g'�"`'lwS r � p %$��c�[kc u ��`$� h ��l�l�&�#�(+g$#m[ h ��l�lT[�##��"[�# p �"#�S-`${ilS-`9c u � p &�ce& � g'&�#e&D\z\-�]\��"` r SV#m[�`$ak�"`�c�Y��$[�#��]� &�abg�\V��} h [�`'lwS p �"#�c u �klwS-c�%'&�cTSV[�` p �"g�S h c�� p S-`9�JSV{�%$#�� � � u �"#��c���[ l��"cel [�nIg$#�[ h ��l�l�[�#el�� lT�"c� � �� ��&y` p l��"cC�� �� ��� h [�#�#���l�g/[�` p cm[ c u � [ r �"#�\_&�g$g�S-`${;#��"{�S-[�`'l S-`��JS-{�%$#�� � &$Y� %$g$g'[�l��+��& hmu g$#�[ h ��l�l�[�#�S-`�[�`$�+{�#�[�%$g9a;%'l�c h [�aka;%$`�S h &�c��@��S-c u ��& hmu SV`�c��"#elT� h c�S-`${9g$#�[ h ��l�l�[�#�S-`�c u �[�c u �"#�{�#�[�%$g��tS�Y���Y-} �k��S-c u �k&�` p� }�&�` p( ��S-c u �k&�` p� �eY��$[�#�c u ���'#el�c�#m[�%$` p [yn h [�aka;%$`�S h &�c�S-[�`+l u [��`

Page 11: O'3 0D. - cs.umd.edu

S-`��JS-{�%$#�� � !I}$&�ak[�`$[�cm[�`�S h a>&yg$g�SV`${ba>&D(k!'��a>&�SV`�ce&DS-`$� p Y ��u ��l�� h [�` p #�[�%$` p � p �"g�S h cm� p S-`��JS-{�%$#�� ��h �u [���� r �"# r S-[�\_&�c���lLc u �;ak[�`$[�c�[�`�S h a>&�g$g�S-`${'Y��tng$#�[ h ��l�l�[�#el5�X&�` p� S-`9c u ���'#elTc�l��"c�&�#��;#��"[�# p �"#�� p � &�`�]�$g'�"`'lwS r �@[�g'�"#]&�c�S-[�`�no[�#�&b\4&y#�{�� h [�\z\-� h c�S-[�`�[yn�g$#�[ h ��l�l�[�#]l]�e}/c u �kak[�`$[�c�[�`�S h a>&�g$g�S-`${�a>&D(+[�` h �@&�{i&DS-`!'��a>&DS-`�ce&DS-`$� p &�l�l u [��`@S-` �JS-{�%$#�� ��p Y

C D

A B

(b)

C D

A B

(c)

C D

B A

(d)

A

B

C

D

(a)

��� ����������� ' 8�* D * �� �8��9 �" � 01/�"." �01+@� /�* /+"?��*,+ �%��')�01+@��*,� $�/��2*�6 �.*%� $�/� %�('�� ' $ * 8 ),8&".� 6��/�*/�+ /�*2� 0 � 8& � 2� *%� � ' 0�* 8&*��.*+),8&"�� 67�G/�*%/�+5/ *�� 0 � 8& � ��.*� � 8&*�6 ' 6 * 8 ),8&".� 6 ��/�*%/%+5/�*�� 0� 8� & 2��*� " / "." /+%��.*%� ��3/ 01�(')')/�� ���(/�� 6&�%�5��*,� H

� =@?$3"?$A�BC?'0D?'*_*4F$*�GPHJ?$3�2-?'*�=@?$3"? G<3�0,�P��3 �I0DF~8

�9� u & r �l��]\-� h c�� p c u #��"�Cl�g'&�c�S_&D\ p &�c]&�l�c�#�% h c�%$#m��lRc u &�cR#m�"g$#���l��"`�cNno%$` p &�ab�"`ice&�\�\-( p S"!I�"#��"`�c�&�g$g$#m[i& hmu ��lRc�[l�c�[�#�S-`${ l�g'&yc�S_&D\ p &yce&;nt[�#�S-akg�\-�"ak�"`ic]&�c�S-[�`XS-`9c u � p &�ce& � g'&y#e&D\z\-�]\��"` r S-#�[�`$ak�"`�c�Y ��u ���'#el�c�l�cm#�% h c�%$#���}/c u �!$% h U��"c�|�x � � %'& p c�#��"� � *�]\_l � � � }<�"akg�\-[�(~l�& p S_lE��[�S-`ic�}J#��"{�%�\_&�# p � h [�akg/[ilwS-c�S-[�`IY ��u �kl�� h [�` p l�cm#�% h c�%$#���}c u � �� c�#��"�B�zW %$c�c(� ��� }N%$c�Sz\zS��"��lk&+`$[�` ��p S4lo� [�S-`�c�}NS-#�#��"{�%�\4&y# p � h [�akg/[ilwS-c�S-[�`IYX�JS-`'&D\z\V(sc u �>c u SV# p l�cm#�% h c�%$#���}c u � � � � c�#��"� � �'&�\V[/� �� }I%'l���l�& p S_lE� [ySV`�c�}PSV#m#��"{�%�\_&�# p � h [�akg/[ilwS-c�S-[�`IY>���]\-[���}I���>l u [�� u [�� c�[�& p &�g$c�c u �c u #��"��lTg'&�c�S_&D\ p &�ce&klTc�#�% h c�%$#���l�c�[k& p &yce& � g'&�#e&�\�\-�]\7�"` r SV#m[�`$ak�"`�c�Y ��u S_l�#���lT%�\Vc]l�S-` p &�ce& � g'&�#e&D\z\-�]\ r &y#�S_&�`ic]l"Y

����� =@?$3"?$ATBC?'0D?'*E*-F$*��-�I���/Fi3kB � �����<?��J3�0�F�F

��`�c u � p &yce& � g'&�#e&�\�\-�]\7�"` r SV#m[�`$ak�"`�c�}1&�\�\J\�S-`$��l�&�#m�CSV`'lT�"#�c�� p lwS-a;%�\Vc]&�`$�"[�%'lw\-(�� u �"` h [�`'l�cm#�% h c�S-`${>&kl�g'&yc�S_&D\p &�ce&bl�c�#�% h c�%$#m��Y ��u %'l�c u �"#���S_l�`$[>g'&y#�c�S h %�\_&�# [�# p �"#�S-`${>[yn�c u � p &�ce&b%$g'[�` S-`'l��"#�c�S-[�`IY ��u � h [�` r �"`�c�S-[�`'&D\�tS�Y���Y-}<l�� � %$�"`icTS4&�\o��|�x � � %'& p cm#��"��� l�`$[ p �kl�g�\zS-c�c�S-`${�#m%�\V�MS4lC[�`$��c u &�c�l�g�\zS-cel�&b`$[ p � [�` h �M&y` p [�`�\V(�[�` h �� u �"`�&�\zSV`$��S4lb!'�]S-`${�S-`'l��"#�cm� p Y ��u S_l;S_lbc u � h &�lT�+� r �"`�Szn�c u ��`i%$a;!'�"#@[�nC\zSV`$��l@c u &�ck#���l�%�\-c@�]� h �"� p lc u ��`$[ p ��� l h &yg'& h S-c (�Y � % hmu &>l�g�\zS-c�c�S-`${+#�%�\-�;S_lC`$[�` p �"cm�"#�a;S-`�S_l�c�S h S-`Xc u �kl��"`'l��;c u &�cc u � p � h [�akg'[il SVcTSV[�`p �"g'�"` p lC[�`+c u ��[�# p �"#�S-`�� u S h�u c u �C\zSV`$��l�&y#��CS-`'l��"#�c�� p Y�� [�#�]�'&�akg�\-��} h [�`'l S p �"#�c u ��lwS-c�%'&�c�S-[�` p �"g�S h c�� pS-` �JS-{�%$#�� � � u �"#m� hmu &�`${�S-`${kc u �CS-`'l��"#�cTSV[�`�[�# p �"#�[�nI\zS-`$��l�@&�` p� #���l�%�\-cel�S-` p S"!I�"#��"`�c p � h [�akg/[ilwS-c�S-[�`'l"Y��u S_l�`$[�` p �"cm�"#�a;S-`�S_l�a S_l�%$`'& h"h �"g$ce&y!�\V��� u �"`+a>&�`�(�\zS-`$��lC&�#���S-`'l��"#�cm� p SV`�&�`$[ p �ql SVa;%�\-ce&�`$�"[�%'lw\-(�&�lR���p [@`$[�c U�`$[�� u [�� a@&�`i(+cTSVab��lCc u ��`$[ p �kl u [�%�\ p !'�kl�g�\zS-c�YC��`�[�# p �"# cm[ & r [�S p c u S_l�lwS-c�%'&�c�S-[�`I}/��� hmu [il��

��

Page 12: O'3 0D. - cs.umd.edu

c u �!$% h U��"c�|�x � � %'& p c�#��"��nt[�#Rc u � p &yce& � g'&�#e&�\�\-�]\<�"` r S-#�[�`$ak�"`�c�!/� h &�%'l���S-cel�l u &�g'�S4l S-` p �"g'�"` p �"`�c[�n<c u �[�# p �"#NS-`@� u S h�u c u ��\�S-`$��l�&�#��SV`'lT�"#�c�� p &�` p !'� h &�%'l���[�n'S-cel ���]\z\ � !'� u & r � p !$% h U��"c�l�g�\zS-c�c�S-`${;#�%�\-���tS�Y���Y4}�c u �"#��S_lC`$[ &ya !�S-{�%�S-c�(��SVc u #m��l�g'� h c�c�[ u [�� a@&�`i(�lT%$! p S r S_lwS-[�`'l�ce&yU���g�\_& h �;� u �"`9l�� r �"#]&D\7\zS-`$��l�&y#���S-`'l��"#�cm� plwS-a;%�\-ce&�`$�"[�%'lw\-(/�eY

1 2

4

3

(a)

1 2

3

4

(b)

��� ����������� ' 8�*4D * �� 8&�9 �" � ')�����%�%*,+-� 8&" ACE B�����8%6�+-���(� %4� +@<�89'1 �".� +5+@��*,� +@<����('1<%/�" 69/+"� � %4� +@< +@<%�9".��*,�(' ��*,')�%�3+5�6 �.* *����?�%�5� 0(8�"%/�� 6&�%� � 8&*�6 ' $ * +@<%� �3�('���" +-�.*%� ACE B�� � 8%6&+@���(�%4<%�%*?+-<,� �.*%')�%��+@� /�*?/�� 6&�%�C� ' '1".� � <,+-" =���/ 6�� # �6 ')/ +@<�8�+ ".�.*%�� � ':��*,')�%�3+5�6 $���" /���� ".�.*%� � H

lines

nodes

a b c d e f g h i

1

ab

c

d

ef

gi

h

1

��� � �2�3������ *�� +-� 8&" 6�8�+ 8�) �8%� 8&"�" �%" A E B�����8%6�+-���(� ���/�01�(')')/2� 8�')'1� ��*����%*+5'(H

� !$% h U��"c |�x � � %'& p c�#m�"��S_l�!$%�Sz\-c�&�l�nt[�\z\V[�� l YR��`�S-c�S_&D\z\-(�}I&klwS-`${�\-�;g$#�[ h ��l�l�[�#�S_lC&�l�lwS-{�`$� p cm[k��& hmu \�S-`$�S-`>c u � p &yce&�l��"cD}�&�` p [�`$�g$#m[ h ��l�lT[�#�c�[�c u �#���l�%�\-ce&�`�cR!$% h U��"c�|�x � � %'& p c�#��"� &�l p �"g�S h c�� p nt[�#�c u �l�&yakg�\-�p &�ce&Xl��"c�S-` �JS-{�%$#��1�s����S-c u c u �@�]� &yakg�\-� p &�ce&�l��"c�}R&�l�l�%$ab�>��� u & r � &�`��� �� � %'& p c�#m�"�+[�n a>&D��S-a>&D\u �]S-{ u c � �eY vClwS-`${�& p [���`i�&�# p l h &�`X[�g'�"#e&yc�S-[�`I}'c u � `�%$a;!'�"#�[�nR\zS-`$��l�&�l�l�[ h S4&yc�� p ��S-c u c u �klwS-`${�\-�;`$[ p �g$#�[ h ��l�l�[�#�� � S-`Xc u ���]� &�abg�\V����S_l p �"c��"#�a;S-`$� p &�` p c u �"`�g'&�l�l�� p c�[kc u �;`$[ p ��g$#�[ h ��l�l�[�#DY��tn�c u ��`�%$a !/�"#[�n�\�S-`$��l;&�l�lT[ h S_&�c�� p ��S-c u c u �;`$[ p �kg$#�[ h ��l�l�[�#��]� h �"� p lLc u �k!$% h U��"c h &�g'& h S-c�(�� � S-`9[�%$#��]�'&�akg�\-���e}Nc u �"`c u �;`$[ p �ka;%'l�c !/�>l�g�\zS-c�S-`�c�[@no[�%$#�l�%$!$`$[ p ��l�&�` p ��& hmu [�n�c u ��\zS-`$��l�a;%'l�c�!/�;#��"{�#�[�%$g/� p }7& h"h [�# p S-`${�c�[c u ��`$[ p ��l�S-c�S-`ic��"#]l�� h cel"Y

�u ��l�g�\zS-c�c�S-`${�[ h"h %$#el<S-`;c���[lTce&�{���l"Y ��u ��#m�"{�#�[�%$g�S-`${�S4lN&�g$g�\zS-� p &Dntc��"#I��& hmu lTg�\�S-c�&�` p S_l7& hmu S-� r � p ��S-c u&�` � � ��� ��� � [�g/�"#e&�c�S-[�` � ����l�c ����� �w� u �"#���c���[SV`�c��"#�aMS��$� p c (�g'��lR&y#���#���&y#�#e&�`${�� p S-`�c�[�c���[ p S_lE��[�S-`icR{�#m[�%$g'lc��"#�ab� p ����� � ��� ���r S_&�c���[�ab[�`$[�c�[�`�S h a>&�g$g�S-`${il]�]Y ��u �+%$`'l u %/0>�@S_l�%'lT� p c�[ h [�` h �"`icm#e&�c��kc u [il��b\�S-`$�

���

Page 13: O'3 0D. - cs.umd.edu

lines

nodes

a a

1

abc

d

ef

gi

h

1

c d e f g h ib b

� � ��������� ��� " /�*��.*%� ".��*,�('�� 8&* 6�� 6 �,� + / +@<%�%�.�$�.*%+5�%��')�01+-� /�* %4� +@<?+-<,� )�%��+-� 0(8&"2'1 �".� +�H

lines

nodes

a a

1

abc

d

ef

gi

h

1

c d e f g h ib b

��� ������������$D 2 �".� 0(8+-� /�* /+" +-<,�7�2*%'1<2�� � /� ��%� 8�+-� /�*?+ /!+-<,� �!01/�/�� 6 �.*�8�+5� ),8&".�%�?/+" +@<%�01�%*%+5�%� /!" +-<,� $�" /�0��?8')')/�0�� 8�+5�6 %�� +@<�+@<%��*%/ 6&� � &��/�01�(' ')/�� H

g$#�[ h ��l�l�[�#]l�c�[�{��"c u �"#�S-`ic�[@c���[ `$�"� l��"{�ab�"`icel }$��& hmu [�n�� u S hmu9h [�#�#���lTg'[�` p l�c�[>&D\z\7[yn�c u �L\zSV`$�;g$#�[ h ��l�l�[�#el\-(�S-`${X�]S-c u �"#�S-`�� u [�\-�k[�#CS-`�g'&�#�c�&�!/[ r �;[�#�!/�]\V[�� c u � ��h [�[�# p S-`'&�cm� r &D\-%$�@[�nc u � h �"`icm�"#�[�n�c u �k!�\-[ h U&�l�lT[ h S_&�c�� p ��S-c u c u �C`$[ p �Cg$#�[ h ��l�l�[�#C��#��"{�#�[�%$g�S-`${;��S-c u [�%$c�ak[�`$[�cm[�`�S h a>&�g$g�S-`${il u &�l�&D\_l�[;!'�"�"`+cm�"#�ak� p��� �� �,� � � C#�%'l ��= � &�` p � � �)� ��,� � � �R\-�]\�� � & � �eY ��u �k%$`'l u %/0>�@[�g/�"#e&�c�S-[�`XS_l p �"g�S h cm� p SV`��JSV{�%$#�� �� Y �u S4lS_lk& hmu S-� r � p !�(�ab[�`$[�c�[�`�S h &D\z\-( l u Szntc�S-`${�c�[Xc u �@\-�]ntc��w#�S-{ u c �L&�\�\�\�S-`$��g$#�[ h ��lml�[�#el;�SVc u &Xa;S p g'[�S-`�ck\-��l�l��{�#m��&�c��"#"��c u &�`�c u ��l�g�\zSVc h [�[�# p S-`'&�cm� r &�\V%$��Y *�[�c��+c u &�c@&�\zSV`$�Xa>&D(�lTg'&�` c���[X[�#k� r �"`�c u #m�"��`$[ p ��l"}c u %'l�#�� � %�S-#�S-`${+c u ��\zS-`$�;c�[k!'� p %$g�\zS h &yc�� p [�#� r �"`�c�#�S-g�\zS h &�c�� p &�` p u �"` h ���]S-c u �"#�[�`$��[�#�c ��[>& p$p SVcTSV[�`'&D\g$#�[ h ��l�l�[�#]l�S-`�c u �@\zS-`$��g$#m[ h ��l�lT[�#kl��"ck&�#��+&D\z\V[ h &�c�� p no[�#�S-c+��c��"#mak� p � � ��� �,� � � ����l�c ����� �]Y9�$[�#��]� &�abg�\V��}h [�`'lwS p �"#�\zSV`$��l � &�` p��+p %$#�S-`${>c u �Cg$#�[ h ��l�l�[�nRl�%$! p S r S p S-`/{+c u �C�'#el�c�`$[ p �CSV`X�JS-{�%$#�� � Y���� h &�%'l��C\zS-`$��l �&�` p�� S-`ic��"#]l�� h c !/[�c u c u ��cm[�g�&�` p !/[�c�c�[�a u &�\ r ��l[�nNc u ��#�[�[�c�`$[ p ��}'c u �"(+&�#�� h \-[�`$� p Y

�u � l�� h [�` p l�ce&�{����'#el�c h \V[�`$��lR\zS-`$�� ;� p �"g�S h c�� p S-`��JS-{�%$#�� ��� ��S-c u & u ��& r S-�"#�\zS-`$���e}'&�` p c u �"`>&�g$g�\zS-��lc u ��%$`'l u %/0@��c�[9c u ��#���l�%�\-c�S-`${�c���[9l��"{�ak�"`�cel"}�c u �"#��"!�( h #���&�c�S-`${�c���[9l��"c]lk[�n�c���[�lT�"{�ak�"`�celk��& h�u [�n� u S hmu�h [�#�#���l�g/[�` p lCc�[+&D\z\�[�n�c u ��\zS-`$�kg$#�[ h ��l�l�[�#el� u S hmu \zSV�b�]SVc u �"#CSV`s� u [�\-�;[�#S-`Xg'&�#�cCc�[kc u ��\-�]ntc�&�` p#�S-{ u c[�n�c u � � h [�[�# p S-`'&�c�� r &D\-%$�;[�nRc u � h �"`�c��"#C[�nRc u ��!�\-[ h U�&�lml�[ h S_&�cm� p ��S-c u c u ��`$[ p �;g$#�[ h ��lml�[�#�Y ��u �&�g$g�\zS h &�c�S-[�`X[�nRc u S_l�%$`'l u %/0>��[�g'�"#e&�cTSV[�`+S_l p �"g�S h c�� p S-` �JS-{�%$#�� ��� Y

� [�`icTSV`�%�S-`${k��S-c u c u S_l�S-c��"#]&�c�S r ��g$#�[ h ��l�l"}$��& h�u \zS-`$� l��"{�ak�"`ic�{�#�[�%$g p �"c��"#�a;S-`$��l�c u ��`�%$a !/�"#[�nI\zS-`$��l

���

Page 14: O'3 0D. - cs.umd.edu

lines

nodes

a b d e f a b c g

1

abc

d

ef

gi

hh

21

2

i i

� � �������?�&�����C" /�*��.*%� "��.*%� 6 �,�;+5/ � +5' �.*%+5�%��')�01+-� /�* %4� +@<�+@<%��<,/��5� �(/�*%+ 8&",'1 �".� +�H

lines

nodes

a b d e f a b c g

1

abc

d

ef

gi

hh

21

2

i i

��� ������������� D � 2"�� 0(8�+@� /�*�/+" +-<,����*%'�<��� � / ��%� 8�+@� /�*?+5/7+@<%� � 01/2/�� 6���* 8�+5� ),8&"��,� /+" +@<%�01�%*%+5�%� /!" +-<,� $�" /�0��?8')')/�0�� 8�+5�6 %�� +@<9*%/ 6&�(' � 8&*�6�� H

S-c h [�`�ce&DS-`'l"}I&y` p c u �"` h [�aba %$`�S h &�cm��l�c u � h [�%$`�c�c�[+c u �>&�l�l�[ h S4&yc�� p `$[ p �kg$#m[ h ��l�lT[�#�Yk�$[�#��]� &�abg�\V��}PS-`�JS-{�%$#�� ��� }/c u ���'#el�c�\zS-`$�>l��"{�ak�"`�c�{�#�[�%$g�c�#e&y`'l�a;S-celC& h [�%$`�c�[�n � c�[@`$[ p ����}/c u �kl�� h [�` p \zSV`$�@l��"{�ak�"`�c{�#�[�%$g�c�#e&y`'l�a;S-celR& h [�%$`icN[�n � c�[C`$[ p � � }��"c h YRQ�& h�u [�n1c u ��`$[ p ��g$#�[ h ��lml�[�#elJc u �"` p �"c��"#�a;S-`$��l � u �"c u �"#N[�#`$[�c�c u ��c�#]&�`'l�a;S-c�c�� p \zS-`$� h [�%$`ic��]� h �"� p lc u �C!$% h U��"c h &�g'& h S-c�(�YR� n�c u ��!$% h U��"c h &�g'& h S-c�(bS4l�]� h �"� p � p }/c u �`$[ p ����Sz\z\�l�%$! p S r S p ��}I&�` p c u ��&�l�l�[ h S_&�c�� p \zS-`$��l��Sz\z\R!'��#��"{�#m[�%$g'� p & h"h [�# p S-`${kc�[b� u S h�u [�nRc u ��#���lT%�\VcTSV`${l�%$!$`$[ p ��lCc u �"(bSV`�c��"#elT� h c�Y�$[�#��]� &�abg�\V��} S-` �JS-{�%$#�� ��� }$`$[ p ��l ��&�` p ��Sz\z\ l�%$! p S r S p ��}I#m��l�%�\-c�S-`${kS-`Xc u �lwS-c�%'&�cTSV[�` p �"g�S h c�� p S-`X�JSV{�%$#�� �"� Y

�u S4l�S-c��"#]&�c�S r �>l�%$! p S r S_lwS-[�`�g$#�[ h ��l�l h [�`�c�S-`�%$��l�%$`�c�Sz\�&D\z\�`$[ p ��lqSV`sc u �k!$% h U��"c�|�x � � %'& p c�#��"� u & r �&b\zS-`$� h [�%$`�cC\-��l�l�c u &�`X[�#�� � %'&�\�c�[>c u �k!$% h U��"c h &�g'& h S-c�(�}I[�#�c u �;a>&��iS-a>&D\�#m��l�[�\-%$c�S-[�`9[�n�c u � � %'& p c�#��"�

lines

nodes

b d e a f b c g h

1 2 3 4

ii a

abc

d

ef

gi

h

1 2

3 4

� � �������������4B �('���" + /+" +@<%�;# ��')+;*,/�6��;'1� $26 � )&� '1� / * ��".�.*%�?6 �2 �".� 0(8+-� /�* �28&* 6��2* '1<2�� �.*%� H

���

Page 15: O'3 0D. - cs.umd.edu

lines

nodes

d d e b e a i c g

1 2 3 4

i g hf b

abc

d

ef

gi

h

5 6 7 8 9 10

a

1 2

3 4

6

5

7

9

8

10

� � ���������#4 �:B �('1�2" + /+" +@<%�?')�01/�*�69�3/��2*�6 /+" *,/�6��;'1� $26 � )&� '1� / *,'(H

u &�lC!/�"�"`�#���& h�u � p �tS�Y���Y-}I&@`$[ p �k[�nlwS��"� � � �eY ��u S_lCS_lL`$[�c�&@g$#�[�!�\-�"a�}J!'� h &�%'l��Mno[�#�g$#]& h c�S h &D\�!$% h U��"ch &�g'& h S-c�S-��l��tS�Y���Y4}��k&�` p &�!'[ r ���e}�c u S_l�lwS-c�%'&yc�S-[�`+S_l��]� h �"� p S-`${�\-(X#e&�#���&y` p ��Sz\�\�`$[�c h &�%'l��;&�`i(+&D\-{�[�#TSVc u a;S hp Sz� h %�\-c�S-��l�g$#�[ r S p � p c u &�c�c u ��!$% h U��"c�|�x � � %'& p c�#��"�;&D\-{�[�#�S-c u a>l p [k`$[�c�&�l�lT%$ak��&�`�%$g$g/�"# !/[�%$` p [�`c u ��`�%$a;!'�"#C[�n7\zS-`$��lC&�l�l�[ h S_&�c�� p �SVc u &;{�S r �"`�`$[ p ��Y

lines

nodes

d d e b e a i c g

1 2 3 4

i g hf b

abc

d

ef

gi

h

5 6 7 8 9 10111213

a c

1

3

2

4

5

11

13

6 8

12

��� � �2�3�G� � � B �('1�2" + /+" +-<,� $���0����(+ ACE B�����8%6�+-���(� $2���." 6 &��/�01�(' '(H

��� h &�%'lT� `$[ p ��� � lN!$% h U��"c h &�g'& h S-c�(�S4l��]� h �"� p � p � l u [��`;S-`+�JS-{�%$#�� �"� �e}�&�` p c u �a@&D�iS-a>&�\1#���l�[y\V%$cTSV[�`u &�lC`$[�c�(��"c�!'�"�"`�#���& hmu � p }7&�`$[�c u �"#�#�[�%$` p [�nl�%$! p S r S_lwS-[�`�S_l�`$� h ��l�l�&y#�(�Y ��u �;#���l�%�\-c�[yn�c u �kc u SV# p &�` p�'`'&D\l�%$! p S r S4l SV[�`�nt[�#�[�%$#��]�'&�akg�\-� p &�ce&+l��"cLS_l l u [���`XS-`��JS-{�%$#�� � =$Y�*�[�c��;c u &yc�[�`$�k[ync u � � %'& p c�#��"�`$[ p ��l+��`$[ p ��� � l�cTS�\z\ u &�lMSVc]l;!$% h U��"c h &�g'& h SVc�(��]� h �"� p � p Y���` c u ���]�'&�akg�\-��}c u �+a>&D��SVa@&D\ #���l�[y\V%$cTSV[�`u &�lC!/�"�"`�#���& h�u � p � S Y ��Y-}�� )���eY ��u �"#��]nt[�#���}<`$[ p ��� ��Sz\�\�`$[�c�!'�@l�%$! p S r S p � p no%$#mc u �"#�YbWS r �"`�&�`�� ��S-a>&�{���} c u � p &�c]& � g'&�#e&D\z\-�]\7!$% h U��"c |�x � � %'& p c�#��"��!$%�Sz\ p S-`${�[�g/�"#e&�c�S-[�`�ce&�U���l S-`�c u ����[�#el�c ��h &�l����M�t\-[�{��y�c�S-ak��}�� u �"#��C��& h�u [�n1c u � �;�t\-[�{����lT%$! p S r S_lwS-[�`Xl�ce&�{���lN#�� � %�S-#���l �;� � � h [�akg$%$ce&�cTSV[�`'l�� & h [�`'l�ce&�`�cR`�%$a !/�"#[�nl h &�`'l�&y` p %$`'l u %/0>��l]�eY;�w`9c u �>& r �"#e&y{�� h &�l��;� u �"#��kc u ���s\zSV`$�+l��"{�ab�"`icel�&y#���]#�[�%${ u \-(��@%$`�Sznt[�#�a;\-(p S_l�c�#�S-!$%$c�� p }�c u � u �]S-{ u c;[�nc u �@c�#��"�@&�` p `�%$a;!'�"#;[�n l�%$! p S r S_lwS-[�` l�ce&�{���lCS_l �;�t\-[�{(�I��&�l�� u �"`�&+`$[ p �h [�`�ce&DS-`�S-`${)��\zSV`$��l S4l�l�%$! p S r S p � p }RS-c;#���l�%�\-celqSV`snt[�%$# hmu Sz\ p #m�"`�c u &yc h [�`�ce&DS-`�&�g$g$#m[���S-a>&�c��]\-()� $ � \�S-`$��l"Y��u �!$% h U��"c�lwS��"� [�nIc u � � %'& p cm#��"�[�`�\-(k&�!I� h celRc u � u �]S-{ u c�[�nIc u �#���lT%�\VcTSV`${;c�#m�"��}���S-c u \_&�#m{��"#�!$% h U��"c�l S �"��l(�SV�]\ p S-`${+l u &D\z\-[����"#�c�#��"��l Y �u � !$% h U��"c�l S �"� u &�l�`$[�!'��&�#TSV`${b[�`kc u �C`i%$a;!/�"#�[yn h [�akg$%$ce&�c�S-[�`'l�g/�"#�no[�#�ak� pp %$#�S-`${@��& h�u l�%$! p S r S_lwS-[�`�l�c��"gIY ��u %'l }�S-`�c u �;& r �"#e&�{�� h &�l���}'& p &�ce& � g'&�#]&D\z\V�]\R|�x � � %'& p c�#m�"� h [�`ic]&DS-`�SV`${

�"�

Page 16: O'3 0D. - cs.umd.edu

� \zSV`$�kl��"{�ak�"`ic]l h &�`+!'��!$%�Sz\Vc�S-`��M�t\-[�{��J��c�S-ak�b�tS�Y���Y-} �;� \V[�{��J��l�%$! p S r S_lwS-[�`�l�c]&�{���l"}���& hmu [�n h [�akg�\-�]�iS-c�(�;� � ���eY

lines

N0

count 9 8 7 6 5 4 3 2 1

1

a b c d e f g h i

ab

c

d

ef

gi

h

1

� � ��������� ���� *�� +-� 8&" ��3/ 01�(')')/�� 8�' '1� ��*2���%*+ ' H

����� =@?$3"?$ATBC?'0D?'*E*-F$* �kA�3�0DFiF$8

��u � p &�ce& � g'&�#e&D\z\-�]\ ��� c�#��"� h [�`'lTc�#�% h c�S-[�`;&D\-{�[�#�S-c u a p S"!I�"#elJnt#�[�a c u ��l�� � %$�"`�c�S_&D\1&D\-{�[�#�S-c u a S-`;c u &�cD}�#e&�c u �"#c u &�`�S-`'l��"#mc�S-`${�\�S-`$�9l��"{�ab�"`icelbl�� � %$�"`�c�S_&D\z\-( SV`�c�[9c u � p &�ce&sl�c�#�% h c�%$#m��}�&D\z\C\zSV`$�9l��"{�ak�"`ic]lk&�#��@S-`'l��"#�cm� plwS-a;%�\-ce&�`$�"[�%'lw\-(�Y ��u � p &�ce& � g'&y#e&D\z\-�]\ ��� cm#��"� h [�`'lTc�#�% h c�S-[�`�&D\-{�[�#�S-c u a g$#m[ h �"� p lC&�l�nt[�\z\-[��Cl"Y��w`�S-c�S_&D\z\V(�}J[�`$�g$#�[ h ��l�l�[�#�S_l�&�l�lwS-{�`$� p c�[@��& hmu \zS-`$�k[�n�c u � p &�c]&kl��"c�}<&�` p [�`$��g$#m[ h ��l�lT[�#�c�[kc u �;#���lT%�\Vc]&�`ic p &�ce& � g'&�#e&D\z\-�]\��� c�#m�"��}~&�l p �"g�S h c�� p no[�#&;l�&yakg�\-� p &�c]&�l��"c�S-`��JSV{�%$#�� �D� Y &%$#�]� &yakg�\-��&�l�l�%$ak��l�&�`@[�# p �"#C� � � � � ��� cm#��"��Y��`@c u ���'{�%$#���}�c u �\_&�!/�]\���� p �"`$[�c���l�c u � ��� c�#��"�C`$[ p �Cg$#�[ h ��l�l�[�#�l��"c�}���S-c u c u �q&�lml�[ h S_&�cm� p l � %'&�#��C#��"{�S-[�`h [�`�ce&DS-`�S-`${>c u �CS p �"`�c�Sz�'�"#C[�n�c u � ��� c�#��"��`$[ p � &�lml�[ h S_&�cm� p ��S-c u c u � ��� c�#m�"��`$[ p ��g$#�[ h ��lml�[�#�Y6�s��%'l���c u �c��"#�a ����� � ��� c�[b#��]no�"#�cm[kc u � h [�\z\-� h c�S-[�`9[�nR\zS-`$�kg$#�[ h ��l�l�[�#]l &�lml�[ h S_&�cm� p ��S-c u &bg'&�#�c�S h %�\_&�# ��� c�#m�"��`$[ p �g$#�[ h ��l�l�[�#DYB� S-c u S-`�c u �b\zS-`$��g$#�[ h ��l�l�[�#kl��"cD}7c u �+`�SV`$��l � %'&�#m�>#��"{ySV[�`'l h [�`ice&�SV`�c u �k\zS-`$�+S p �"`�c�Sz�'�"#el"Y �p [��`��&y# p l h &�`X[�g/�"#e&�c�S-[�` S4lCg/�"#�nt[�#�ak� p [�`Xc u ��\zS-`$�kg$#�[ h ��l�l�[�#�l��"cCc�[ p �"c��"#�a;S-`$�;c u �;`i%$a;!/�"# [�nR\zS-`$��l&�l�lT[ h S_&�c�� p ��S-c u c u �+lwS-`${�\-� ��� c�#��"�@`$[ p �@g$#�[ h ��l�l�[�#DY ��u S_l�S_l;l u [��`XS-` �JS-{�%$#�� ��� &�lLc u � ��� , " . �'�]\ p!'�"`$��&yc u c u �L\zSV`$�;g$#�[ h ��l�l�[�# l��"c�Y �u ��`�%$a !/�"# [ynI\zSV`$��l�S-`Xc u ��l��"{�ak�"`icS4l�c u �"`�g'&�l�l�� p !�(+c u �C�'#el�c\�S-`$�S-`+c u �C\zS-`$��&�#[�# p �"#TSV`${bc�[;c u �ql SV`${y\V� ��� c�#��"��`$[ p ��g$#�[ h ��l�l�[�#C� p �"g�S h c�� p S-`X�JSV{�%$#�� �D� !�(kc u ��&y#�#�[���nt#�[�a\zS-`$� � c�[�`$[ p ���y�eYb�tnc u �@`i%$a;!'�"#�[�n�\zS-`$��l�S-`�c u �>l��"{�ab�"`ic��]� h �"� p l�c u �k`$[ p � h &�g'& h SVc�( � }7c u �"`9c u �p &�ce& � g'&�#e&D\z\-�]\ ��� c�#��"��#�[�[�cN`$[ p ��a %'lTc7!/�lTg�\�S-c SV`�c�[�c���[\-��&Dn<`$[ p ��lR&y` p &C#m[i[�cN`$[ p � ��&�lJS_lRlwS-a;Sz\4&y#�\-( p [�`$���S-c u c u �>l�� � %$�"`ic�S_&D\ ��� c�#��"���]Y ��u �kc���[@`$�"� \-��&Dn`$[ p ��l;&�#m��S-`'l��"#mc�� p S-`�c�[�c u � �� c�#��"�@`$[ p �kg$#m[ h ��l�lT[�#l��"c�} ��S-c u c u �Cnt[�#�ak�"##m[i[�c�`$[ p � � g$#�[ h ��l�l�[�#C%$g p &yc�� p c�[;#��1J'� h cCc u ��c���[;`$�"� h�u Sz\ p #��"`IY

� =

Page 17: O'3 0D. - cs.umd.edu

�+.��JF�GPHN*_243"3�2 O1,�)+*-,/.10�2-3�5N698

��u ��c�[�g�S h [yn u [���c�[>l�g�\zS-c�&�`>[ r �"# J'[��SV`${b`$[ p � u &�l!'�"�"`�c u ��l�%$!$��� h c[�n7a;% hmu #���l���&�# hmu [�`�l�� � %$�"`�c�S_&D\��� c�#m�"��l"YR�$[�#��]� &�abg�\V��}�c u � ���]� c�#��"�$� ��� h U �� � S4l�&�` ��� cm#��"� r &�#�S_&�`�cRc u &�cR%'l���l�&Cak[�#��l�[�g u S_l�c�S h &�c�� p `$[ p �S-`'l��"#�c�S-[�`+&�` p l�g�\zS-c�c�S-`${k&D\-{�[�#�S-c u a c u &�`bc u [il��g$#m[ r S p � p �SVc u c u � h [�` r �"`ic�S-[�`'&�\ p �]�'`�SVcTSV[�`+[�nIc u � �� c�#��"��zWC%$c�c9� ��� Yk�$[�#�c u � p &�ce& � g'&y#e&D\z\-�]\ ��� c�#m�"��}I��� u & r � p � r �]\-[�g'� p c���[>`$[ p � lTg�\�S-c�cTSV`${9&D\-{�[�#�S-c u a>l"}J��& h�u [�nr &y#�(�S-`${ h [�akg$%$ce&yc�S-[�`'&D\ h [�akg�\-�]��SVc�(�Y

�w`Xc u �;�'#el�c�&�` p l SVabg�\V��lTc &D\-{�[�#TSVc u a�}<c u �>l�g�\zS-c�c�S-`${X&D�iS_lM�tS�Y���Y-} �X[�# ��� &D�iS_lqSV`sc u �;c ��[ ��p S-ak�"`'l SV[�`'&D\h &�l���� &y` p c u � h [i[�# p S-`'&�c�� r &D\-%$�>&�#�� p �"c��"#�aMSV`$� p !�(+�'` p S-`${Xc u �kak��&�` r &D\-%$��l &�\V[�`${+��& h�u &D��S_l�[�n�c u �a;S p g'[ySV`�celN[�n'&D\z\$!'[�%$` p S-`${�!'[D�$��l/S-`;c u �R\zS-`$��g$#�[ h ��lml�[�#7l��"cJS-`�g'&�#]&D\z\V�]\ r S4&C&l�� � %$�"` h ��[�n'l h &�`�[�g'�"#e&�cTSV[�`'l"Y�$[�# ��& hmu &D��S_l�&�` p l��"{�ak�"`�c�{�#�[�%$gI}<c u �;a;S p g'[�S-`�cel�[�n�c u �;!'[�%$` p S-`${�!'[D�~��l�&�#��L�'#el�c�l�%$akab� p %'l SV`${X&p [��`��&y# p S-` h \V%'l S r �>l��"{�ak�"`�c�� p l h &�`X[�g'�"#]&�c�S-[�`9�w��S-c u c u �;& p$p S-c�S-[�`X[�g'�"#]&�c�[�#"�]Y ��u ���'#elTc`$[ p ��S-`Xc u �l��"{�ab�"`ic�{�#�[�%$g�c u �"` p S r S p ��l;c u �+l�%$a !i(Xc u �@`�%$a !/�"#;[�n!'[�%$` p S-`${9!/[��$��lLS-`�c u �>l��"{�ab�"`ic;{�#�[�%$gXS-`[�# p �"#Cc�[@[�!$ce&DS-`Xc u ��ak��&�` r &D\-%$�k[yn�c u ��a;S p g/[�S-`icelL[�n�c u ��!'[�%$` p S-`${X!'[D�$��l"Y ��u S_lCak��&y` r &D\-%$�;S_lCc u �"`%'l�� p &�l�c u ��l�g�\zSVc h [i[�# p SV`'&yc�� r &D\-%$��&�` p S4l�!$#�[�& p$h &�l�c�c�[k&D\z\1[�c u �"#�`$[ p ��l SV`+c u �ql��"{�ak�"`ic�{�#�[�%$g@��S-c u &�`%$g��&y# p lT�"{�ak�"`�c�� p l h &�`X��%'l SV`${bc u � h [�g�(k[�g'�"#]&�c�[�#"�]Y � c�c u S4lg'[�S-`�c�}$��& hmu `$[ p � p �"cm�"#�a;S-`$��l� u �"c u �"#�S-c\zS-��l�S-`9c u �;\-�]noc�[�#�#TSV{ u c�#���lT%�\VcTSV`${X!/[�%$` p S-`${ !/[D�~��lC!�( h [�akg'&�#�S-`${+c u �ba;S p g'[�S-`�c�[�n�SVc]l�!'[�%$` p SV`${X!/[����S-c u c u �;!$#�[i& p$h &�lTc�� p l�g�\zS-c h [i[�# p SV`'&yc�� r &D\-%$��YC��`�c u � h &�lT��[�n�&�` � � &D��S_l lTg�\�S-c�}/Szn�c u ��`$[ p ��� l�!'[�%$` p S-`${!'[D�9a;S p g'[ySV`�c;S_lL\-��l�l;c u &�`sc u �>!$#m[i& p$h &�l�c;l�g�\zS-c h [�[�# p S-`'&�cm� r &D\-%$��}Rc u �"`�c u �>`$[ p ��� l�!'[�%$` p SV`${s!'[D�XS4l&�l�l SV{�`$� p cm[�c u ��\V�]ntcR#���l�%�\-c�S-`${�!'[�%$` p S-`${�!/[D�PYN�tn<c u ��`$[ p ��� lN!'[�%$` p S-`${�!/[D� a;S p g'[ySV`�cRS_lN{�#m��&�c��"#Nc u &�`;c u �!$#�[i& p$h &�l�c�lTg�\�S-c h [�[�# p S-`'&�c�� r &D\-%$��}$c u �"`kc u �C!'[�%$` p S-`${k!/[��;S_l�&�l�lwS-{�`$� p c�[�c u � #TSV{ u c�#���l�%�\-c�S-`${;!'[�%$` p S-`${!'[D�IY��JSV`'&�\�\-(�}N&+l�a>&D\z\�l�� � %$�"` h �b[�n�%$gi�&�# p &�` pXp [��`��&y# p S-` h \V%'l S r � l h &y` [�g'�"#e&�cTSV[�`'l���%'lwS-`${+�]S-c u �"#�&a;S-`�[�#�a>&�� [�g/�"#e&�c�[�#D} p �"g'�"` p S-`${9%$g/[�`�c u �k`'&�c�%$#m�k[�nc u �>l h &y`<�S_l�%'l�� p cm[ p �"c��"#�a;S-`$�@c u �>g u ($lwS h &D\�]�$c��"`ic]l�[�nRc u ��c���[;#���lT%�\VcTSV`${@!'[�%$` p SV`${+!/[D�~��l"Y

�u � l�g�\zS-c�&D��S4lC&�` p�h [i[�# p SV`'&yc�� r &D\-%$�k&�#�� h�u [ilT�"`+nt#�[�a c u ��c���[bg'[il�l SV!�\-�>lTg�\�S-cel�� S Y ��Y-}$c u ��!'[�%$` p S-`${!'[D�;ak��&�`'lN&D\-[�`${�c u � � � &D��S_lR&�` p c u � ��� &D��S_l]�7l�[�&�lIcm[ a;S-`�S-a;S��"�Cc u �&�ak[�%$`�c7[yn1&�#���& h [�akak[�`;c�[Cc u ��c ��[#���l�%�\-c�S-`${�`$[ p ��l"Y-*��]�$c�}Ic u ���'#elTc�`$[ p �bS-`9��& hmu lT�"{�ak�"`�c�{�#�[�%$gI}<� u S hmu h [�`ice&�SV`'lCc u �kg u ($lwS h &D\��]�$c��"`�cel[�nc u �kc���[+#���l�%�\-c�S-`${9!/[�%$` p S-`${9!'[D�$��l�&D\-[�`${���& hmu &D��S_l"}Rl��]\-� h cel�c u �k!/��l�ckl�g�\zSVcDY � �'`'&D\�%$gi�&�# p l h &�`[�g/�"#e&�c�S-[�` h [�aka;%$`�S h &�c���l�c u �ql��]\-� h c�S-[�`X&�ak[�`${;��& hmu `$[ p �CS-`+c u ��l��"{�ak�"`�c�{�#�[�%$gIY ��u S_l�[�g'�"#e&�cTSV[�`@S4l�[�nh [�akg�\-�]��S-c ( �M� � ��&�c���& hmu l�ce&�{�� [�nRc u ��!$%�Sz\ p S-`${�[�g/�"#e&�c�S-[�`I}$&�l& h [�`'l�ce&�`�c�`i%$a;!/�"#[�n�l h &�`'l p [�aMSV`'&yc���lc u � h [�abg$%$ce&�c�S-[�`IY

� `+�]�'&�akg�\-��Sz\z\-%'l�c�#e&�cTSV`${+c u S4l�`$[ p � l�g�\zS-c�c�S-`${�&D\-{�[�#TSVc u a S_l l u [��`@S-`X�JSV{�%$#�� ��� Y � [�`'lwS p �"#Cc u �Cnt[�%$#

���

Page 18: O'3 0D. - cs.umd.edu

10 20 30 40 50 60 70 80

A

B

CD

45 45 45 45 L L R R

mm:midpoint mean lr: L/R side

L Bbox

R Bbox

ls: left side rs: right sidem: midpoint

10 25 35 6030 45 65 9020 35 50 75

ms: midpoint sum 180 160 125 75 down-scan(mp,,+,in)scan type

A B C D

up-scan(ms,,copy,in)if (m < mm) then L else R

90

10 25 - - 45 45 - -

L Bbox left sideL Bbox right side

L:down-scan(ls,,min,in)L:down-scan(rs,,max,in)

- - 35 35 - - 65 90

R Bbox left sideR Bbox right side

R:up-scan(ls,,min,in)R:up-scan(rs,,max,in)

��� ������� ��� � �! �8��9 �" �!<�� � <2"�� ��<%+@��*,� +-<,� )%8%�5� /��%' ' 0(8&* + =� ��(' 8&* 6 +@<%�%�.�:8& 2 �".� 0(8�+@� / *�+ /6&�(+5�%�5�9�.*&�.*%� +@<%� � 501/�/2� 6���* 8�+ ��)%8�"��,�(' " /�� +-<,�7" ��" +�8&* 6��5� � <,+($�/���*�6���*,� $�/� �H

!'[�%$` p SV`${ !'[D�$��l;\_&�!/�]\V� p ��� }R� u S hmu &�#m� &�l�lT%$ak� p c�[ h [�akg$#�S_l��Xc u �Xl�&�ak�Xl��"{�ak�"`�ck{�#�[�%$gIY���`�c u S_l�]�'&�akg�\-��}I� u S hmu�p �"g�S h cel�c u �MlT�]\V� h cTSV[�`�[�n�c u � �s&D�iS_l�l�g�\zS-c h [i[�# p S-`'&�c�� r &D\-%$��}J���k&�#m� [�`�\V( h [�`'lwS p �"#�S-`${c u � � ��h [�[�# p S-`'&�c�� r &D\-%$��lC[�n�c u ��!'[�%$` p SV`${+!/[D�~��l"Y ��` �JS-{�%$#m� ��� } c u � h [i[�# p S-`'&�c�� r &D\-%$��l[yn�c u �L\-�]noc�&�` p#�S-{ u clwS p ��l[�nNc u �Cno[�%$#�`$[ p ��l&�#m�CSV` p S h &�cm� p [�`+c u ��\zS-`$��l�\4&y!'�]\-� p ������� � � . � �$ � &�` p�) ��� ) �� . � �$ � }#���l�g/� h c�S r �]\-(�Y+�$[�#��]�'&�akg�\-��}N`$[ p � � u &�lq\V�]ntc &y` p #�S-{ u c � ��h [�[�# p S-`'&�c�� r &D\-%$��l � ��&�` p�� �'}<#���lTg'� h c�S r �]\-(�Y� [ !/�"{�S-`�c u �@`$[ p �+l�g�\zS-c�c�S-`${�g$#m[ h ��l�l }7��& h�u `$[ p �@S-`�g'&�#e&D\z\-�]\ p �"c��"#ma;S-`$��l;c u � ��&D��S_l;a;S p g'[ySV`�c r &D\-%$�[�nS-celM!'[�%$` p S-`${�!'[D�PY �u � r &D\-%$��lk&�#m�knt[�%$` p S-`�c u �@�'{�%$#��@[�`�c u �b\zS-`$�+\_&�!'�]\-� p + � + *$ ' �% 2" . Y &` h �&D\z\�a;S p g'[ySV`�celX&�#�� h [�abg$%$c�� p }�& p [���`i�&�# p S-` h \-%'lwS r � l h &�`�[�g/�"#e&�c�S-[�` %'lwS-`${ c u �9& p$p S-c�S-[�` [�g'�"#]&�c�[�#p �"c��"#�aMSV`$��lMc u �>l�%$a [�nc u �kaMS p g/[�S-`ic r &D\-%$��l���c u S_lLS4l p �"g�S h c�� p S-`�\zS-`$� + ��� + �$ ' �% 2" . � , + Y ��u �;�'#]l�c`$[ p ��S-`9c u � l��"{�ab�"`ic�{�#m[�%$g�c u �"` p �"c��"#ma;S-`$��lCc u �;a;S p g'[�S-`�c�ak��&�`�!i( p S r S p S-`${Xc u �;a;S p g'[�S-`�c�l�%$a !i(c u �;`�%$a !/�"#�[�n�`$[ p ��l�SV`sc u �kl��"{�ak�"`�c {�#�[�%$gIY ��u S_lCa;S p g'[�S-`�c�ak��&y`�S_lCc u �"`X!$#�[�& p$h &�l�cC��S-c u &D\z\�[�c u �"#`$[ p ��l�S-`�c u �>l��"{�ak�"`ic r S_&X&�`9%$g��&�# p S-` h \-%'lwS r �Xl h &�`9[�g/�"#e&�c�S-[�`s%'lwS-`${ c u � h [�g�(X[�g'�"#]&�c�[�#;� l u [���`XS-`c u ��\zS-`$�k\_&�!/�]\V� p + + � + *$ ' �% 2" . + � � "1�eY ��u �;a;S p g'[ySV`�c;ak��&�`�nt%$` h c�S-[�`'l�&�lCc u � �9&D��S_l h &�` p S p &�c��@l�g�\zSVch [�[�# p S-`'&�c�� r &D\-%$��YXQ�& hmu `$[ p �>c u �"`9S-`�g'&�#e&D\z\-�]\ p �"c��"#�a;S-`$��l;� u �"c u �"#�S-cel�a;S p g'[�S-`�c;\zS-��l�cm[�c u �b\-�]noc�[�##�S-{ u c�[�n�c u S4lLa;S p g'[�S-`�c�ak��&y` r &D\-%$��Y;� n�&@`$[ p ��� lCa;S p g/[�S-`ic r &�\V%$�MS4lq\-��l�l�c u &y` c u �ka;S p g'[�S-`�c�ak��&y`I}<S-c

���

Page 19: O'3 0D. - cs.umd.edu

��Sz\z\7!'��{�#�[�%$g'� p �SVc u &D\z\7`$[ p ��lc�[;c u �\-�]ntc[�n7c u ��a;S p g'[�S-`�c ak��&y` �i[�c u �"#���S_l���}�S-c��Sz\z\7!'��{�#�[�%$g/� p ��S-c u`$[ p ��l�n�&D\z\zSV`${@c�[kc u ��#�S-{ u c�[�n�c u ��a;S p g'[�S-`�c�ak��&�`IY

� lT� � %$�"` h �k[yn�l h &�`X[�g'�"#]&�c�S-[�`'l h &�`X!'�;%'l�� p c�[ p �"c��"#�aMSV`$�bc u ��#���lT%�\VcTSV`${ \-�]noc�&�` p #�S-{ u cC!'[�%$` p S-`${!'[D�$��l"YR�w`�SVcTS4&�\�\-(�}<c u ��!/[�%$` p S-`${+!'[D�@\V�]ntc &�` p #�S-{ u c � h [i[�# p S-`'&�c�� r &D\-%$��l�S�\z\R[�`�\-(>!/��nt[�%$` p S-`�c u �C�'#]l�c&�` p \_&�l�c;`$[ p ��l�[�nc u �+l��"{�ab�"`ic;{�#�[�%$g��tS�Y���Y-}N`$[ p ��l6�9&�` p }I#m��l�g'� h c�S r �]\-(/�eY�&�n h [�%$#]l���}Rc u ��l�� r &�\V%$��la>&D(+\_&�cm�"#�!'�k!$#�[�& p$h &�l�c�c�[�&�\�\�`$[ p ��lCS-`�c u �kl��"{�ak�"`�c�{�#�[�%$g r S_&+&+l�� � %$�"` h �@[�n�nt[�%$#�l h &�`s[�g'�"#e&yc�S-[�`'l%'lwS-`${9& h [�gi(X[�g/�"#e&�c�[�#�Y � l;l u [��`XS-` �JS-{�%$#�� ��� }N& p [��`��&�# p a;S-`�S-a;%$a S-` h \-%'lwS r � l h &y`9[�`�c u �k\-�]ntc� h [�[�# p S-`'&�c�� r &D\-%$�Xno[�# &D\z\�`$[ p ��l+c�[�!'�X{�#m[�%$g'� p S-`�c u ��\-�]noc�!'[�%$` p S-`${ !'[D� S_l@%'l�� p cm[ p �"c��"#ma;S-`$�c u �L\V�]ntc�� ��h [i[�# p SV`'&yc�� r &D\-%$��nt[�#c u �C\V�]ntcC!'[�%$` p S-`${+!'[D�9��� � � & � � � . � �$ � �eY � S-a;Sz\_&�#�\-(�}7& p [���`i�&�# pa>&D��S-a;%$a SV` h \-%'lwS r ��l h &�`;[�`�c u ��#�S-{ u c � ��h [�[�# p S-`'&�c�� r &�\V%$��l�no[�#7`$[ p ��lN{�#�[�%$g/� p [�`�c u ��\V�]ntcR��Sz\z\1��l�c]&�!�\zS4l uc u �;#�S-{ u c � ��h [i[�# p S-`'&�c�� r &D\-%$�;nt[�#Cc u �;#���l�%�\-c�S-`${+\-�]ntc�!'[�%$` p S-`${�!'[D����� � � & ) � . � �$ � �eY �u %'l"}/nt[�#c u ��#���l�%�\-c�S-`${k\-�]ntc !/[�%$` p S-`${+!'[D�I}$c u �C\-�]noc�&�` p #�S-{ u c�� ��h [�[�# p S-`'&�c�� r &D\-%$��l�&�#������@&�` p �'}�#���lTg'� h c�S r �]\-(�Y��u ��l�� r &D\-%$��lC&�#��Cnt[�%$` p S-`�c u �C�'#]l�c`$[ p �k��`$[ p ���'��[�`+#�[�� l�[�n��JSV{�%$#�� ��� \_&�!/�]\V� p � � � & � � � . � *$ �

&�` p � � � & ) � . � *$ � Y � `'&D\-[�{�[�%'lC%$g��&�# p a;S-` � a>&�� �]� h \V%'l S r �>l h &�`'l�&�#m��%'l�� p cm[ p �"c��"#ma;S-`$�kc u �\-�]noc&�` p #�S-{ u c�� ��h [�[�# p S-`'&�c�� r &�\V%$��l�[�nIc u ��#���l�%�\-c�S-`${;#�S-{ u c�!'[�%$` p S-`${k!/[D�PY �9�[�!'l��"# r �c u &�c�c u �\V�]ntc&�` p#�S-{ u c � ��h [�[�# p S-`'&�c�� r &D\-%$��lCnt[�# c u � #m��l�%�\-c�S-`${�#�S-{ u c !/[�%$` p S-`${X!'[D��&�#m� � ��&�` p ���/}<#���l�g/� h c�S r �]\-(�Y ��u ��l��r &�\V%$��lC&�#���nt[�%$` p S-`+c u �C\_&�l�c�`$[ p ��[yn�c u ��l��"{�ab�"`ic�{�#�[�%$gX��`$[ p � ��[�`@\�S-`$��l�� � � & � � � . � *$ � &�` p �

� � & ) �� . � �$ � }$#m��l�g'� h c�S r �]\-(�Y

�u �lT� h [�` p `$[ p � l�g�\zS-c�c�S-`${k&D\-{�[�#TSVc u a �'#el�c�lT[�#�celR&D\z\$\zS-`$��l SV`@c u � lT�"{�ak�"`�c�& h"h [�# p S-`${�cm[�c u ��\-�]noc�� p {��[�nRc u �]S-# !/[�%$` p S-`${+!'[D�$��l"Y � l�� � %$�"` h �;[�n�%$g��&�# p l h &y`�[�g/�"#e&�c�S-[�`'l&y#���%'l�� p cm[ p �"c��"#�a;S-`$�;c u ���]�$c��"`�cel[�n7c u ��!'[�%$` p S-`${k!/[��@nt[�#�ak� p !i(@&D\z\I\zSV`$��l�g$#�� h � p S-`${+&�\zS-`$��S-`+c u ��lT[�#�c�� p l��"{�ak�"`�c�Y � lwS-a;Sz\_&�#�l�� � %$�"` h �[�n p [��`��&�# p l h &�`'l���Sz\z\ p �"cm�"#�a;S-`$�kc u ��!'[�%$` p S-`${+!'[D�+nt[�#�&D\z\7nt[�\z\-[��SV`${@\zS-`$��l�S-`Xc u � l��"{�ak�"`icDY �$[�# &D\z\� ��� � � � � �)�� �� � S Y ��Y-}R� u �"#��@��& hmu [yn c u �+c���[+#���l�%�\-c�S-`${�`$[ p ��l�#�� h �]S r ��l@&�c�\-��&�l�c � $�� [�n c u �b\zS-`$��lk!/�]SV`${#�� p S_l�c�#TSV!$%$cm� p �e}Ic u �;&�ak[�%$`�cC[�n�!'[�%$` p S-`${X!'[D��[ r �"#�\_&�g�S_l h &D\ h %�\_&�c�� p }J��S-c u c u � l�g�\zS-c h [�#�#���l�g/[�` p S-`${�c�[c u �;a;S-`�S-a>&D\&�ak[�%$`�c�[�n�[ r �"#T\4&yg !/�]S-`${ l��]\-� h c�� p &�lCc u � � � &��iS_l h &y` p S p &yc��>l�g�\zS-c h [�[�# p S-`'&�c�� r &D\-%$��Y � `&�`'&D\-[�{�[�%'lCg$#�[ h � p %$#���S4lL�"akg�\-[�(�� p no[�#Cc u � ��� &D�iS_l�S-`9[�!$c]&DS-`�SV`${�c u � ��� &��iS_l h &�` p S p &�c��@l�g�\zSVc h [i[�# p S-`'&�c��r &�\V%$��Y &` h � c u ��c ��[ h &�` p S p &�c���l�g�\zS-c h [�[�# p S-`'&�cm� r &D\-%$��l�&�#�� p �"c��"#�a;S-`$� p }�c u �[�`$� h [�#�#���l�g/[�` p S-`${;c�[�c u �a;S-`�S-a>&D\I!'[�%$` p SV`${b!'[D�k[ r �"#�\_&�g;S_l�l��]\-� h c�� p YR��`@c u �C� r �"`�c�[�n7&�cTSV��}�l�[�ak��[�c u �"#�ab�"c�#�S h lT% h�u &�l hmu [�[ilwS-`${c u ��l�g�\zS-c���S-c u c u ��aMSV`�S-a>&�\�!/[�%$` p S-`${+!'[D� g/�"#�S-ak�"c��"#�\-�"`${�c u l�a>&D(k!'���"akg�\-[�(�� p Y

W�S r �"` �b\zS-`$��l"}/c u S_l�`$[ p ��l�g�\zS-c�c�S-`${>&D\-{�[�#TSVc u a ce&�U���l#�;� \V[�{��J�Rc�S-ak�S-`@c u �C��[�#el�c ��h &�lT��}�&�lR���C�"akg�\-[�(c���[��M�t\-[�{��J��lT[�#�cel��tS-`kc u �l h &�`kak[ p �]\1[�n h [�akg$%$ce&yc�S-[�`I}�[�`$� h &�`;g'�"#�nt[�#�a &C#e& p Sz�>l�[�#�cR[�n �bS-c��"a>lR%'l SV`${�;� \V[�{��J��l h &�`'l ��&�` p & h [�`'lTce&�`�c�`�%$a;!'�"#C[�nR%$gi�&�# p &y` p+p [���`i�&�# p l h &�`+[�g'�"#e&�cTSV[�`'l"Y

� �

Page 20: O'3 0D. - cs.umd.edu

down-scan(ls,-,min,ex)down-scan(rs,-,max,ex)

up-scan(ls,-,min,in)up-scan(rs,-,max,in)

10 20 30 40 50 60 70 80

A

B

CD

20 40 60 080 80 80 0

R Bbox left sideR Bbox right side

L Bbox

R Bbox

ls: left side rs: right side

10 20 40 6030 50 70 80

L Bbox left sideL Bbox right side

10 10 10 1030 50 70 80

scan type

A B C D

��� ������� ��� � �! �8��9 �" �!<�� � <2"�� ��<%+@��*,� +-<,� )%8%�5� /��%' ' 0(8&* + =� ��(' 8&* 6 +@<%�%�.�:8& 2 �".� 0(8�+@� / *�+ /6&�(+5�%�5�9�.*&�.*%� +@<%� � 501/�/2� 6���* 8�+ ��)%8�"��,�(' " /�� +-<,�7" ��" +�8&* 6��5� � <,+($�/���*�6���*,� $�/� %�('(H

���]\-[�� ���CSz\�\-%'l�cm#e&�c�� u [�� c�[ h &D\ h %�\4&yc���c u �L\-�"{i&D\�l�g�\zS-cel"Y � [�`'l S p �"#�c u ���]� &yakg�\-� l u [��`@S-` �JS-{�%$#m� � �h [�`'lwS_l�cTSV`${b[�nInt[�%$#�!'[�%$` p S-`${@!'[D�~��l \_&�!/�]\V� p � � � u �"#���c u �C`$[ p ��l u & r � !/�"�"`�l�[�#�cm� p & h"h [�# p S-`${kc�[�c u �]SV#\-�]noc � ��h [�[�# p S-`'&�c�� r &�\V%$��l Y>�w`9c u S_l��]�'&�akg�\-��}N���>&�#��;[�`�\-( h [�`'lwS p �"#�S-`${ c u � � ��h [�[�# p S-`'&�c�� r &D\-%$��l�[�nc u �!'[�%$` p SV`${+!/[D�~��l"} c u [�%${ u SV` h [�#�g'[�#]&�c�S-[�`�[yn ����h [i[�# p S-`'&�c�� r &D\-%$��l�S_l l�cm#e&DS-{ u c�no[�#��&�# p YN��`�c u �C�'{�%$#���}/c u �\-�]noc�&�` p #�S-{ u c h [�[�# p S-`'&�c�� r &D\-%$��l�[�nRc u �Cno[�%$#`$[ p ��lC&�#��CS-` p S h &�c�� p [�`+c u �C\�S-`$��l�\_&�!/�]\V� p � ��� � � � . � *$ �

&�` p ) ��� ) � . � *$ � }<#m��l�g'� h c�S r �]\-(�Y+�$[�# �]�'&�akg�\-��}N`$[ p � �u &�l�\-�]ntc &�` p #TSV{ u c � ��h [i[�# p SV`'&yc�� r &�\V%$��l � �&�` p � �'}<#���lTg'� h c�S r �]\-( �R� u Sz\-�k`$[ p � � u &�l�\-�]ntc�&�` p #�S-{ u c � ��h [�[�# p S-`'&�c�� r &D\-%$��l ��&�` p � �/}'#���lTg'� h c�S r �]\-(�Y� l�l�%$a;S-`${kc u &yc &�`$[ p �LS4l{�#�[�%$g/� p ��S-c u &D\z\7`$[ p ��l�[�`@S-cel�\-�]ntc� u �"`+nt[�#�aMSV`${;c u ��!/[�%$` p S-`${+!'[D�$��lC�tS�Y���Y-}`$[ p � �bS_lC{�#m[�%$g'� p ��S-c u `$[ p ��l5��&�` p � u �"`�no[�#�a;S-`${>`$[ p � ��� l�\-�]noc�&�` p #�S-{ u c !/[�%$` p S-`${�!'[D�$��l]�e}/c u �nt[�\z\V[���S-`${>lT� � %$�"` h ��[�n7l h &y`>[�g/�"#e&�c�S-[�`'l h &�`+!/� %'lT� p c�[ p �"c��"#ma;S-`$��c u � !/[�%$` p S-`${>!/[D�~��l�[�`kc u �\-�]ntc &�` pc u �#TSV{ u cNnt[�#R��& hmu `$[ p ��YR�w`kg'&�#�cTS h %�\_&�#D}~&�lRl u [��`�SV`@�JSV{�%$#�� � �$}�&y`k%$gi�&�# p aMSV`�S-a;%$a S-` h \-%'lwS r ��l h &y`k[�`c u �L\V�]ntc h [i[�# p SV`'&yc�� r &D\-%$��S_lC%'l�� p c�[ p �"c��"#ma;S-`$� c u ��\-�]noc � ��h [�[�# p S-`'&�cm� r &D\-%$��no[�#�c u ��!/[�%$` p S-`${+!'[D��[�`&�`$[ p ��� l�\-�]noclwS p �k� � � � & � � � . � *$ � �]Y � S-a;Sz\_&�#�\-(�}I&�`@%$gi�&�# p a>&D��S-a;%$a S-` h \-%'lwS r �kl h &�`@[�`+c u �C#�S-{ u c� ��h [�[�# p S-`'&�cm� r &D\-%$��l���Sz\z\I��l�ce&�!�\zS_l u c u �#�S-{ u c � ��h [�[�# p S-`'&�c�� r &�\V%$��nt[�#Rc u �!/[�%$` p S-`${ !/[D�M[�`>&�`$[ p ��� lN\-�]ntclwS p ����� � � & ) �� . � �$ � �eY �u %'l"}Jnt[�#�`$[ p � }<���>l��"�kc u &yc�c u �;\-�]ntc &�` p #�S-{ u c � ��h [�[�# p S-`'&�c�� r &�\V%$��lnt[�# c u ��!'[�%$` p SV`${�!'[D��c�[bS-cel�\-�]noc��tS�Y���Y-}/c u �;!'[�%$` p S-`${�!'[D� h [�`�ce&DS-`�S-`${+`$[ p ��l5��&�` p� }�\_&�!'�]\-� p � � � &

S-` �JS-{�%$#�� � ����&y#���� �+&y` p ���/}$#���l�g/� h c�S r �]\-(�Y ��u ��lT� r &�\V%$��l�&y#��Cno[�%$` p S-`Xc u ��#�[�� l�[�n��JS-{�%$#�� � ��\_&�!'�]\-� p

���

Page 21: O'3 0D. - cs.umd.edu

� � � & � � � . � �$ � &�` p � � � & ) �� . � *$ � Y � `'&D\-[�{�[�%'l p [��`i�&�# p a;S-` � a>&�� �]� h \V%'l S r � l h &y`'l�&�#��%'l�� p c�[ p �"c��"#�a;S-`$�;c u ��\-�]noc�&y` p #�S-{ u c � ��h [�[�# p S-`'&�c�� r &D\-%$��lC[�n�c u �;!'[�%$` p S-`${�!'[D��c�[@c u �;#�S-{ u cC[�n���& hmu`$[ p ��Y1�9�@[�!'l��"# r �kc u &�c�c u �b\V�]ntck&�` p #�S-{ u c � ��h [�[�# p S-`'&�c�� r &D\-%$��l�nt[�#�c u �b!'[�%$` p S-`${�!'[D�9c�[�c u �@#�S-{ u c[�nR`$[ p � �tS�Y���Y-}<&;!'[�%$` p SV`${+!/[D� h [�`ic]&DS-`�SV`${@`$[ p ��l �>&�` p } \_&�!'�]\-� p � � � & � � � . � �$ � &�` p � � � &

) � . � *$ � }i#m��l�g'� h c�S r �]\-( SV`X�JS-{�%$#�� � ����&�#�� �>&�` p � �/}$#���l�g/� h c�S r �]\-(�Y

a b c d e f g h i j k l m n o p q r s t1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0

1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9

N N N Y Y Y N N N N N N N Y Y Y N N N N

datasegment flag

position

elements legal split

10

10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10

10

� � ������������ �! 8&�9 2" �;" �(�28&"2'1 �".� +5'(%4<%�%��� +-<,���9�.*�� � 8&"/�0(0��2 �8&* 01=�" � )�%" � ' 4 ���!H

� u �"`�l��]\-� h c�S-`${9c u �b\-[ h &D\z\-(�[�g$c�S-a>&D\`$[ p � l�g�\zS-ck��S-c u c u � ��� c�#��"��}�SVc�S_l�`$� h ��l�l�&�#m(9c�[��"`'lT%$#��+c u &�cc u � hmu [il��"`�l�g�\zS-c�#m��l�%�\-cel�S-`9��& hmu `$[ p �k#�� h �]S r S-`${�&yc\-��&�l�c � $�� [�n�c u ��\zS-`$��l�!'�]S-`${X#�� p S_l�c�#�S-!$%$c�� p Y � \z\h &�` p S p &�c��@l�g�\zSVc]l�c u &�c�l�&�cTS4l no(�c u S_l h #�S-c��"#�S-[�`�&�#m� cm�"#�ak� p � ��� � � � � �)�� �� Y��$[�#��]� &�abg�\V��}J{�S r �"`9&@a;S-`�S-a %$a[ h"h %$g'&�` h (@\-� r �]\7[�n �� �� }�c u ��#�S-{ u c�� p {���l�[�nI\zS-`$��l5$ � �@&�` p " � ' S-`��JSV{�%$#�� ��� &�#���\-�"{i&D\�l�g�\zS-cCg'[ilwS-c�S-[�`'l �eY��u �C\-�"{i&D\7l�g�\zS-cel�a>&D(;!'� p �"c��"#�aMSV`$� p !i(b�'#el�c��"`�%$ak�"#e&�cTSV`${bc u � �]\-�"ak�"`�cel�S-`�c u �qlT�"{�ak�"`�c�{�#�[�%$g@��S-c u &lwS-`${�\-��%$g��&y# p S-` h \-%'lwS r �kl h &�`@[�g/�"#e&�c�S-[�`�� p �"`$[�c�� p !�( ' � � . ��";S-`+�JSV{�%$#�� ��� �eY � p [��`��&�# p S-` h \-%'lwS r �l h &�`;[�g/�"#e&�c�S-[�`�S_lNc u �"`;%'l�� p c�[ h [�g�(�c u ��`i%$a;!'�"#R[yn1�]\-�"ak�"`�celJS-` c u �lT�"{�ak�"`�c7{�#m[�%$gk& h #�[il�lJc u ��l��"{�ak�"`�c{�#�[�%$g9� p �"`$[�cm� p !�(+c u � � � �#+!� " . � �'�]\ p SV`Xc u �L�'{�%$#����eYC�JS-`'&D\z\V(�}<��& h�u �]\V�"ab�"`ic p �"c��"#ma;S-`$��lC� u �"c u �"#C[�#`$[�c SVc h [�#�#���lTg'[�` p l�c�[�&q\V�"{�&D\Pl�g�\zS-c�!i( p S r S p S-`${bS-celR�"`�%$ak�"#e&�cm� p g'[il SVcTSV[�`�� ' � � . � "1�I!�(;c u �`�%$a !/�"#�[�n�]\-�"ak�"`�cel�S-`�c u ��l��"{�ak�"`�c{�#m[�%$gX� � � �#+ � " . � �eYI� n�c u ��#���l�%�\-c�S_l�!'�"c����"�"` � $�� &�` p � ��� ��� $�� }$c u �"`+S-ch [�#�#m��l�g'[�` p l�c�[k&L\-�"{i&D\7l�g�\zS-c�Y���`@c u ���]� &yakg�\-��}ic u ��#���l�%�\-c�[�n7c u S_l p �"c��"#ma;S-`'&�c�S-[�`@S_ll u [��`;S-`+c u � � � � �� ' � . �'�]\ p Y

lines

N0

a b c d e f g h i

1

ab

c

d

ef

gi

h

1

� � ��������� �����C*%'1<2�� �:/ ��%� 8�+@� /�* H

&` h �;c u �kl�g�\zS-c�c�S-`${X&D�iS_l�&�` p c u � h [�[�# p S-`'&�c�� r &D\-%$�>&�#�� hmu [il��"`I}I&�`�%$`'l u %/0@�k[�g'�"#]&�c�S-[�`�S_lC%'l�� p c�[h [�` h �"`�c�#e&�cm� c u [�l��\zS-`$��g$#�[ h ��l�l�[�#]l�cm[�{��"c u �"#�S-`icm[ c���[�`$�"� l��"{�ak�"`ic]l"}���& hmu [�nI� u S hmu ��Sz\�\ h [�#�#���l�g/[�` p c�[

��

Page 22: O'3 0D. - cs.umd.edu

[�`$�;[�n�c u �;c ��[ �� c�#��"�;\-��&Dn�`$[ p �;g$#�[ h ��l�l�[�#]l�&�l p �"g�S h c�� p S-`��JS-{�%$#�� �� Y��$[�#C�]� &yakg�\-��}7&D\z\R\zS-`$��l�� u S hmuu & r � &@aMS p g/[�S-`ic�c u &�c�S_lC\-��l�lCc u &�`Xc u �kl�g�\zS-c h [�[�# p S-`'&�cm� r &D\-%$�>&�#��;ak[�`$[�c�[�`�S h &D\z\-(9l u Sznoc�� p c�[��&y# p c u �\-�]nocD}�� u Sz\-� c u [il���� u [il���a;S p g/[�S-`ic�S_lR{�#m��&�c��"#Rc u &�`;c u �Cl�g�\zSVc h [i[�# p S-`'&�c�� r &D\-%$�q&�#m��ab[�`$[�c�[�`�S h &D\z\-(kl u Sznocm� pc�[��&�# p c u �;#�S-{ u c�&yak[�`${+c u ��\zS-`$�>g$#�[ h ��l�l�[�#el"Y ��u �;#���l�%�\-c�[�n�c u �;%$`'l u %/0>�k[�g/�"#e&�c�S-[�`9[�` c u ��\zS-`$��lLS-`�JS-{�%$#�� �� S_l�l u [��`@S-`9�JSV{�%$#�� �$� Y *�[�c���c u &yc c u ��#m[i[�c�`$[ p �;[�nRc u � p &yce& � g'&�#e&�\�\-�]\ ��� c�#��"�LS_l�&�l�l�[ h S_&�c�� p��S-c u c���[;l��"{�ak�"`�cel�SV`@c u ��\zSV`$��g$#�[ h ��l�l�[�#�l��"c �>� S Y ��Y-}/� � � � � ��� �<�7&�` p � � � $ � � � � ��m�e}�&y` p a;%'l�c�S-cel��]\zn7!/�l�%$! p S r S p � p S-` &�`�&y`'&D\-[�{�[�%'l�a@&�`$`$�"#�Y

b c d e i a f g hlines

N0 1

abc

d

ef

gi

h

��� ���2�3�������;B��('1��" + /+" +-<,�7�2*%'1<2�� �4/� ��%� 8�+-� /�*�H

�u %'l"}/&�cc u S_l�l�ce&y{���&Dntc��"#c u �L�'#el�cC#�[i[�c`$[ p �;l�g�\zS-c�&�` p \zS-`$�k#�� p S_l�c�#TSV!$%$cTSV[�`I}<������Sz\z\���S-` p %$gX��S-c uc���[�l��"{�ak�"`�celNS-`@c u ��\�S-`$��g$#�[ h ��l�l�[�#�l��"c�}�&�` p c���[ p S"!P�"#m�"`ic ��� c�#m�"� g$#�[ h ��l�l�[�#�l��"cel � � &�` p �����w��& h�u l��"ch [�#�#m��l�g'[�` p S-`${@c�[>&;`$[ p ��&�c & p S !I�"#��"`�c u �]S-{ u cS-`�c u � p &�ce& � g'&y#e&D\z\-�]\ ��� cm#��"���e}$&�ll u [��`@S-`X�JSV{�%$#�� ��� Y

2 3

b c d e i a f g h

1

abc

d

ef

gi

h1

2

3

lines

N0

N1

��� ������������� � / �! �" �(+@� /�*:/+" ��/�/�+�*,/�6��;'1 2"�� +$/� ��%� 8�+@� /�*�H

�u � !$%�Sz\ p S-`${�&D\-{�[�#�S-c u a �S�\z\7`$[���g$#�[ h �"� p S-c��"#e&yc�S r �]\-(�}$��S-c u ��& hmu l��"{�ak�"`�c�S-`+c u � h [�\z\-� h c�S-[�`�[�nJ\�S-`$�g$#�[ h ��l�l�[�#]l p �"c��"#�a;S-`�S-`${�c u ��`�%$a;!'�"#R[�n/\�S-`$��l�SVc h [�`�ce&DS-`'l"}�&�` p c�#e&y`'l�a;S-c�c�S-`${�c u � h [�%$`�c7cm[�c u �&�l�l�[ h S_&�c�� p��� c�#m�"�k`$[ p �;g$#�[ h ��l�l�[�#�Y�� nc u �;`i%$a;!'�"#�[yn�\zS-`$��l�S-`9c u �MlT�"{�ak�"`�c��]� h �"� p lLc u �;`$[ p � h &yg'& h S-c (�� }Jc u �"`c u ��l��"{�ak�"`�cC� &�` p+h [�#m#���l�g'[�` p SV`${ ��� c�#��"��`$[ p ��g$#�[ h ��l�l�[�#"�R��Sz\z\7!/�Cno[�# h � p c�[kl�%$! p S r S p ��Y *�[�c��Cc u &�c�c u S_ll�%$! p S r S_lwS-[�`9g$#�[ h ��l�l�a@&�(b#���l�%�\-c�S-`�g$#�[ h ��l�l�[�#el�c u &�c h [�#m#���l�g'[�` p c�[�SV`�c��"#�`'&�\7`$[ p ��l�SV`�c u � p &�ce& � g'&�#e&D\z\-�]\��� c�#m�"�lTg�\�S-c�cTSV`${�c u �"a>l��]\ r ��l�����S-c u c u ��l��l�g�\zS-celNg'[�l�lwS-!�\-( g$#m[�g'&�{i&�cTSV`${C%$g��&y# p c u #m[�%${ u c u � p &�ce& � g'&�#e&D\z\-�]\��� c�#m�"���eY

�$�

Page 23: O'3 0D. - cs.umd.edu

2 3

b c d e i a f g h

1

abc

d

ef

gi

h1

2

3

lines

N0

N1

count: 5 4 3 2 1 4 3 2 1

� � ��������� �������3/28%620(8�')+@��*,��+@<%��".��*,�?01/ �2*%+5' +5/7+@<%�?8')')/�0�� 8�+5�6 *%/ 6&�('(H

�u ��!$%�Sz\ p SV`${�g$#�[ h ��l�lcm�"#�a;S-`'&�c���l�� u �"` &�\�\R`$[ p ��l�S-`Xc u � �� c�#��"��`$[ p ��g$#m[ h ��l�lT[�#qlT�"c u & r � &�c�ak[il�c� hmu S�\ p g$#m[ h ��l�lT[�#elL���]S-c u �"#S-`�c��"#�`'&D\ ��� c�#m�"� `$[ p ��l�[�#\zS-`$�kg$#�[ h ��l�l�[�#el]��&�lCl u [��` SV`9�JS-{�%$#�� ��� no[�#�[�%$#�]�'&�akg�\-� p &�ce&�lT�"c�Y ��u � p &�ce& � g'&�#e&D\z\-�]\ ��� c�#��"�C#�[�[�c�`$[ p � h [�#�#���lTg'[�` p l�c�[�c u �ql SV`${y\V��g$#m[ h ��l�lT[�#RS-`�l��"c ���$}c u ��\-��&Dn<`$[ p ��l�&�#�� h [�`ice&�SV`$� p SV`bg$#�[ h ��lml�[�#�l��"c � � }�&�` p &D\z\'\zS-`$��l�&�#���{�#�[�%$g/� p S-`>l��"{�ab�"`icelN[yn'\-�"`${�c u \-��l�lc u &�`�[�#C� � %'&D\�cm[ � S-` c u ��\zS-`$�kg$#�[ h ��l�l�[�#ql��"c���#�� h &�\�\�c u &�c���k&�#�� p ��&�\�S-`${���S-c u &�`X[�# p �"#�� � � � � �� c�#��"�S-`�[�%$#��]� &�abg�\V���]Y

d e b c i g h a f

1

2 3

4 5 6 7

lines

N0

N1

N2

abc

d

ef

gi

h1

2

34

5

6

7

��� ���2�3��� 4 � � /��9 �" �(+@� / *:/+" +@<%�?628�+)8�) �8%� 8&"." �%" B +@���(� $2���." 6���*,� /� ��%� 8�+-� /�*�H

W�S r �"` ��\�S-`$��l"} c u � p &�ce& � g'&�#e&D\z\-�]\ ��� c�#��"�MS4lL[�n��[�#el�c ��h &�l���a>&��iS-a>&D\�cm#��"� u �]S-{ u c �;� \V[�{#�I�C� u S h�u S4l[�!$ce&�SV`$� p !�(k[�!'l��"# r S-`${;c u &�c���& h�u+��� c�#��"�C`$[ p � h [�`�ce&DS-`'l�&�c \V��&�l�c�c ��[��]\-�"ak�"`�cel"YR�w`>g$#]& h c�S h ��}$��& hmu `$[ p �[�nRc u � �� c�#��"� h [�`ice&�SV`'l h [�`'lwS p �"#e&y!�\V(�ak[�#���c u &�`+c���[;�]\V�"ab�"`icel �<c u %'lc u ��c�#m�"� u �]S-{ u cS_l�a % hmu lTa>&D\z\-�"#�Y� l�l�%$a;S-`${�&�a>&D��S-a>&D\c�#��"� u �]S-{ u c��;�t\-[�{(�J�e}Rc u � p &�c]& � g'&�#e&D\z\-�]\ ��� c�#��"� h [�`'l�c�#�% h c�S-[�`�[�g'�"#e&�cTSV[�`�ce&�U���l�;� \V[�{ d �J� c�S-ak��} � u �"#��@��& h�u [�nc u � �;�t\-[�{(�J�LlT%$! p S r S_lwS-[�`�l�ce&�{���l�#�� � %�S-#���l �;�t\-[�{(�I� h [�abg$%$ce&�c�S-[�`'lb� &h [�`'l�c]&�`ic�`�%$a;!'�"#C[�n l h &�`'l&D\-[�`${k�SVc u c���[�!'[�%$` p SV`${+!/[D� l�[�#�cel]�eY

����� =@?$3"?$ATHJ?'0D?'*_*4F$*$� � A�3�0DFiF$8

��u � � � � c�#��"� h [�`'l�c�#m% h c�S-[�`�&D\-{�[�#TSVc u a S4l�lwS-a;Sz\_&�#;c�[+c u &�c�[�n�c u � ��� c�#��"�b��S-c u &bnt�"� ak[ p Sz� h &�c�S-[�`'l"Y;�w`[�# p �"#�c�[�n & h S�\zS-ce&�cm�>c u � ��N� c�#m�"��� l p S_lE��[�S-`ic p � h [�akg'[�lwS-c�S-[�`I}Rc u �@ak�"c u [ p nt[�# u &�` p \zSV`${�l�g�\zSVcmc�S-`${9`$[ p ��la;%'l�c!/� ab[ p Sz�'� p Y �u � ���N� c�#��"��`$[ p �MlTg�\�S-c�cTSV`${�&�\V{�[�#�S-c u a �'#el�c�l�[�#�cel�&D\z\7\zS-`$��l�S-` c u ��`$[ p � & h"h [�# p SV`${

���

Page 24: O'3 0D. - cs.umd.edu

c�[�c u ��\-�]noc�� p {���l [�nIc u �]S-#�!'[�%$` p S-`${;!'[D�$��l�&�lNS_l�lwS-a;Sz\_&�#�\-( p [�`$��no[�#�c u � ��� cm#��"��Y *�[�c���c u &�c�c u S_l�lTg�\�S-c�cTSV`${g$#�[ h ��l�l S_l p ��l h #�S-!/� p nt[�#�l��]\-� h c�S-`${>&�g/[il�lwS-!�\-� � � &��iS_l�l�g�\zS-c��'&�`>&y`'&D\-[�{�[�%'l g$#�[ h � p %$#m� ��Sz\z\I!'��no[y\�\-[���� p nt[�#l��]\-� h c�S-`${9&@g'[ilmlwS-!�\V� ��� &D�iS_l�l�g�\zSVcDY�*��]�~c�}Pno[�# ��& hmu `$[ p �>l�g�\zS-c;� u [il��;#���l�%�\-c;l�&�c�S_lw�'��l�&@g$#�� � ��l�ce&�!�\zS_l u � p� �.� � � � � ������� ����� � � � ��- ��� [yn � $�� \�S-`$��lJS-`;c u ��c���[�#���l�%�\-c�S-`${�`$[ p ��l���c��"#�ak� p &\-�"{i&D\~lTg�\�S-cNS-` � � h c�S-[�` � Y � �]}c u � h [�[�# p S-`'&�c�� r &D\-%$��[�n�c u �C\V�]ntcC� p {��CS_l!$#�[�& p$h &�l�ccm[ ��& h�u [�nRc u �C\zS-`$��l�S-`�c u ��`$[ p ��!/�]SV`${�lTg�\�S-c�Y

�w`9&�`+S-c��"#e&yc�S r �;g$#�[ h ��lmlC� u S h�u9p �"g'�"` p lL[�`Xc u ��`�%$a;!'�"#�[�nR\-�"{i&�\�l�g�\zSVc]l�SV`�&k`$[ p ��}<��& hmu `$[ p �kc u &�ch [�#�#m��l�g'[�` p l�c�[+&;\-�"{i&�\ l�g�\zS-cCS-`Xc�%$#�`�!$#m[i& p$h &�l�c]l�c u � h [�[�# p S-`'&�cm� r &D\-%$�;[�nRS-cel#TSV{ u c�lwS p ��Y�Q�& hmu \zSV`$��}PS-`g'&�#e&�\�\-�]\�} h \zS-g'l�SVc]l��]\zn&�{i&�SV`'lTcc u � lTg�\�S-c h [i[�# p S-`'&�c�� r &D\-%$��Y ��u � h \zSVgX#���lT%�\Vc]l�S-`X�]S-c u �"# [�`$�k��c u �C\zS-`$� p [���l`$[�c�S-`icm�"#el�� h c�c u ��l�g�\zSVc h [i[�# p SV`'&yc�� r &D\-%$����[�#�c���[�\zS-`$��l���c u �\zS-`$�CS-`ic��"#]l�� h cel�c u ��l�g�\zS-c h [�[�# p S-`'&�c�� r &D\-%$���eYQ�& h�u #���l�%�\-c�S-`${k\zS-`$� p �"c��"#ma;S-`$��l�S-`X� u S h�u [�nRc u ��c ��[;`$�"� `$[ p ��lS-cS_l h [�`�ce&DS-`$� p Y�$[�#�]� &yakg�\-��}$S-`Xc u �h &�l���[yn�&�` � � &��iS_lCl�g�\zSVcD}'&�\zS-`$� h &�` \�S-�LSV`��]S-c u �"#c u ��`$[ p ��� u S hmu S_l h [�abg$#�S_l�� p [�nR&D\z\I\zSV`$��lCcm[ c u �C\V�]ntc[�nc u ��l�g�\zS-c h [i[�# p S-`'&�c�� r &D\-%$��}�[�#�c u �`$[ p ��� u S h�u+h [�`'lwS_l�c]l�[yn�&D\z\'\zS-`$��l�c�[�c u � #TSV{ u c�[�nIc u ��l�g�\zS-c h [i[�# p S-`'&�c��r &�\V%$��Y ��u � p �]�'`�S-c�S-[�`�[�n�&�` ��N� c�#��"��#�� � %�S-#���lLc u &�c��& h�u `$[ p �M&ycq&b{�S r �"`�\-� r �]\�[�n�c u ��c�#��"��S_l p S_lE��[�S-`icnt#�[�a &�\�\[�c u �"# `$[ p ��l"Y���`�[�# p �"# cm[��"`'l�%$#��+c u S4l p S_lE��[�S-`ic p � h [�akg'[�lwS-c�S-[�`I}�lT[�ak�;\zS-`$��lk�S�\z\ u & r �@c�[�!/�l�g�\zS-c& h #�[il�lNa;%�\-c�S-g�\-��`$[ p ��l�S-`>c u ��'`'&D\ p � h [�abg'[ilwS-c�S-[�`IY ��u S_l�l SVcm%'&�c�S-[�`>&D\_l�[;&�#�S_l���l�SV`@c u �!$% h U��"c�|�x �

� %'& p c�#��"��Y &` h �C��& h�u \zS-`$� p �"c��"#ma;S-`$��l�c u � `$[ p ��S-`>� u S hmu SVc�\zS-��l"}$&�l�� � %$�"` h ��[�nIl h &�`k[�g/�"#e&�c�S-[�`'l S_lR%'lT� pc�[ p �"c��"#ma;S-`$��c u �!'[�%$` p SV`${b!'[D�kc u &�c h [�`�ce&DS-`'lRc u ��\zSV`$��l�SV`@c u �c���[�`$�"� `$[ p ��l"Y��JS-`'&D\z\-(�}$c u ��g'�"#�S-ak�"c��"#[�nRc u ��c���[ #m��l�%�\-c�S-`${>!/[�%$` p S-`${+!'[D�~��l�S4l h [�akg$%$cm� p Y

�u �MlTg�\�S-c�cTSV`${�g$#�[ h ��l�l h [�`�c�S-`�%$��l�no[�#���& h�u [�n�c u �M\V�"{�&D\�`$[ p �kl�g�\zS-cel�&�` p l�g�\zS-c &D�$��l"Y?&` h �@&D\z\R\V�"{�&D\`$[ p �>l�g�\zS-cel u & r �;!'�"�"` p �"c��"#�a;S-`$� p &�` p c u �;#���l�%�\-c�S-`${X`$[ p �kg/�"#�S-ak�"c��"#el�&�#�� h [�akg$%$c�� p }Jc u �kl�g�\zSVck&D��S_l&�` p;h [�[�# p S-`'&�c�� r &D\-%$�c u &yc h [�#m#���l�g'[�` p c�[Cc u ��a;S-`�S-a>&D\'g'�"#TSVab�"c��"#R[�n'c u ��c ��[#m��l�%�\-c�S-`${�`$[ p ��lJS4lRlT�]\V� h cm� p&�lLc u �;�'`'&D\�`$[ p �+l�g�\zS-c r &D\-%$��Y+��`�c u �k� r �"`ic�[�n &+c�S-��}Rl�[�ak�b[�c u �"#�ab�"c�#�S h l�% hmu &�l�c u �>lTg�\�S-c;��S-c u c u �a;S-`�S-a>&D\<!'[�%$` p S-`${;!'[D�M&y#���&�lNa>&D(�!'���"akg�\-[�(�� p Y � ntc��"# h�u [�[ilwS-`${�c u � l�g�\zS-c�c�S-`${ &��iS_l�&y` p c u � h [i[�# p S-`'&�c��r &�\V%$��}<&�`+%$`'l u %/0>��[�g'�"#e&yc�S-[�` h [�` h �"`�c�#e&yc���l�c u [il��C\zS-`$�;g$#�[ h ��lml�[�#el�cm[�{��"c u �"#�S-`�c�[kc���[;`$�"� `$[ p ��l }'��& hmu[�nR� u S h�uXh [�#�#���lTg'[�` p l�cm[k[�`$��[�nRc u ��c���[ � � � c�#��"�C\-��&Dn�`$[ p ��g$#�[ h ��l�l�[�#]l"Y

�u � !$%�Sz\ p S-`${ &D\-{�[�#TSVc u a g$#m[ h �"� p lS-c��"#e&�c�S r �]\-(�}$�SVc u ��& h�u `$[ p � p �"c��"#�aMSV`�S-`${@c u ��`�%$a !/�"#[�nI\zS-`$��l�S-ch [�`�ce&DS-`'l"}I&�` p c�#e&�`'l�aMSVcmc�S-`${+c u � h [�%$`ic�cm[+c u �k&�l�l�[ h S_&�c�� pX��N� c�#��"�b`$[ p �;g$#�[ h ��l�l�[�#DY�� nc u � `�%$a;!'�"#�[�n\zS-`$��l�S-`�c u �b`$[ p �k�]� h �"� p l�c u �@`$[ p � h &yg'& h S-c ( � }Jc u �"`9c u �@`$[ p � � &�` p9h [�#m#���l�g'[�` p SV`${ � � � cm#��"�k`$[ p �g$#�[ h ��l�l�[�# �L&y#�� lTg�\�S-c�Y � S-a;Sz\_&�#@c�[�c u � �� c�#��"�+!$%�Sz\ p SV`${ &�\V{�[�#�S-c u a�}Rc u � � � � c�#��"� h [�`'l�c�#m% h c�S-[�`�g$#�[ h ��l�lc��"#�aMSV`'&yc���l�� u �"`�&D\z\7`$[ p ��l�S-`�c u � � � � c�#��"��`$[ p ��g$#�[ h ��l�l�[�# lT�"c u & r �q&yc�ab[il�c � hmu Sz\ p #��"`9&�ll u [��`bS-`�JS-{�%$#�� ��� no[�#�[�%$#�]�'&�akg�\-� p &�c]&�l��"c�Y

*�[�c���c u &ycRc u ��\-��&Dn7`$[ p � l�%$! p S r S_lwS-[�`�g$#m[ h ��l�l a>&D(�#���lT%�\Vc�S-`@g$#�[ h ��lml�[�#elNc u &yc h [�#�#���l�g/[�` p c�[CS-`ic��"#m`'&D\���

Page 25: O'3 0D. - cs.umd.edu

2 3

a b d e f a c g h i

1

abc

d

ef

gi

h1

2

3lines

N0

N1

��� ������� � ��� B �('���" +�/+" +-<,�C# ��')+ �3/���* 6$/+" B � +-���(��*,/�6�� '1 �".� +5+@��*,� " /��2+-<,� 6�8�+ 8��.*?��� ������� ��H

ab

c

d

ef

g

i

h1

2

7

56

4

3b d e a f c i g h

1

2 3

4 5 6 7

lines

N0

N1

N2

��� ���2�3��� ��� � /��9 �" �(+@� /�*4/+" +@<%�G6�8�+ 8�) 8 � 8&"." �%" B � +@���(� $2���." 6���*,� /� ��%� 8�+-� /�*�H

`$[ p ��l;S-` c u � � � � c�#��"��!'�]S-`${9nt[�# h � p cm[�l�g�\zS-c>� u �"` c u ��`�%$a;!'�"#k[ynqc u �]S-# h�u Sz\ p #��"` ����Y�{/Y-}N\-��&Dn�`$[ p ��l]��]� h �"� p lc u ��`$[ p � h &yg'& h S-c (�Y ��u ��l���S-`�c��"#�`'&D\N`$[ p �;l�g�\zSVc]la>&D(@g'[ilmlwS-!�\V(+g$#m[�g'&�{i&�cm� %$g�c�[kc u ��#�[�[�c�`$[ p �[�nRc u � � � � c�#m�"�;� &�` p &�#���cm�"#�ak� p � �3� ��� � � � �)� �� �eY

� `�& p$p S-c�S-[�`'&D\ h [�akg�\zS h &�c�S-[�`�S-`�c u �@`$[ p ��lTg�\�S-c�cTSV`${sg$#�[ h ��lml &y#�S_l���lLS�n�c u �+l�g�\zS-c�c�S-`${9[�n &�`sS-`ic��"#m`'&D\`$[ p �Cno[�# h ��l�c u ��l�g�\zSVcmc�S-`${k[�n�l�[�ak� [yn7c u � p ��l h �"` p �"`�celC��!/[�c u `$[ p ��l�&�` p \zSV`$��l ��[�n7c u ��`$[ p ��!'�]S-`${>lTg�\�S-c�Yv�`�\�S-U��bc u � ��� c�#��"�;� u S hmu�p [���lC`$[�cC�"`�no[�# h �k& p S_lE��[�S-`ic p � h [�akg/[ilwS-c�S-[�`I}7&y`�%$g��&y# p S-`�c��"#�`'&D\�`$[ p �kl�g�\zSVca>&D(k#���lT%�\VcSV`�c u ��l��]\-� h c�S-[�`�[�n &;l�g�\zS-c�&D�iS_l&y` p & h [i[�# p S-`'&�c�� r &�\V%$��c u &�c�S-`icm�"#el�� h cel�c u � p ��l h �"` p �"`ic]l[�nc u ��l�g�\zSVcmc�S-`${�`$[ p ��Y ��u �Nn�& h cIc u &ycIc u � p � h [�akg'[il SVcTSV[�`�S-` p % h � p !�(�c u � ��N� c�#��"��a;%'l�cI!'� p S_lE� [ySV`�cN#�� � %�S-#���lc u &�cC&�`i(@S-`�c��"#el�� h cTSV`${ p ��l h �"` p �"`icel��w`$[ p ��lC[�#\�S-`$��l]�a;%'l�c�&D\_l�[@!'�kl�g�\zS-c�Y � g�\zS-c�c�S-`${�c u � p ��l h �"` p �"`�celC[�n&@`$[ p �;S_l�c��"#�ab� p & � � � �0� ��� � � � �)�� Y ��u � � � � c�#��"� h [�`'l�cm#�% h c�S-[�`9g$#�[ h ��l�lLc��"#�a;S-`'&�c���lC� u �"`�&D\z\�`$[ p ��lS-`9c u �k`$[ p �kg$#�[ h ��l�l�[�# l��"c u & r �k&�c�ak[�l�c � h�u Sz\ p g$#m[ h ��l�lT[�#el����]S-c u �"#LSV`�c��"#�`'&�\ � � � c�#��"�k`$[ p ��l�[�#C\�S-`$�g$#�[ h ��l�l�[�#]l]�eY

�wc�S_l�S-akg/[�#�ce&y`ic�c�[k`$[�c���c u &�c�%$`�\zS-U��;c u � ��� cm#��"��[�# � � � cm#��"��}$c u � � � � cm#��"� p [i��l�`$[�c u & r ��&;a;S-`�S-a>&D\`$[ p �k[ h"h %$g'&y` h (�\-� r �]\ �XY ��u S_l�S4l�& p S-#�� h c�#���l�%�\-c�[�n�c u � p [���`i�&�# p `$[ p �kl�g�\zS-cel"Y:� u �"`�& p [���`i�&�# p`$[ p � l�g�\zS-ckS_l h�u [�l��"`I}�c u �+#���l�%�\-c�S-`${�`$[ p ��[ h"h %$g'&�` h (�\-� r �]\_l@[�n�&�`�( p ��l h �"` p �"`�c+`$[ p ��l;c u &�cka>&D(9!/�&�!I� h c�� p S_l�`$[�c h [�`'lwS p �"#�� p Y ��u %'l"}R& p [��`��&�# p `$[ p ��lTg�\�S-c;a>&D(X#���l�%�\-c�S-` & p ��l h �"` p �"`�c;`$[ p �+!/�]SV`${l�g�\zS-c�S-`�c�[�c���[ lT%$!$`$[ p ��lL[�n r �"#m(�%$`�!'&D\_&�` h � p�h &yg'& h S-c (s�tS�Y���Y-}I&@`$[ p �k��S-c u��� �]\V�"ab�"`icel h [�%�\ p !'�@l�g�\zSVc

���

Page 26: O'3 0D. - cs.umd.edu

S-`icm[kc���[;`$[ p ��l"}$c u �L�'#el�c h [�`ice&�SV`�S-`${kc���[;�]\-�"ak�"`ic]l"}1&y` p c u � l�� h [�` p+h [�`ic]&DS-`�SV`${ � �;�]\-�"ak�"`�cel]�]Y

A

B

C

D

E FA

B

C

D

E1 F1E2

F2

A1

B

C

D

E1 F1E4

F2

A2

E3

(a) (b) (c)

��� ������� � ��� �! �8��9 �" � /+" �� �% 8%� 6 8&* 6 6�/+%�*&% 8 � 6 '1 2"�� +5'�� ' 8�*�'�<%/+% ' *%/�6��('�� 8&*�6��'1 2"�� + +@�.*%� � ' $ * '1<%/&%$' +@<%�����('1�2" + /+" +-<,� + % /9*%/ 6&�:'1 �".� +5'48&* 6�+-<,���3�('1�2" +@�.*%� �� �% 8 � 6 '1 �".� +/+" *,/�6&� � � 8&* 6 ' 0�* 6��% �� 01+ '4+@<%�����('1��" + /!" +-<,���� �% 8%� 6 '1 �".� +$/+" � H

� [�#�]�'&�akg�\-��} h [�`'lwS p �"#�c u � l SVcm%'&�c�S-[�` p �"g�S h c�� p SV`9�JS-{�%$#�� ��� � u �"#m� `$[ p � �@S_l�c u ��g'&y#��"`icC[�nR`$[ p ��l } �'} } � }I&y` p�� Y � l�l�%$ak�kc u &�c�c u �k`$[ p � h &�g'& h S-c�(+S_l:=$}7&�` p c u &yc�`$[ p ��l � &y` p�� S-`��JS-{�%$#�� ��� &@&�#��!'�]S-`${>lTg�\�S-c�Y ��u �#���l�%�\-c�[�nIc u �]S-#l�%$! p S r S_lwS-[�`+S-`�c�[�`$[ p ��l � � } � �'} � � }$&�` p�� �LS4l�l u [��`MSV`+�JS-{�%$#�� ��� !IY��� h &�%'l���g'&�#m�"`ic`$[ p ���k`$[�� u &�l�l�� r �"` h�u Sz\ p #��"`I}/c u ��l�g�\zS-c�c�S-`${>[yn7`$[ p ��l � &�` p�� #���l�%�\-cel�S-` &y`>%$g��&�# pl�g�\zS-c�[�n �1Y � l�l�%$a;S-`${;c u &�cR`$[ p ��kl�g�\zS-cel�&D\-[�`${�c u � p &�l u � p \zSV`$��l u [��`;S-`+�JS-{�%$#�� ��� !I}�& p [��`��&y# p l�g�\zSVc[�n hmu Sz\ p `$[ p � � �@��Sz\�\�!/�;`$� h ��l�l�&�#�(@S-`X[�# p �"#Cc�[@a>&DS-`�ce&DS-`Xc u � p S_lE��[�S-`ic p � h [�akg'[il SVcTSV[�`IY �u � #m��l�%�\-c [�ng'&�#��"`�cC`$[ p �6� � l lT%$! p S r S_lwS-[�`sS-`icm[>`$[ p ��l5� � &�` p � �/}1&�` p c u � p [��`i�&�# p l�g�\zS-c�[�n�`$[ p � � �bS_l�l u [��`S-` �JS-{�%$#�� �~��h Y

A

C

B

E

D

x

��� �������#� ���#�! �8��9 �" � <2� ��<�".� � <,+-�.*%� +@<%�4" ��" +C8�*�6;� � ��<%+ $�/���*�6���*,� $�/� %�(' %4<�� 0�<401/��5�3�('� �/ * 6+5/7+@<%� '� �".� +�01/�/�� 6 �.*�8+ � ),8&"��,� � 8�')')/ 0�� 8+ �6 %4� +@< $�/��2*�6 �.*%� $�/� � 6����5��*,� +@<%�!B � +-���(�*%/ 6&�:'1 �".� +5+@��*,� ���/�01�(')' H

�w` h [�akg'&�#�S_l�[�`sc�[�c u �bc u � p &yce& � g'&�#e&�\�\-�]\ ��� c�#��"��}Rc u � p &�ce& � g'&y#e&D\z\-�]\ � � � c�#��"� h [�`'lTc�#�% h c�S-[�`�g$#�[ h ��l�ll�%/!I�"#el���S-c u #���lTg'� h cc�[;c u ��`�%$a;!'�"#[yn�l h &�`+[�g/�"#e&�c�S-[�`'l`$� h ��l�l�&�#�(bc�[ h�u [�[il���c u �C\-[ h &D\z\-(+[�g$c�S-a>&D\I`$[ p �

� =

Page 27: O'3 0D. - cs.umd.edu

l�g�\zS-c�Y � l��&�l p ��l h #�S-!/� p SV` � � h c�S-[�` � Y � � &�` p@p �"g�S h cm� p SV`+�JS-{�%$#�� � ���e}�&�l�� � %$�"` h ��[�n7&�g$g$#�[D�iS-a>&yc��]\-(kc��"`l h &�`'l�S4l�&D\z\7c u &�c�S_l�`$� h ��l�l�&y#�(>cm[MlT�]\V� h cCc u ��`$[ p ��l�g�\zS-cq&D��S_l&�` p+h [�[�# p S-`'&�c��Cnt[�# & p &�c]& � g'&�#e&D\z\-�]\ ��� cm#��"��Y�$[�#Rc u � � � � c�#��"� &y` p S-cel p S_lE� [ySV`�c p � h [�akg'[il SVcTSV[�`>[�nIl�g'& h ��}�c u ��g$#�[ h ��lmlR#�� � %�S-#���l�lwS-{�`�Sz� h &�`�c�\-(kak[�#��l h &�`[�g/�"#e&�c�S-[�`'l"Y+jC%$�@c�[+c u � p S_lE� [ySV`�c p � h [�akg/[ilwS-c�S-[�`I}NS-c�S_l;l�[�ab�"c�S-ak��l�`$� h ��l�lm&�#�(9c�[�lTg�\�S-ckc u � h�u Sz\ p #��"`�[�nS-`icm�"#�`'&D\'`$[ p ��l��tS�Y���Y-} p [��`��&�# p l�g�\zS-cel]� p %$#�S-`${�c u �l�%$! p S r S_lwS-[�`+g$#�[ h ��l�lR&�lRl u [���`�S-`>�JS-{�%$#m� �~� Y7� [�#Rc u S_l#���&�lT[�`I}�S-c!/� h [�ak��l�`$� h ��l�l�&�#m(kc�[�a@&�U��C%'l�� [yn�& p$p S-c�S-[�`'&D\IU�`$[��\V� p {�� [�nNc u � h [�`ic��"`�cel [�n7c u � h�u Sz\ p #��"`+[�n&kl�g�\zS-c�c�S-`${@`$[ p �b����Y�{'Y4}ic u ��l�g'&�c�S_&D\7�]�$c��"`�cel�[�nNc u ��{�#]&�` p$h�u Sz\ p #��"`<��� u �"` lTg�\�S-c�cTSV`${+c u ��`$[ p ��Y

� [�`'lwS p �"#;c u � l SVcm%'&�c�S-[�`�l u [��`9S-`��JS-{�%$#�� � ��� u �"#��@`$[ p ��l � � � #��"g$#���l��"`�c�� r � l SV!�\zS-`${ilMS-` &+`$[ p �� u S hmu S4lM!'�]S-`${ lTg�\�S-c�Y � lml�%$ak�+c u &�c ��#��"g$#m��l��"`ic]l;c u � h�u [ilT�"` � � &D��S_lkl�g�\zS-c h [i[�# p S-`'&�c�� r &�\V%$��Y�� u �"`#��"{�#m[�%$g�S-`${�`$[ p ��l � � � }<`$[ p � � S_l�{�#�[�%$g'� p SV`sS-cel��"`�c�S-#��"c�(X��S-c u c u �kg'[�#�c�S-[�`'l�[yn`$[ p ��l � &�` p c u &�cn�&D\z\qc�[sc u �+\-�]ntc>[�n�c u �Xl�g�\zSVc h [�[�# p S-`'&�cm� r &�\V%$� �JY � SVaMS�\_&�#T\V(�}C`$[ p ��l &y` p � &�#��+{�#�[�%$g'� p ��S-c u c u �g'[�#�c�S-[�`'lR[ynP`$[ p ��l � &�` p( c u &�cNn�&D\z\1c�[�c u �#�S-{ u c�[�nIc u � lTg�\�S-c h [�[�# p S-`'&�c�� r &D\-%$� �IYN�tnI������"#��cm[�&�g$g�\-(>&lwS-a;Sz\_&�#l�� � %$�"` h � [�nIl h &�`k[�g'�"#e&�cTSV[�`'l�&�l �&�l p [�`$���S-c u c u � p &�ce& � g'&y#e&D\z\-�]\ ��� c�#m�"��}�c u �"`@��& hmu `$[ p � h [�%�\ pS-` p �"g'�"` p �"`�c�\-(�� &�` p S-`9g'&�#e&�\�\-�]\t� p �"c��"#�a;S-`$�@c u �;c���[+&�l�lT[ h S_&�c�� p !'[�%$` p S-`${X!'[D�$��l�c u &�c h [�#�#���l�g/[�` p c�[&D\z\Rg'[�#�cTSV[�`'l[�nR`$[ p ��lCc�[kc u �L\V�]ntcC[�n�c u � l�g�\zS-c h [i[�# p S-`'&�c�� r &D\-%$� �9� S Y ��Y-}$c u �L\V�]ntc u &D\ r ��l[yn�`$[ p ��l ��&�` p }~&y` p &D\z\7[yn7`$[ p � � �e}�&�` p &D\z\Ig'[�#�cTSV[�`'l�[yn7`$[ p ��lc�[;c u � #TSV{ u c[yn7c u ��l�g�\zSVc h [i[�# p SV`'&yc�� r &D\-%$� ���tS�Y���Y-}�c u �#�S-{ u c u &D\ r ��l�[�n7`$[ p ��l�+&�` p }$&�` p &D\z\7[�n7`$[ p ��l &�` p � �eY

� [�#N�]� &�abg�\V��}yS-`M�JS-{�%$#m� � �$}�c u ��\-�]nocR!/[�%$` p S-`${�!'[D� h [�#�#���l�g/[�` p S-`${�c�[�c u ��l�g�\zSVc�&�l�l�[ h S_&�c�� p ��S-c u `$[ p �� h [�`'l S4lTcel�[�nIc u �\-�]ntc�g'[�#�cTSV[�`'l�[ynP`$[ p ��l �>&�` p( }�&�lR���]\z\7&�lR`$[ p � �LS-`@SVc]l��"`�c�S-#��"c�(�Y � S-a;Sz\4&y#�\-(�}'c u �C#�S-{ u c!'[�%$` p SV`${+!/[D� h [�`'lwS_l�cel�[�n�c u ��#�S-{ u cCg'[�#�cTSV[�`'l[�nR`$[ p ��l5� &�` p }<&�` p `$[ p ��l &�` p�� S-`Xc u �]S-# �"`�c�S-#��"c�(�Y*�[�c��;c u &�c�c u S_l�&�g$g$#�[i& hmu S-{�`$[�#���lCc u � h [�`icm�"`icel�[�n&D\z\�`$[ p ��l;�tS�Y���Y-}<`$[ p ��l�� � � ��� u �"` p �"c��"#�a;S-`�S-`${Xc u �\-�]noc�&�` p #�S-{ u c!/[�%$` p S-`${+!'[D�~��l h [�#�#���l�g/[�` p S-`${>cm[>&;{�S r �"`�l�g�\zS-c�&D�iS_lC&�` p+h [�[�# p S-`'&�c�� r &D\-%$��Y

Z�[���� r �"#�}I�"abg�\V[�(�S-`${�c u � ��� c�#m�"� � \�S-U��X&�g$g$#�[i& h�u c�[+nt[�#�aMSV`${Xc u �@!'[�%$` p SV`${�!'[D�$��lLno[�#k&�` � � � c�#m�"�S_l J1&���� p Y���� h &�%'lT�>[�nc u � p S_lE��[�S-`ic p � h [�akg/[ilwS-c�S-[�`�[�n l�g'& h � &�` p c u � lTce&�` p &�# p #�� � %�S-#��"ab�"`ic;c u &�c;&D\z\!'[�%$` p SV`${�!'[D�$��l�S-`'lwS p �;�]S-c u �"#�c u � �� c�#��"�;[�#c u � � � � c�#��"�;!/� aMSV`�S-a>&�\�!/[�%$` p S-`${�!'[D�$��l"} SVc�l�[�ab�"c�S-ak��l!'� h [�ak��lk`$� h ��lml�&�#�(�c�[ h [�`'lwS p �"#@c u � h [�`�c��"`ic]l�[ynqc u �+`$[ p ��l@�tS�Y���Y4}R`$[ p ��l(� � � S-` c u �+�]�'&�akg�\-����� u �"`p �"c��"#�aMSV`�S-`${+c u �L\-�]noc�&�` p #�S-{ u c!'[�%$` p S-`${�!'[D�~��l�c u &�c���[�%�\ p #���l�%�\-cCnt#�[�a & h &y` p S p &yc��kl�g�\zSVcDY � [�`'l S p �"#c u �XlwS-c�%'&�c�S-[�` p �"g�S h cm� p S-` �JS-{�%$#�� ��� &X� u �"#m� `$[ p � � h [�`ice&�SV`'l ��� � � c���[ h�u Sz\ p #��"`I}�\_&�!'�]\-� p � � &�` p� � Y � S-a;Sz\_&�#�\-(�}N\-�"c�`$[ p � &�\4lT[ h [�`ic]&DS-`9c���[ h�u Sz\ p #��"`I}J\_&�!'�]\-� p � �>&�` p ��� Y�� [�#�c u �;g$%$#�g/[il��k[�n�c u S_lp S_l h %'l�lwS-[�`I}/S-c�S_l�`$[�c�`$� h ��l�l�&�#m(+c�[kl u [�� &�`�( hmu Sz\ p #m�"` [yn�`$[ p ��l�� � � Y

� n [�`$�X���"#��Xc�[�%'l��Xc u � ��� cm#��"� � \zSVU�� &�g$g$#m[i& hmu ��&�l p �"ce&DSz\-� p S-` � � h c�S-[�` � Y � �e}�� u S hmu S-{�`$[�#���l c u �p S_l�c�#�S-!$%$c�S-[�`�[�nRc u � hmu Sz\ p #��"`X`$[ p ��l�� u �"` p �"c��"#�aMSV`�S-`${+&�`$[ p �;l�g�\zSVcD}$c u �"`+c u �C\-�]ntc &�` p #�S-{ u c�!'[�%$` p S-`${

���

Page 28: O'3 0D. - cs.umd.edu

A

C

B

E

a1

a2

b1b2

A

C

B

E

a1

D

a2

b1b2

A

C

B

E

x x x

a1

D

a2

b1b2

D

(a) (b) (c)

��� ������� � ��� ' 8�* �+ �8&�! �" � ")��/�� ��� � �2�3� � � %�� +@<9+@<%�!8�')'����9 ,+-� /�*?+-< 8�+ *,/�6&�(' � 8&* 6� /�*�" = <�8�)�4+ % /�0�<2��" 6 ���%* ' 6&�% �� 01+5�6�8�' 0���/&' ')�6 $�/� ,�('�* � ' $ * +-<,� *%/ 6&� '� �".� + %�<2� 0�<����('1�2" +5'")��/�� �%'1�.*%� +@<%� ')+ 8&*�628 � 6�B +@�3�(� )".� ��� 8& � ���/�8,0�< � 8&* 6 ' 0�* +@<%��01/��5�3�01+!B�� +-���(� *,/�6��'1 2"�� + %4<�� 0�<G01/�*%'1� 6&�%��' +@<%�?01/�*%+5�%*%+5'4/!" +@<%� *%/ 6&�(' ' �IH ��H ��+-<,�?0��3/�')' �6 $�/� %�(' *1H

!'[D�$��lC��[�%�\ p h [�#�#���l�g/[�` p c�[@c u �;c���[>l u & p � p #��"{�S-[�`'l�S-`��JS-{�%$#m� ��� !IY�W�S r �"` c u &�c `$[ p ��l5��&�` p� [�`�\-(h [�`�ce&DS-`�c ��[ hmu Sz\ p #m�"` &�l p ��l h #�S-!'� p &�!/[ r ��}Nc u � h [�#�#m� h c !/[�%$` p S-`${9!'[D�$��l�c u &yc���[�%�\ p #m��l�%�\-c�nt#�[�a�c u �� � &��iS_ll�g�\zS-c%'lwS-`${+l�g�\zS-c h [i[�# p S-`'&�c�� ��&y#�� � %�S-c�� p S"!I�"#��"`icDY��$[�#�c u �C�]�'&�akg�\-� p &�c]&�l��"cRS-`X�JSV{�%$#�� ��� &$}�c u �h [�#�#m� h c�\-�]nocC!'[�%$` p S-`${+!/[�� h [�#�#���l�g/[�` p S-`${>c�[@l�g�\zSVc h [�[�# p S-`'&�cm� r &�\V%$� � h [�`ic]&DS-`'lc u ��#��"{�S-[�` no[�#mak� p !i(c u �g/[�#�c�S-[�`'l [�n1`$[ p ��l �;&�` p6 c u &�cN\zS-� c�[�c u ��\-�]noc�[�n1c u �Cl�g�\zSVc h [�[�# p S-`'&�c��L�tS�Y���Y-}�#��"{�S-[�`'l � � &�` p�� � �]}�&�l���]\z\�&�l�`$[ p � �MS-`@S-cel��"`�c�S-#��"c�(�Y �u � h [�#�#�� h c!/[�%$` p S-`${>!/[D� h [�`�ce&DS-`�S-`${ � � } � � }$&�` p � S4l�l u [��`�&�l�c u �\-�]noc;l u & p � p #m�"{�S-[�`�SV`��JSV{�%$#�� ����h Y?*�[�c�S h �;c u &�c�c u S_l�l u & p � p #��"{�S-[�`XS_l h [�`'lwS p �"#e&�!�\-(�l�a>&�\�\-�"#�c u &�`Xc u �\-�]noc�!'[�%$` p S-`${@!'[D�>nt[�#�ab� p %'lwS-`${@c u � ��� c�#��"� � \zS-U��;c�� hmu `�S � %$��S-`X�JSV{�%$#�� ��� !IY � S-a;Sz\_&�#�\-(�}<c u ��& h c�%'&D\I#�S-{ u c!'[�%$` p SV`${�!'[D� c u &�c h [�#�#m��l�g'[�` p lCcm[ l�g�\zS-c h [�[�# p S-`'&�cm� r &D\-%$� ��S_l�l u [��` &�l�c u �;#�S-{ u cql u & p � p #��"{�S-[�`�S-`�JS-{�%$#�� ����h Y � lR��� h &y`$`$[�c�& h"h %$#]&�c��]\-( p �"c��"#�aMSV`$��c u �\-�]ntc&y` p #�S-{ u c�!/[�%$` p S-`${k!'[D�$��l h [�#�#���l�g/[�` p S-`${kc�[��& hmu h &�` p S p &�cm� l�g�\zS-c %'l SV`${+c u ��lwS-akg�\-� !$%$c�n�&�l�c ��� cm#��"� � \zSVU�� ab�"c u [ p }~SVcC!'� h [�ak��l`$� h ��lml�&�#�(+c�[b�"akg�\-[�(&;a;% hmu ak[�#�� h [�abg$%$ce&�c�S-[�`'&D\z\-(+�]�$g'�"`'lwS r �;c�� hmu `�S � %$��Y

� #�[�a c u S_l��]�'&�akg�\-��}�S-c�S_l h \V��&y#� u (>c u ��l SVabg�\V� ��� c�#��"��`$[ p � lTg�\�S-c�cTSV`${@c�� hmu `�S � %$��c u &�c%'l���l�& lTa>&D\z\l�� � %$�"` h �k[�nl h &�`X[�g'�"#]&�c�S-[�`'l�S_l�`$[�c�&yg$g�\�S h &�!�\-�@c�[@c u � � � � c�#m�"��}I&�lU�`$[���\-� p {��k[�n�c u � h [�`�c��"`ic]l[�n�c u �`$[ p ��l;!'�]S-`${�#��"{�#�[�%$g/� p &�` p g'[il�l SV!�\-( l�g�\zS-c@a %'lTcM&�\4lT[ !/� h [�`'lwS p �"#�� p � u �"` p �"c��"#�a;S-`�S-`${�c u �k\-[ h &D\z\-([�g$c�S-a>&�\`$[ p �+l�g�\zSVcDY9��`�c��"#���lTc�S-`${�\-(�}RSzn [�`$�+���"#��bc�[X�"akg�\-[�(sc u � ��� c�#��"� � \zS-U��+`$[ p ��l�g�\zS-c�c�S-`${�cm� h�u `�S � %$�&D\-[�`${9�SVc u c u � p S_lE� [ySV`�c p � h [�abg'[ilwS-c�S-[�` [�n�l�g'& h �+#�� � %�S-#��"ak�"`�c�}�c u �+�"`'l�%�S-`${ h [�`'lTc�#�% h c�S-[�` &D\-{�[�#�S-c u a��[�%�\ p !$%�Sz\ p & p &�ce& � g'&y#e&D\z\-�]\ � ��p�� ��c�#��"�-� � [�!�S�� �� Y

���

Page 29: O'3 0D. - cs.umd.edu

( =@?$3"?$A�BC?'0D?'*_*4F$*�GPHJ?$3�2-?'* ���<F~0�24F~8

|R&�#e&�\�\-�]\�l�g'&�c�S_&D\ � %$�"#�S-��lC���"#m���]�'&�a;S-`$� p nt[�#c u �;c u #��"�LS-akg�\-�"ak�"`icm� p9p &�ce& � g'&y#e&D\z\-�]\�l�g'&�c�S_&D\ p &yce&>lTc�#�% h]�c�%$#���lS-`X[�# p �"#c�[bnt%$#�c u �"#C%$` p �"#el�ce&�` p c u �]S-#�!'� u & r SV[�#e&D\Rc�#e& p �"[ !7l&y` p�p S"!I�"#��"` h ��l�S-` c u � p &�ce& � g'&�#e&D\z\-�]\�"` r S-#�[�`$ab�"`ic�Y:�9� hmu [il��;c�[bSVabg�\V�"ab�"`ic;c u #��"� p S"!I�"#��"`�c�l�g'&�c�S_&D\ � %$�"#�S-��lCnt[�#C��& h�u9p &�c]&+l�c�#�% h c�%$#m��Y ��u ��'#el�c�l�g'&�c�S_&D\ � %$�"#m(k�&�lNg'[�\-(�{�[�`�S���&�c�S-[�`IY�|N[�\-(�{�[�`�S���&�c�S-[�`bS_l�c u � g$#�[ h ��l�l [�n p �"c��"#�a;S-`�S-`${>&D\z\ h \-[il�� p g'[�\-( �{�[�`'lLnt[�#�ak� p !�(�& h [�\z\-� h c�S-[�` [yn g�\_&�`'&�#�\zSV`$�9l��"{�ak�"`ic]l"Y1�s�@S p �"`�c�Sznt(���& h�u g'[y\V(�{�[�`�%$`�S � %$�]\-( !�(9c u �!'[�# p �"#�S-`${X\zS-`$� �SVc u c u �k\-�]��S h [�{�#e&�g u S h &D\z\-(�a;S-`�S-a %$a S p �"`�c�Sz�'�"#��tS�Y���Y-}N\zS-`$�X`i%$a;!'�"# �L&y` p c u ��lwS p �+[�`� u S hmu c u �;g'[�\-(�{�[�`X!'[�# p �"#elCc u ��\zS-`$��Yk|N[�\-(i{�[�`�S ��&yc�S-[�` h &�`X!'�k& hmu SV� r � p ��S-c u [�%$c�%'lwS-`${X&>l�g'&yc�S_&D\ p &�ce&l�c�#m% h c�%$#���Y ��&�l S h &�\�\-(�}Jc u � ��\zS-`$��l h [�%�\ p !'� lT[�#�c�� p SV`Xg'&�#]&D\z\V�]\�!'&�l�� p %$g'[�`Xc u �]S-#�S p �"`�c�Sz�'�"#�S-` �;� \V[�{��J�c�S-ak��}�c u �"` ��& h�u \zS-`$�+S-` lT[�#�c�� p l�� � %$�"` h ����[�%�\ p c�#e&�`'l�aMSVc�S-celb�"` p g'[�S-`�c h [�[�# p S-`'&�cm��l"}R\zS-`$��S p �"`ic�Sz�'�"#�}&�` p�h %$#�#m�"`ic;\-�]ntc &y` p #�S-{ u cbg'[�\-(�{�[�`�S p �"`�c�Sz�'�"#elbc�[�&D\z\nt[�\z\-[��SV`${�\�S-`$��l r S_&�&Xl�� � %$�"` h �X[�n��;�/�I�;l h &�`[�g/�"#e&�c�S-[�`'l"Y@Q�& hmu \zS-`$� h &y`XS-` p �"g'�"` p �"`�c�\-( p �"c��"#�a;S-`$�@c u �;S p �"`icTS��'�"#]l�[ync u �;\-�]noc;&�` p #�S-{ u c�g/[�\-(i{�[�`'l"Y��u � p #e&D�!'& h UbS_l�c u &�c�S-c�S_lC&�` �;�/�I��[�g'�"#e&yc�S-[�`+��S-c u &�\_&�#�{���`i%$a;!'�"#C[�n�l h &�`'l"YRj�&�c]& � g'&�#e&D\z\-�]\ r &�#�S_&�`�cel[�n7l�g'&�cTS4&�\ p &�ce&�l�c�#�% h cm%$#���l�l�% hmu &�lRc u ��!$% h U��"c|�x � � %'& p c�#��"��}$&�lR���]\z\P&�lRc u � ��� c�#��"��&�` pk� � � c�#��"��} h &�`#�� p % h ��c u �C`�%$a !/�"#�[�nI{�\-[�!'&D\7l h &�`@[�g'�"#]&�c�S-[�`'l��tS�Y���Y-}�&�l h &�`+& h #�[�l�lRc u �C�"`�c�S-#���g$#�[ h ��l�l�[�#�l��"c"�R!i(�S-`'l�c���& p#��]\-(�SV`${@%$g'[�` l��"{�ab�"`ic�� p l h &�`'l�]�$� h %$c�� p SV`�g'&�#e&D\z\-�]\�Y

�u �lT� h [�` p &y` p c u S-# p � %$�"#�S-��lNn�&D\z\'S-`�c�[�c u � h \_&�l�l S�� h &yc�S-[�`+[�nPlTg'&�c�S_&D\���[�S-`'l"YN��`@g'&�#�c�S h %�\_&�#�}����\V[�[�Uk&�ca>&�gMSV`�c��"#elT� h c�S-[�`>&�` p &�l�g'&�c�S_&D\'#]&�`${�� � %$�"#m(>�w��Y�{'Y-}D�'` p &�\�\/\zSV`$��l S-`@[�`$�a>&�g;c u &yc�&�#����S-c u S-` p S_l�ce&�` h ���[�n7&�`�(;\zS-`$�CSV`�&�l�� h [�` p a>&�g<�eYRQ�& h�u [�nIc u ��l�� � %$�"#�S-��l h [�%�\ p l SVaMS�\_&�#T\V(+!/�qlT[�\ r � p !�( u & r SV`${k&D\z\Ic u ��\zS-`$��lS-`�[�`$��a>&�g+!$#�[�& p$h &�l�cc u �]SV#C�"` p g'[ySV`�c h [i[�# p SV`'&yc���lcm[kc u �C\zS-`$��l�SV`X&kl�� h [�` p a>&�g SV`X&�` �;�/�I��g$#�[ h ��lml"Y� l�S_lc u � h &�l�����S-c u g/[�\-(i{�[�`�S���&�c�S-[�`I} p &�ce& � g'&�#]&D\z\V�]\�l�g'&�cTS4&�\ p &yce&kl�c�#m% h c�%$#���l h &�`+!/��%'l�� p c�[k#�� p % h ��c u �`�%$a !/�"#�[�n7l h &y`k[�g'�"#]&�c�S-[�`'l�� &�{i&�SV`;!�(;�"akg�\-[�(�S-`${>l��"{�ab�"`ic�� p l h &�`'l]�e}�c u %'lRl�g'�"� p S-`${kc u � h [�akg$%$ce&�cTSV[�`'l"Y

(���� =@?$3"?$ATBC?'0D?'*E*-F$*��-�I���/Fi3kB � �����<?��J3�0�F�F�GPHJ?$3�24?'* � �1F$0�2-F$8

� lc u �;!$% h U��"c�|�x � � %'& p c�#m�"� u &�l � � � p {���l"}Il�g'&yc�S_&D\ � %$�"#�( &D\-{�[�#�S-c u a>lno[�#C!'[�c u l�� � %$�"`�c�S_&D\�&�` p�p &yce& �g'&�#e&�\�\-�]\7!$% h U��"c|�x � � %'& p c�#��"��l�&�#��C#�� � %�S-#�� p c�[;ce&�U��SV`�c�[ h [�`'lwS p �"#e&yc�S-[�`+c u � h [�akg�\-�]��S-c�S-��l�S-`�c�#�[ p % h � p!�( c u �>�]��S_l�c��"` h �@[�n � � � p {���lb�tS�Y���Y4}7a;%�\-c�S-g�\-�@no��&yc�%$#��k#��"g$#m��l��"`ic]&�c�S-[�`<�eY � l��&�l�g$#m� r S-[�%'lw\-(�ak�"`�c�S-[�`$� p }

� � � p {���l&�#��C&�!�(kg$#�[ p % h c[�nNc u � p S_lE��[�S-`�c p � h [�akg/[ilwS-c�S-[�`@S-akg'[�l�� p !�(kc u �C!$% h U��"c|�x � � %'& p c�#��"����c u S_lS_l�&D\_l�[@c u � h &�lT� �SVc u � � � c�#m�"��l"}I&�`$[�c u �"# p S4lo� [�S-`�c p � h [�akg/[ilwS-c�S-[�`<�eY �u ���]��S4lTc��"` h �k[�n � � � p {���lC#�� � %�S-#���l& p$p S-c�S-[�`'&D\ h [�akg$%$c]&�c�S-[�`9� S Y ��Y-} p %$g�\zS h &�c�� p �]\-�"c�S-[�`<�� u �"`�ab�"#�{�S-`${ l SV!�\zS-`${+`$[ p ��l p %$#�S-`${>c u ���]�~� h %$cTSV[�`[�n�l�[�ak��[yn7c u � &�\V{�[�#�S-c u a>l"Y

� �

Page 30: O'3 0D. - cs.umd.edu

(���� ��� BC.1*��I,/.IOI2���?$3�24.IO

WS r �"`@&�!$% h U��"c�|�x � � %'& p c�#m�"��}�c u �g/[�\-(i{�[�`�S���&�c�S-[�`@g$#�[ h ��lmlR!'�"{ySV`'l�!�( h [�`'lTc�#�% h c�S-`${ &Lg'&�#�c�S_&D\'�SV`${�� p��� p {���#��"g$#m��l��"`ic]&�c�S-[�`B� ��&�%$a ����� � &�`+&�l�l�[ h S_&�c�S-[�`+!/�"c ���"�"`@c u �CS-` h S p �"`ic�\zSV`$�;l��"{�ak�"`�cel nt[�#�a;S-`${;c u �Ca;S-` �S-a>&D\ &�` p a>&��iS-a>&D\ &�`${y\V��l;&�c;��& hmu �"` p g'[ySV`�ck[�nC��& h�u lT�"{�ak�"`�c"�eY ��u S_l;#��"g$#���l��"`�ce&�cTSV[�`��"`'&�!�\-��l;%'l;c�[p �"c��"#�aMSV`$�@&D\z\�� p {���lCc u &�c h [�akg$#�S_l��k&kg/[�\-(i{�[�`I}7&�` p &D\z\�� p {���lCc u &�cCak�"�"c�&�c�& r �"#mc��]��S-`Xc�S-ak�;g$#�[�g/[�# �c�S-[�`'&D\$c�[c u ��`�%$a !/�"#R[�n'� p {���l"YJ��` h [�`'l�cm#�% h c�S-`${�c u ��g'&y#�c�S_&D\i��S-`${�� p�� � p {��#��"g$#���l��"`�ce&�cTSV[�`I}�c u ���"` p g/[�S-`icel[�n��& hmu \zS-`$�@SV`�&+`$[ p �+&�#��k!$#�[�& p$h &�l�c�c�[X&D\z\�[�c u �"#�\zS-`$��l�S-`�c u �b`$[ p �@c u #�[�%${ u &�l��"#TSV��l�[�n l h &y`'l"Y+��(��� ����������� ��� ab��&�`>c u � g$#�[ h ��l�l�[�n7cm#e&�`'l�a;S-c�cTSV`${k& h [�`'l�c]&�`ic r &D\-%$�Cnt#�[�a &�l SV`${y\V��g$#�[ h ��l�l�[�#�c�[;&D\z\P[�c u �"#g$#�[ h ��l�l�[�#]lRS-`+c u ��lm&�ak�C`$[ p � r S_&k&;l h &�`+[�g/�"#e&�c�S-[�`��tS�Y���Y-}�c u � r � h cm[�#$����� � ��������� � ��� � �eY � [ h &D\z\-(�}'��& hmu \�S-`$�g$#�[ h ��l�l�[�#�a>&DS-`�ce&DS-`'lRc u ��a;S-`�SVa@&D\P&�` p a>&D��SVa@&D\P&�`${y\V��l�no[�#�ak� p &�c���& h�u �"` p g/[�S-`ic�[�n<c u � h [�#m#���l�g'[�` p SV`${\zS-`$��&�lN���]\�\I&�lRc u ��S p �"`ic�S-c�S-��l�[�nIc u ��\zS-`$��l no[�#�ak� p !�(;c u ��l�� &�`${y\V��l Y'&` h � c u �!$#�[i& p$h &�l�celR&�#�� p [�`$��}���& hmu\zS-`$��g$#�[ h ��l�l�[�#\V[ h &D\z\-(�&�l�lwS-{�`'l�&�`@S-`�SVcTS4&�\7g'[�\-(�{�[�` S p �"`�c�Sz�'�"#�no[�#�c u ��!/[�# p �"#�S-`${kg/[�\-(i{�[�`+[�`+c u �C\-�]ntc &�` p#�S-{ u c lwS p �k�wak[ r S-`${;nt#�[�a l�[�%$# h ��c�[ p ��l�c�S-`'&�cTSV[�`��"` p g'[ySV`�c"�eY

min

maxmax

min

zw

x

y

v

��� � �2�3� � � � ���%" �01+@��*,�9+@<%���.*�� +-� 8&"� �/�" =���/�*�� 6&�%*%+@� #��%��'(H

�w` �JS-{�%$#m� �� }�c u �\-�]ntcg'[�\-(�{�[�`@S p �"`�c�Sz�'�"#�no[�#�\zS-`$� lT�"{�ak�"`�c��;S_ll��]\-� h c�� p no#m[�a c u �Ca;S-`�S-a;%$a S p �"`ic�S ��'�"#el [�n1c u �Cl�[�%$# h ��"` p g/[�S-`ic�a;S-`�S-a>&D\7&�`${�\-��� � }�� u �"#�� � S_lRc u �\�S-`$��S p �"`ic�Sz�'�"#&�` p � p �"`$[�cm��lNc u �#�S-{ u clwS p �@[�n � �e}Jc u � p ��l�c�S-`'&�c�S-[�`��"` p g'[�S-`�c;a>&D��SVa@&D\&�`${y\V����� �e}R&�` p c u �;\zSV`$�@S p �"`�c�Sz�'�"#;S-cel��]\zn���� /�eY+�$[�#c u �@#�S-{ u c�g'[y\V(�{�[�`sS p �"`icTS��'�"#D}�l��]\-� h c;c u �>aMSV`�S-a;%$a S p �"`�c�Sz�'�"#>&�ak[�`${+c u � l�[�%$# h �k�"` p g'[ySV`�cka>&��iS-a;%$a&�`${�\-�;� & /�e}�c u � p ��l�c�S-`'&�c�S-[�`��"` p g'[�S-`�c aMSV`�S-a>&�\ &�`${y\V�;����/�e}$&�` p c u �CS p �"`�c�S-c (@\zS-`$��S p �"`ic�Sz�'�"#����'�eYN�w`�JS-{�%$#�� �� } \�S-`$���@S_lC&�l�lwS-{�`$� p�� &�l�c u ��S-`�S-c�S_&D\R\-�]noc�g/[�\-(i{�[�`�S p �"`�c�Sz�'�"#�}I&�` p � &�lc u ��#�S-{ u c g/[�\-(i{�[�`S p �"`icTS��'�"#DY �JS-{�%$#�� �$� l u [��Cl�c u ��S-`�S-c�S_&D\�g/[�\-(i{�[�` &�l�l SV{�`$ak�"`ic�nt[�#c u � p �"g�S h cm� p �]�'&�akg�\-�;� u �"#���c u ��\-�]ntc&�` p #�S-{ u cg/[�\-(i{�[�`+S p �"`icTS��'�"#]l�&�#�� h [�`�ce&DS-`$� p S-` ����� &�` p �����1} #���l�g'� h cTS r �]\V(�Y

� c]&�#�c�S-`${�&�c�c u ��\-��&Dn<\-� r �]\�}~l SV!�\zS-`${k`$[ p ��l�&�#���c u �"`@ak�"#�{�� p cm[�{��"c u �"#NS-`�c�[�c u �]S-#�g'&�#��"`�c�`$[ p ��l��tS�Y���Y-}yS-`�JS-{�%$#�� �$� }�\-��&Dn�`$[ p ��l ���@&�#���ab�"#�{�� p c�[�{��"c u �"#�}�#���l�%�\-c�S-`${bSV` \-��&Dn�`$[ p � S-`X�JSV{�%$#�� ��� �eY � \z\7c u �C\zS-`$��lS-`Xc u ��ak�"#�{�� p lwS-!�\zSV`${ \-��&Dn�`$[ p ��lC&�#��;l�[�#�cm� p }'&�` p &y`i( p %$g�\zS h &yc��;\zS-`$��l�&�#���a@&�#�U�� p Y���`X�JSV{�%$#�� �$� }$c u �ak�"#�{ySV`${@[�n�lwS-!�\zS-`${�\V��&�n�`$[ p ��l ���@��Sz\z\�#���l�%�\-c�SV`s[�`$��g'&DS-#�[�n p %$g�\zS h &�c��;\zS-`$��l;�t\zS-`$� � �&�l�\zS-`$� � [ h"h %$#el

���

Page 31: O'3 0D. - cs.umd.edu

a b

cd

ef

g

h

a f h a b b b e g c e d f c d ga f a a a b b e b c c d d c d dL L R L L L L L R L L L L L L La f a a a b b b e c c d d c c cR R L R R R R L L R R R R R R L

LID

RID

nodes

lines

1 2 3 4 5 6 7 8 9 10

� � �������������� *�� +-� 8&"� �/�" =��/�*�8')'1� � *2���%*+5'(H

a b

cd

ef

g

h

a f h a b b b e g c e d f c d ga f a a a b b e b c c d d c d dL L R L L L L L R L L L L L L La f a a a b b b e c c d d c c cR R L R R R R L L R R R R R R L

LID

RID

nodes

lines

1 2 3 4 5 6 7

��� ������� ����� B �('���" +;8 " +5�%��# �3')+ ��/���*�6�/+"4���%�����.*%�?8&* 6 ��5� /�� +5/ 6��� 2"�� 0(8�+5�?6&�%" �(+-� /�* ' 6 � �".� 0(8�+ ���.*%' +)8&* 01�('4/!" ".��*,�('48%�3� '1<,/+%4* '�<�8%6��6 *�H

S-`X!'[�c u `$[ p ��l �+&�` p �'Y ��u � p %$g�\zS h &yc��kS-`'l�c]&�` h ��lC[�nR\zS-`$� � &�#�� u S-{ u \zS-{ u cm� p !i(+c u � %'lT� [yn�l u & p S-`${@S-`�JS-{�%$#�� ��� � u S h�u l u [�� l�c u ��#���lT%�\Vc]l[�nNak�"#�{�S-`${@`$[ p ��l ���bg$#�S-[�#c�[ p %$g�\�S h &�cm� p �]\-�"c�S-[�`IY

a f h a b b e g c e d f c d ga f a a a b e b c c d d c d dL L R L L L L R L L L L L L La f a a a b b e c c d d c c cR R L R R R L L R R R R R R R

a b

cd

ef

g LID

RID

nodes

lines

1 2 3 4 5 6 7

h

��� ������� � ��� A�/�" =���/�* 8�')'1� ��*����%*+5'�8 " +5�%�;+@<%� # ��')+ �3/��2*�6 /+"�" �8 " *,/�6&� �G�%�3�2��*,� 8&*�66 �2 �".� 0(8+ �?"��.*%�?6��%" �(+@� /�* H

�w`�[�# p �"# c�[b�"`'l�%$#���c u &�c��& hmu p %$g�\zS h &�c��;\zS-`$� u &�l h [�`'lwS_l�c��"`�c g/[�\-(i{�[�`+S p �"`�c�Sz�'�"#el�&�l���]\z\�&�l h [�#m#�� h c��S-`${�� p�� � p {���#��"g$#���l��"`�ce&�c�S-[�`'l }���& hmukp %$g�\�S h &�cm�\zS-`$� u &�lJSVc]lN�"` p g'[�S-`�cel�&�` p g/[�\-(i{�[�`;S p �"`ic�Sz�'�"#el�!$#�[�& p$h &�l�cc�[+c u �b[�c u �"# p %$g�\zS h &�c��b\zS-`$��l�S-`�c u �bak�"#�{�� p `$[ p ��Y>� n &�`i(X[�n�c u � p %$g�\zS h &�c���l�Ng/[�\-(i{�[�`9S p �"`�c�Sz�'�"#el;&�#��%$g p &yc�� p }Nc u ��S p �"`�c�Sz�'�"#;%$g p &�cm��l�a;%'l�c�&D\_l�[�c u �"`9!'�b!$#�[i& p$h &�lTc�&�ak[�`${+&D\z\�[�c u �"#C\�S-`$��lLS-`9c u �kab�"#�{�� p`$[ p ��l"Y���( � ��� �� � }<����ab��&�` &�lmlwS-{�`�S-`${�&;\-�]��S h [�{�#e&�g u S h &D\z\-(�l�a>&�\�\-�"#�g/[�\-(i{�[�`�S p �"`�c�Sz�'�"#�Y�� [�#S-`'l�c]&�` h ��}S-`��JS-{�%$#�� ��� c u �kak�"#�{ySV`${�[�nl SV!�\zS-`${�\-��&Dn`$[ p ��l � � � ��Sz\z\#m��l�%�\-c�S-`9c���[>g'&DS-#elL[�n p %$g�\zS h &�c��b\zS-`$��l@�tS�Y���Y-}

��

Page 32: O'3 0D. - cs.umd.edu

\zS-`$��l � &�` p � �&�lCl u [��` SV`9�JS-{�%$#�� ��� Y � S-c u c u � p %$g�\�S h &�cm�;\zSV`$� � SV`sc u ��ak�"#m{�� p `$[ p ��}/S-`�S-c�S_&D\z\-(9[�`$�S-`'l�ce&�` h � u &�lq\V�]ntck&�` p #�S-{ u c�g'[�\-(�{�[�`sS p �"`ic�Sz�'�"#el � 9&�` p � <}�&y` p c u �@l�� h [�` p SV`'lTce&�` h � u &�l�g/[�\-(i{�[�`S p �"`icTS��'�"#]l � &y` p � <Y ��u �;\-�]ntc�&�` p #�S-{ u c�g/[�\-(i{�[�`XS p �"`icTS��'�"#]l�[�n�c u �kl�� h [�` p S-`'l�ce&y` h �k[�n�\zS-`$� � &�#��%$g p &yc�� p nt#�[�a � c�[ � }'&�` p�� cm[ � #���l�g/� h c�S r �]\-(�Y

a f h a b b c e e g d f c d ga f a a a b c e c b d d c d dL L R L L L L L L R L L L L La f a a a b c b c e d d c c cR R L R R R R L R L R R R R R

a b

cd

ef

g LID

RID

nodes

lines

1 2 3 4

h

��� ������� ��4 �?B �('1�2" +4/+" +-<,��')�01/�*�6 ��/���* 6 /+"4�G�%�3���.*�� �� � /�� + /�6 �2 �".� 0(8�+5�?6&�%" �(+@� /�* ' 6 � �".� 0(8�+ ���.*%' +)8&* 01�('4/!" ".��*,�('48%�3� '1<,/+%4* '�<�8%6��6 *�H

� u �"`Xc u �>lT� h [�` p S-`'l�ce&�` h �b[�n�\zS-`$� � S_l�%$g p &�c�� p }Jc u �kc���[kS p �"`�c�Sz�'�"# %$g p &�c���l�&�#��;c u �"`9!$#�[�& p$h &�l�cc�[+&D\z\�[�c u �"#C\zS-`$��lCS-`9c u �;ak�"#m{�� p `$[ p ��Y;�$[�#���& h�u [�c u �"#�\zS-`$�kS-`9c u �;ak�"#m{�� p `$[ p ��}PS�n�c u �;c�#e&�`'lTa;S-c�c�� pg'[y\V(�{�[�` S p �"`ic�Sz�'�"#C%$g p &�cm��a>&�c h�u ��l��]S-c u �"#C[�nNS-cel h %$#�#��"`�c�\-�]ntc[�##�S-{ u cg/[�\-(i{�[�`+S p �"`icTS��'�"#]l��tS�Y���Y4}$c u � � �c�[ � � %$g p &�cm�ka>&�c hmu ��l�&y`i(�\zS-`$��� lL\V�]ntc;[�#�#TSV{ u c�g'[�\-(�{�[�`XS p �"`�c�Sz�'�"# u & r S-`${ r &D\-%$� � � �e}Ic u �"`9c u �b\�S-`$��� lg'[y\V(�{�[�`�S p �"`�c�Sz�'�"#RS_l h�u &y`${�� p c�[ � � S-`k[�# p �"#Nc�[C#��1J'� h cRc u ��!$#�[i& p$h &�l�cI%$g p &yc�� &�` p c u ��\V�]��S h [�{�#e&yg u S h &�\�\-(l�a>&�\�\-�"#CS p �"`�c�Sz�'�"#�Y � S-a;Sz\_&�#�\-(�}Ic u � p %$g�\zS h &�c���\zSV`$� � #���l�%�\-celSV`�c���[@& p$p S-c�S-[�`'&D\NS p �"`�c�Sz�'�"#�%$g p &�c���l � c u &�cS_l"} � � c�[ � � }/&�` p � � c�[ � � Y �qh c�%'&�\�\-(�}/\zS-`$� � � l � � r &�\V%$�;�&�l�g$#m� r S-[�%'lw\-(X%$g p &yc�� p c�[ � � p %$#�S-`${@\zS-`$� �%$g p &yc���!$#�[�& p$h &�l�cel Y

a b b c e e ga a a c c c aL L L L L L Ra a a a a a cR R R L L L L

LID

RID

lines a b b c e e ga a b c e c bL L L L L L Ra a b c b c eR R R R L R LbLbR

aLaR(a)

eLcR

cLaL

(b)

a b b c e e ga a a c e c aL L L L L L Ra a a c a c eR R R R L R L

(c)

��� ������� � ��� ' 8�* �! �8��9 �" �:/+"46��� �".� 0(8�+ � ".��*,� � �/�" =���/�*9� 6&�%*,+-� #��%�4�� 2628�+@��*,�96����5��*,��+@<%� �/�" =��/�*�� �8�+-� /�* ���%�>���.*%� ��3/ 01�(')'1" /�� +@<%�:'1� +@��8+-� /�*?8&" ')/�6��% �� 01+ �6 ��*!��� � �2�3� � 4 � ' $ * +@<%��� 2628�+@��*,� /!" 6��� �".� 0(8�+ �?"��.*%������': �/ " =�&/�*?� 6��%*%+@� # �%�3' � 8&*�6 ' 0�* +-<,���3�('1�2" + /+" �� 2628�+@��*,�?8&"�"6 �2 �".� 0(8+ �? �/ " =�&/�*�� 6&�%*,+-� #��%��'(H

� [�#N�]� &�abg�\V��} h [�`'lwS p �"#�c u �l SVcm%'&�c�S-[�` p �"g�S h c�� p S-`>�JS-{�%$#�� � =C� u S hmu S4l ce&�U��"`Lno#m[�a c u ��ab�"#�{�S-`${�`$[ p ��ll u [��` SV`9�JS-{�%$#�� ��� Y ��u � p %$g�\zS h &yc��;\zS-`$� � � l�#���l�%�\-c�SV`Xc���[kg'[y\V(�{�[�`X%$g p &�c���lL�tS�Y���Y-} � c�[ � &�` p �

�$�

Page 33: O'3 0D. - cs.umd.edu

c�[ � �R!'�]S-`${k!$#�[i& p$h &�l�c�cm[ c u � [�c u �"#R\zS-`$��l�S-`+c u ��l��"{�ak�"`�c�{�#�[�%$gIY ��u �C[�c u �"#�\zSV`$��l�� u [ilT��\-�]noc[�#�#�S-{ u cg'[y\V(�{�[�`�S p �"`�c�Sz�'�"#el�&�#���c u �"`;%$g p &�cm� p &�#���l u [��`k&�l h S-# h \-� p S-c��"a>lNS-`k�JS-{�%$#�� � =�&�� S Y ��Y-}�c u ��#�S-{ u c7g/[�\-(i{�[�`S p �"`icTS��'�"#;[�n�c u ���'#el�cC\zS-`$� � }I&�` p c u �;\-�]ntc�g'[�\-(�{�[�`XS p �"`�c�Sz�'�"#;[�n�\zS-`$� /�eY ��p$p S-c�S-[�`'&D\z\-(�} p %$g�\zS h &�c��b\�S-`$�� &D\_l�[@#���l�%�\-celS-` c���[k!$#�[�& p$h &�l�c�� p g/[�\-(i{�[�`X%$g p &�c���lL� � c�[ � &�` p � c�[ � S-`9�JSV{�%$#�� � =y!<�eY ��u ��'`'&D\�#���lT%�\Vc�[�n�c u � !$#m[i& p$h &�l�cTSV`${+[yn�g'[y\V(�{�[�`�S p �"`�c�Sz�'�"#el�`$� h ��l�lwS-ce&�c�� p !i(�c u � p %$g�\zS h &�c��b\�S-`$��lLS_l�l u [��`S-` �JS-{�%$#�� � = h Y

(a) (b)

ag

c

heb

f

daL

aLaLaRaRaR

cL

cL

bLbR

bL

bL

bR

dR

dR

dR

A B

C D

ag

c

heb

f

daL

aLaLaRaRaR

cL

cL

aLaR

aL

aL

aR

dR

dR

dR

��� ������� � � � ' 8�*��! 8&�9 �" � /+"C+ % /!" �8 "�*%/ 6&�(' � 8�*�6 ���%������*,� ' +@<%� 01/�*,+ �%*,+ ' /+" '1��$�".��*,�*%/ 6&�(' � 8&*�6��8 ��� *,/&+ '1<,/+%�* * ��8&* 6 ' $ * +@<%� �3�('1�2" + /+" +-<,�7�G�%�>�&�4/� ��%� 8�+-� /�*�H

�JS-`'&D\z\-(�}/� u �"`�ak�"#m{�S-`${knt[�%$# lwS-!�\zS-`${+`$[ p ��l�c�[�{��"c u �"#�}'&�`�(b\�S-`$�;� u [ilT���"` p g'[�S-`�cCn &D\z\_l�[�`+c u � l u &�#�� p`$[ p ��!'[�# p �"#C����Y {'Y-}�\zS-`$��l � &y` p � S-`��JS-{�%$#�� ��� &~�7a;%'l�c&D\_l�[ u & r ��S-cel��"` p g/[�S-`icel�&�` p g/[�\-(i{�[�`kS p �"`�c�Sz�'�"#el!$#�[i& p$h &�l�c &�ab[�`${;c u ��ak�"#m{�� p `$[ p ��l Y � [�`'lwS p �"#Cc u ���]� &yakg�\-��S-`X�JSV{�%$#�� ��� &�� u �"#���nt[�%$# lwS-!�\zS-`${+`$[ p ��l\_&�!'�]\-� p � � &y#��k!'�]S-`${Xak�"#�{�� p �tnt[�#�l�&�U��b[�n h \_&�#�S-c�(�}Nc u � h [�`�c��"`�celC[�n`$[ p ��l �X&�` p &�#��;`$[�c;l u [��`<�eY��u �"#��&�#m��`$[ p %$g�\zS h &�c���\zS-`$��l SV`;c u ��ak�"#m{�S-`${�`$[ p ��l"}�!$%$cN\zS-`$��l � &�` p ��u & r ��&�`;�"` p g/[�S-`ic�c u &�cJSV`�c��"#elT� h celc u � h [�akak[�`+`$[ p ��!/[�# p �"#�Y ��u ���"` p g'[�S-`�c h [�[�# p S-`'&�c���lC&�` p g'[�\-(�{�[�`+S p �"`�c�Sz�'�"#elC[�nRc u ��l���c ��[�\zS-`$��l�&�#��!$#�[i& p$h &�l�c�&�ak[�`${>c u �bak�"#�{�� p \zS-`$��l"}R&�` p &�`�(9&�g$g$#�[�g$#�S_&�cm� �SV`${�� p�� � p {��>%$g p &�c���l�&�#��;a>& p �@�tS�Y���Y-}Jc u �l�[�%$# h �R�"` p g'[�S-`�cR[�ni\zS-`$� � S_lJ%$g p &�cm� p c�[#m�1J'� h c7c u �NS-` h S p �"` h �[�n�\zS-`$� � �eYN�$[�#7&�\�\�\�S-`$��lN� u [�l�����S-`${�� p�� � p {��#��"g$#���lT�"`ice&yc�S-[�`'l�&�#���%$g p &�c�� p }Jc u �;g'[�\-(�{�[�`XS p �"`�c�Sz�'�"#el�&y#�� hmu � h U�� p no[�# g/[il�lwS-!�\-�>%$g p &�c���l"Y��JSV{�%$#�� ��� !l u [�� l�c u ��#���l�%�\-c�S-`${>g/[�\-(i{�[�`+S p �"`�c�Sz�'�"#el"Y

a f h a b c e g d f c d ga f a a a c c a d d c d dL L R L L L L R L L L L La f a a a a a c d d c c cR R L R R L L L R R R R L

a b

cd

ef

g LID

RID

nodes

lines

1 2 3 4

h

��� ��������� ���4A�/�" =��/�*?8�')'1� ��*��G�%*%+5' 8 " +5�%�C+@<%� ' �01/ * 6 ��/���*�6?/!"�" �8 " *%/ 6&�?���%������*,��H

���

Page 34: O'3 0D. - cs.umd.edu

�u � ab�"#�{�S-`${ &�` p %$g p &�c�S-`${ g$#�[ h ��l�l h [�`�c�S-`�%$��l+%$g�c u �9�"`�c�S-#��X!$% h U��"c�|�x � � %'& p c�#��"�X%$`�c�Sz\ &D\z\\zS-`$��l+&�#�� h [�`ic]&DS-`$� p S-` &XlwS-`${�\-�X`$[ p ��&y` p &D\z\ `$� h ��l�l�&�#m(�!$#�[�& p$h &�l�cel u & r �>!/�"�"` a>& p �X��&�l;l u [��`�S-`�JS-{�%$#���l �~� � ��� }���S-c u c u ���'`'&D\�&�l�lwS-{�`$� p g'[y\V(�{�[�` S p �"`ic�Sz�'�"#el h S-# h \-� p �eY

a a b c c d d e f f g g ha a a c c d d c f d a d aL L L L L L L L L L R L Ra a a a c d c a f d c c aR R R L R R R L R R L L L

a b

cd

ef

g LID

RID

nodes

lines

1

h

��� ������� � ����B��('1��" +4/!" # *�8&" �3/���* 67/+"4���%�����.*%� � &�5� /�� + / 6��� 2"�� 0(8�+5��6��%" �(+@� /�* ' 6��� 2"�� 0(8�+5��.*%')+ 8&*�01�('�/!"�"��.*%�(' 8 ��� '1<%/&%�*?'1< 8%6&�6 *1H

a b c d e f g ha a c a c a a aL L L R L R R Ra a a a a a c aR R L L L L L L

a b

cd

ef

g LID

RID

nodes

lines

1

h

aR cL

aL

��� � �2�3� � � � B �('1�2" + /+" +-<,�� �/ " =�&/�*2� �8�+@� / *:/� ��%� 8+-� /�*�H

�u �>!$% h U��"ck|�x � � %'& p c�#��"��� l;l�g'&�cTS4&�\l�[�#mc {�#���&�c�\-(�\zSVaMSVc]lkc u �+&�ak[�%$`ic�[�nS-`icm�"# � l��"{�ak�"`�c h [�aka;% �`�S h &�c�S-[�`9`$� h ��lml�&�#�(X&�l h [�akg'&�#m� p �SVc u &@`$[�` � l�g'&�c�S_&D\z\-(�l�[�#mc�� p�p &�c]&�l��"c�� u �"#��k&D\z\R\zS-`$��l���[�%�\ p�u & r �;c�[h [�aka;%$`�S h &�c���c u �]S-#�"` p g'[ySV`�cel�&�` p g/[�\-(i{�[�`+S p �"`�c�Sz�'�"#elcm[>&D\z\7[�c u �"#]l"Y

�w`�c u ����[�#]l�c h &�lT��}�� u �"#m� &D\z\ [�nCc u ��� \zS-`$��lT�"{�ak�"`�celLSV` c u ��|�x � � %'& p c�#��"�@S-`icm�"#el�� h ckc u �@�'#]l�cl�g�\zS-c &D��S_l�S-`9�]S-c u �"#�c u � �X[�# ��p S-ak�"`'lwS-[�`I}J`$[@\�S-`$��l�a>&D(+!'�b#��"ak[ r � p no#m[�a h [�`'lwS p �"#e&�c�S-[�` p %$#TSV`${�c u �`$[ p �kak�"#�{�S-`${�g$#�[ h ��lml"Y ��u %'l"}PSV`sc u �k��[�#el�c h &�l���}Jc u �kg/[�\-(i{�[�`�S ��&yc�S-[�`�g$#m[ h ��l�lL��Sz\z\�!'�@[�n h [�akg�\-�]�iS-c�(�;�/��\V[�{��J�eY

(���� ��� � ?'H � O/3"F~0�8"F$��3�24.IO

��`Xc u ��nt[�\z\-[��SV`${�&�\V{�[�#�S-c u a p ��l h #�S-g$c�S-[�`I}N&�l�l�%$ab��c u &�cC��� &�#m� l�ce&y#�c�S-`${>�SVc u c���[ p &�c]& � g'&�#e&D\z\-�]\�!$% h U��"c|�x � � %'& p c�#m�"��l��$[�`$��c��"#mak� p c u � �#��� � ��� � %'& p c�#��"��}/&�` p c u ��l�� h [�` p c��"#�ak� p c u � ��������� � %'& p c�#m�"��Y ��u �

� %'& p c�#��"��l;&�#��@[�n � � %'&D\ lwS��"�9� S Y ��Y-}Nc u �"(�#m�"g$#���l��"`�c c u ��l�&�ak� �� ���&�#���&~�eY �u � l�[�%$# h � � %'& p c�#��"�@��Sz\�\h [�`�ce&DS-`Xc u �;#��]nt�"#��"` h �kl��"c�[�nR\zS-`$��l�c�[bS-`ic��"#]l�� h c�&�{i&DS-`'l�c;�w��Y�{'Y-}$c u � !/[�# p �"#�[�n�c u � h S-c�(/�e}1&y` p c u � c]&�#�{��"c

���

Page 35: O'3 0D. - cs.umd.edu

� %'& p c�#��"� h [�`ice&�SV`'l c u ��\�S-`$��l�� u S hmu ��Sz\�\<!'� p �"c��"#�a;S-`$� p c�[CS-`�c��"#el�� h c�c u ��[�!$��� h celJS-`>c u ��l�[�%$# h � � %'& p c�#��"�����Y�{/Y-}�c u ��#�[i& p l�no[�%$` p S-`�c u � h [�%$`�c (/�eY

lines

nodes

lines

nodes

target quadtree

mapping quadtree

source quadtree

ab

c

d

ef

gi

d d e b e a f b i a c c g i g h

m o n q n u m p s p s

m

n

p

oq

r

nodes

h

s

t

u

r s u r r t

1 2 3 4 5 6 7 8 9 10111213141516

1 2 3 4 5 6 7 8 9 10111213

1

��� ������� 4 ���#�! �8��9 �" � /+" 8 ')/���� 01� 8�*�6�+ 8%�3���(+ 628�+)8�) �8%� 8&"." �%" $���0����(+ A E B � ��8,6&+@�3�(� ' �8%0�<%4� +@< 8 $���0����(+?0(8& 8%0�� + =!/+"�� * 8&* 6 8 � 8� � ���*,� � ��8,6&+@�3�(� �� � /�� +5/ +@<%� # ��')+�� 8& � 2��*�*%/ 6&�:'1� $26�� )�� '�� /�*�H

W�S r �"`�c u � p &�ce& � g'&�#]&D\z\V�]\�l�[�%$# h �+&�` p ce&�#m{��"c�!$% h U��"c>|�x � � %'& p cm#��"��l"}R���b�'#el�c;��l�ce&�!�\zS_l u & h [�#�#�� �l�g/[�` p �"` h �9!'�"c����"�"`�c u �9l�[�%$# h �9&�` p ce&y#�{��"c � %'& p cm#��"�X`$[ p ��l"Y ��u S_l+��Sz\z\�n & h S�\zS-ce&�cm�9c u ��\-��l�l��"`�S-`${ [�nh [�aka;%$`�S h &�c�S-[�`X!/�"c ���"�"`�c u ��c���[ � %'& p cm#��"��l� u �"`�g'�"#Tno[�#ma;S-`${>c u �;& h c�%'&D\JSV`�c��"#elT� h c�S-[�`IY � u Sz\-� ��lTce&�! �\zS_l u S-`${ c u � l�[�%$# h �&�` p ce&�#�{��"cN`$[ p � h [�#�#���lTg'[�` p �"` h ��}$&Cc u S-# p cm�"akg'[�#]&�#�(�l��"cR[�n � %'& p c�#��"�`$[ p ��l"}�cm�"#�ak� pc u � � ��� � �.��� � � ��� �� ��� }�S_lR�"abg�\V[�(�� p Y ��u � a@&�g$g�S-`${ � %'& p c�#m�"��S_l p S_l h &y# p � p no[y\�\-[���S-`${ h [�akg�\-�"c�S-[�`@[�nIc u �[�g/�"#e&�c�S-[�`IY

�u �+a>&�g$g�S-`${ � %'& p c�#��"� SV`�S-c�S_&D\z\-( h [�`'lwS_l�celb[�nq&9lwS-`${�\-� \4&y#�{��+`$[ p ��}�� � %'&D\�S-` g u ($lwS h &D\Ll S �"��c�[Xc u ��]�$c��"#�S-[�# p S-ak�"`'lwS-[�` [yn c u �+l�[�%$# h �+&�` p ce&�#m{��"c � %'& p c�#��"��l@�tS�Y���Y4} � �y�eY ��u �+lwS-`${�\-��a>&�g$g�S-`${9`$[ p �bS4l&�l�lT[ h S_&�c�� p �SVc u c u ���"`�c�S-#�� h [�\z\-� h c�S-[�`�[�n7!'[�c u l�[�%$# h ��&�` p ce&y#�{��"c � %'& p c�#m�"�C\V��&�n7`$[ p ��lq� &�l�&�`@�]� &�abg�\V��}h [�`'lwS p �"#+c u ��l SVcm%'&�c�S-[�` p �"g�S h c�� p SV`��JS-{�%$#�� �� �eY ��u ��a>&yg$g�SV`${ � %'& p c�#��"��`$[ p ��l ��[�n�� u S h�u c u �"#m�@S4l

���

Page 36: O'3 0D. - cs.umd.edu

����������������������������

�����������������������������������

lines

nodes

lines

nodes

target quadtree

mapping quadtree

source quadtree

d d e b e a f b i a c c g i g h

m o n q n u m p s p s

m

n

p

oq

r

nodes

s

t

u

r s u r r t

����������������������������

ab

c

d

ef

gi

h

1 2 3 4 5 6 7 8 9 10111213141516

1 2 3 4

1 2 3 4 5 6 7 8 9 10111213

��� ������� 4�����E�8& � 2��*,� � ��8,6&+@�3�(�4*%/ 6&�(' 8+C+@<%�:01/��9 �" �(+@� / * /+" +-<,� # �3' +C'1� $26 � )&� '1� / * 2<�8�' �%4� +@< 01/��9 �" �(+ �6 � 8& � ��.*��'C'1< 8%6&�6 H

S-`�S-c�S_&D\z\V(@[�`�\-(k[�`$���7&y#���c u �"`k#��"g/��&�c�� p \-(>l�%$! p S r S p � p %$`icTS�\<��& hmu a>&�g$g�S-`${�`$[ p ��S_l�&�l�l�[ h S4&yc�� p ��S-c u �]S-c u �"#&klwS-`${�\-�;l�[�%$# h ��`$[ p ��[�#C&klwS-`${�\-��ce&y#�{��"c�`$[ p ��Y ��u ��l�� lT%$! p S r S_lwS-[�`'l�&�#��Cg'�"#�nt[�#�ab� p %'lwS-`${ h [�\z\V� h cTSV[�`'l[�nl h &�`9&�` pXh \-[�`�S-`${�[�g'�"#e&�cTSV[�`'l�SV`�&�`9&�`'&D\-[�{�[�%'l�n�&�l u S-[�`Xc�[@c u &�cC�"akg�\-[�(�� p S-` h [�`'lTc�#�% h c�S-`${+c u �;!$% h U��"c|�x � � %'& p c�#��"��Y�Q�l�l��"`�c�S_&D\z\-(�}'c u ��a>&�g$g�S-`${@`$[ p ��lC&�#��;l�%$! p S r S p � p %$`icTS�\Rc u �"#��CS_l�&;[�`$� � c�[ � [�`$��}$[�`$� � c�[ �a>&�`�(�}N[�#�a@&�`i( � c�[ � [�`$�k#��]\_&�c�S-[�`'l u S-g���l�c]&�!�\zS4l u � p !'�"c����"�"`�c u �@l�[�%$# h �+&�` p ce&y#�{��"c�`$[ p ��l�c u #�[�%${ u c u �a>&�g$g�S-`${�`$[ p ��l"Y��$[�#R[�%$#R�]�'&�akg�\-� p &yce&�l��"c�l u [��`�S-`>�JS-{�%$#�� �i }�c u � l SV`${y\V��a>&�g$g�S-`${;`$[ p ��S_l�&�l�l�[ h S_&�c�� p��S-c u c u SV#mc��"�"` lT[�%$# h �k`$[ p ��l;&�` p lwSz�$c��"�"`�c]&�#�{��"cC`$[ p ��l Y �u %'lLc u �ka>&�g$g�S-`${X`$[ p �>a;%'l�c�!/� l�g�\zS-ck&�` pc u �>lT[�%$# h �>&�` p ce&y#�{��"c�`$[ p ��l�#���&�lmlwS-{�`$� p c�[+c u �@&�g$g$#�[�g$#�S_&�cm�ka>&�g$g�S-`${�`$[ p ��Y �u �k#���l�%�\-c�[ync u ���'#]l�ca>&�g$g�S-`${�`$[ p ��l�g�\zS-c�S_l�l u [��`;S-`>�JS-{�%$#�� �/� Y � [�`�c�S-`i%�S-`${��SVc u c u S_l�g$#�[ h ��lml"}�c u �Cl u & p � p a>&yg$g�SV`${�`$[ p ��l��} � }�&�` p �CS-`>�JS-{�%$#m� �'��u & r �l�&�c�S_lw�'� p c u �c��"#�aMSV`'&yc�S-[�` h [�` p S-c�S-[�`>&y` pkp [�`$[�c�`$�"� p c�[�!'� lTg�\�S-c no%$#�c u �"#�YxX&�g$g�S-`${>`$[ p � � a %'lTc!'�;l�%$! p S r S p � p no%$#�c u �"#q&�l�SVcS4lC&�l�lT[ h S_&�c�� p ��S-c u lT� r �"` l�[�%$# h ��`$[ p ��lC&�` p l�� r �"`ce&�#m{��"c�`$[ p ��l"Y ��u � #m��l�%�\-c[�n�l�g�\zS-c�c�S-`${@a>&�g$g�S-`${k`$[ p � S-`��JS-{�%$#�� �/� S_ll u [���`kS-` �JS-{�%$#m� �i� Y �u �C�'`'&D\a>&�g$g�S-`${;`$[ p �ql�g�\zS-c���[yn1a>&�g$g�S-`${k`$[ p � S-`+�JS-{�%$#�� �i� �I#���l�%�\-cel S-`@c u �ql SVcm%'&�c�S-[�` p �"g�S h cm� p SV`+�JS-{�%$#�� �i� }� u �"#�����& h�u a>&�g$g�S-`${>`$[ p � h [�#�#m��l�g'[�` p l�c�[;�]S-c u �"#�&klwS-`${�\-�kl�[�%$# h ��[�#C&klwS-`${�\-��ce&y#�{��"c�`$[ p ��Y

&` h ��c u �+a>&�g$g�S-`${ � %'& p c�#��"��l�%$! p S r S_lwS-[�`'l�&y#�� h [�akg�\-�"c�� p � l��"���JS-{�%$#�� �i� � u �"#��+��& h�u a>&yg$g�SV`${

� =

Page 37: O'3 0D. - cs.umd.edu

lines

nodes

lines

nodes

target quadtree

mapping quadtree

source quadtree

ab

c

d

ef

gi

d d e b e a f b i a c c g i g h

m o n q n u m p s p s

m

n

p

oq

r

nodes

h

s

t

u

r s u r r t

1 2 3 4 5 6 7 8 9 10111213141516

1 2 3 4 5 6 7

1 2 3 4 5 6 7 8 9 10111213

��� �������64 ���!E�8& � 2��*,��� � 8%6&+@���(�9*%/ 6&�('?8�+:+-<,� 01/��9 �" �(+-� /�*�/+"4+@<%� ')�01/�*�6 '�� $26 � )�� '1� /�* �< 8�')��H

`$[ p � h [�#�#m��l�g'[�` p lc�[;�]SVc u �"#q&kl SV`${y\V�;l�[�%$# h ��[�#ce&�#�{��"c�`$[ p ���e}$c u �"#����]�iS_l�c]l&;[�`$� � c�[ � [�`$��}$a>&�`�( � c�[ � [�`$��}[�#k[�`$� � c�[ � a>&�`�(�&�l�l�[ h S_&�c�S-[�` !/�"c����"�"`�l�[�%$# h ��&y` p ce&�#m{��"c;`$[ p ��lbc u #�[�%${ u c u �+a>&yg$g�SV`${�`$[ p ��l"Y ��u �l�[�%$# h � &�` p ce&�#m{��"c � %'& p c�#��"��`$[ p ��l�&�#m��c u �"`Xak�"#�{�� p &�l�`$� h ��l�l�&�#m(+S-`X[�# p �"#Cc�[k��l�ce&y!�\�S_l u &k[�`$� � cm[ � [�`$�#��]\_&�c�S-[�`'l u SVg�!'�"c����"�"`+c u ��`$[ p ��l�S-`+c u ��c���[LS-`$g$%$c a>&yg'l"YRx��"#m{�S-`${;no[�%$#l SV!�\zS-`${+`$[ p ��l�S_l& h"h [�akg�\zS_l u � p!�(M& p � %'l�cTSV`${�c u ��x�[�#�c�[�` h [ p ��^�[�n1c u ��'#elTcR`$[ p ����c�[ h [�#m#���l�g'[�` p c�[�c u � x�[�#�c�[�` h [ p � [yn1c u �]S-#�g'&�#��"`�c"�e}&�` p;p �]\-�"c�S-`${�c u ��c u #m�"��[�c u �"#RlwS-!�\zS-`${il r S_&�&Cl�� � %$�"` h ��[�n1l h &�`'lN&�` p &Cg'�"#�a;%$ce&yc�S-[�`�[�g/�"#e&�c�S-[�`IY � S-a;Sz\_&�#�\-(�}c u � h [�#�#���l�g/[�` p S-`${�\zS-`$��l�S-`�c u �;nt[�%$# l��"{�ak�"`ic�{�#�[�%$g'l�&y#��kak�"#�{�� p !i(X#���lT�"c�c�S-`${�c u �@l��"{�ak�"`�c J1&�{�l�c�[�"�"#�[�nt[�#�c u �b�'#el�cL\zSV`$��l SV`�c u � l�� h [�` p }Rc u S-# p }�&�` p nt[�%$#�c u lT�"{�ak�"`�c�{�#�[�%$g'l"YB&` h �+c u �+l��"{�ak�"`�c J1&y{il&�#���g$#m[�g'�"#�\-(+#���lT�"c�}�c u �C\zSV`$��l�S-`�c u �Cno[�%$# lwS-!�\zSV`${+`$[ p ��lC&�#��Cc u �"` l�[�#�c�� p }$&�` p c u �"`X&�`i( p %$g�\zS h &�c���\zS-`$��l&�#�� p �]\-�"c�� p Y��$[�#�S-`'l�c]&�` h ��}$SznRc u �"#���&�#m�Cno[�%$#Cl�[�%$# h ��`$[ p ��l&�l�lT[ h S_&�c�� p ��S-c u &klwS-`${�\-��ce&�#�{��"c�`$[ p �;��#��]nt�"#c�[kc u ���'#el�c�a>&�g$g�S-`${>`$[ p ��S-` �JS-{�%$#�� �i� �e}$c u �"`�c u �Cnt[�%$#�l�[�%$# h ��`$[ p ��l���� u S hmu l u &�#m��c u � l�&yak��g'&�#��"`�c`$[ p �CSV`�c u � � %'& p c�#��"� p � h [�abg'[ilwS-c�S-[�`<�&�#��Cak�"#�{�� p c�[�{��"c u �"#C���SVc u�p %$g�\�S h &�cm��\zS-`$�MlT�"{�ak�"`�cel�#��"ak[ r � p �eY

����� ¢]£t¨t¢e«b± ¢"ªD©��-¢]£��C¢]£tª�©�£N� ��¥��¥m§�§ � «� ��V£t¢�� ¨E¡<¢ ª ����©�«D�E� ¢e«D���-¢e£��"�� ]��©�£�¨t¢�¢e«D©¡I� � ±��;§�£t©��t©�£��e©���¨t��©��t§�¥m¨E��¥�¯¯ ¢"±�¥�¯�� ¨E­k¢��1¨t�D©���¦ ¯ ¨E��¶_ª"����©�«��E� ¢]«�¥�¯7�t§�¥�±�©�� «;¨t�D©�¢]«�©w¶_ª ����© «D�E� ¢e«�¥m¯7�t§�¥m±�©]½�I��©�£t©��t¦"¯ ¨�¢��I�t¦�±w�k¥��¥m§�§"� «� �� ��¥T¯ �t¢�¨t©�£���©�ª¥��t§�¥�±�©w¶��D¯�¯�� «� @± ¦D£��e©�¥m��¨t�D©±�¦�£��]©�ª�©�¨t©�£���� «�©�ª>¬"­;¨t�D© � ¢]£t¨t¢e«b± ¢"ªD© ¡P��¯�¯�§�¥��t��¨t��£t¢]¦� ]�@©T¥m±��b§�¢m� «"¨�� «k¨t�D©���¥� e©��-�t©�©� � £t©�«��eº! y°D¥���©�·]¼e¥�"#�-¢]£$�-¦�£t¨t�D© £Jª�©�¨�¥���¯ �w½

���

Page 38: O'3 0D. - cs.umd.edu

������������������

��������������������

�������������������� � � ����������

� ������� �

lines

nodes

lines

nodes

target quadtree

mapping quadtree

source quadtree

ab

c

d

ef

gi

d d e b e a f b i a c c g i g h

m o n q n u m p s p s

m

n

p

oq

r

nodes

h

s

t

u

r s u r r t

���������

1 2 3 4 5 6 7 8 9 10111213

��������������������������

1 2 3 4 5 6 7 8 9 10

1 2 3 4 5 6 7 8 9 10111213141516

��� ��������4 ��� E�8& 2 ��.*%� ����8%6�+-���(� *,/�6&�('G8�+�+@<%� 01/��! &" �(+@� /�*!/!":+@<%� '1� $26 � )&� '1� /�* 2<�8�' �%4<�� 0�< 0����8�+5�(' / *,� + / /�*%� �G� 8&*=� + / /�*%� ��/��?/ *,� + / )� 8 *,= � 8& 2 &�.*%�,' $��(+ % �(�%* +@<%�')/���� 01�?8&* 6 + 8%�3���(+ � ��8,6&+@�3�(�('(H

��u S_l�#���l�%�\-cel S-`�&�[�`$� � cm[ � [�`$� h [�#�#���l�g/[�` p �"` h ��!'�"c����"�"`@c u ��l���l�[�%$# h ��&�` p ce&�#�{��"cR`$[ p ��lC� lT�"� �JS-{�%$#�� ��� �eY� c�c u � h [�akg�\-�"c�S-[�`+[yn1c u ��l�[�%$# h �C&�` p c]&�#�{��"cR`$[ p � ab�"#�{�S-`${'}�c u �a>&�g$g�S-`${ � %'& p c�#��"�Ca>&D(�!'� p S_l h &�# p � p Y��u �ka@&�g$g�S-`${ � %'& p c�#m�"� h &�`9!/� h [�` h �"g$c�%'&D\zS��"� p &�lLc u �;\-[�����lTc h [�akak[�` p �"`$[�a;S-`'&�c�[�#b��`$[ p � � ��S_l���� [�nc u ��l�[�%$# h � &�` p c]&�#�{��"c � %'& p c�#��"��l"Y

�wc�S_lLS-akg'[�#mce&�`�c�c�[�`$[�cm�kc u &�c�c u �ka>&�g$g�S-`${ � %'& p c�#��"�;S_l�`$[�c;&+%$`�Szno[�#�a {�#TS p Y � `'&�S r � &D\-{�[�#�S-c u aa;S-{ u c��"akg�\-[�(�&@%$`�Sznt[�#�a�{�#�S p S-`9[�# p �"#�cm[+��l�ce&�!�\zS_l u & [�`$� � c�[ � [�`$�;a>&yg$g�SV`${�!'�"c����"�"`9c u �kl�[�%$# h �>&�` pce&�#m{��"c � %'& p c�#m�"� `$[ p ��l"Y ��u �;g$#�[�!�\-�"a �SVc u c u S4l�&yg$g$#�[i& hmu S4lLc u &�cCc u �klwS��"�k[�n�c u �;{�#TS psh �]\�\_l p �"g'�"` p l[�`�c u �>lwS��"�+[�nc u �b\_&�#�{���lTc�g'[�l�lwS-!�\-� � %'& p c�#��"�k`$[ p �X�tS�Y���Y-}Nc u �b[�`$�>� u [il�� h [�#�#���l�g/[�` p S-`${X!�\V[ h U9S_l�c u �\_&�#�{���lTc"�eY ��u %'l"}NSzn [�`$�k[yn c u �kc���[�a>&yg'l h [�`�ce&DS-`$� p & l SV{�`�S�� h &y`ick&�ak[�%$`ic�[�n�"akg$c�(�l�g'& h ��}Nc u �"`�c u �#���l�%�\-c�S-`${ \4&y#�{�� � %'& p c�#��"�k`$[ p ��l���[�%�\ pXp S h ce&�c��>&b%$`�Szno[�#�a {�#TS psh [�akg'[�l�� p [�n�\_&�#�{�� h �]\z\_l"Y ��u %'l }<c u �"#��a;S-{ u cR!'�Ca>&�`�( l�[�%$# h � � %'& p cm#��"�`$[ p ��l�&�l�lT[ h S_&�c�� p ��S-c u &�lwS-a;Sz\_&�#�\-(;\_&�#�{�� h [�\z\-� h c�S-[�`>[ynPc]&�#�{��"c � %'& p c�#��"�`$[ p ��lCg$#�S-[�# cm[>`$[ p ��ak�"#m{�S-`${'Y�w` [�# p �"# cm[ & r [�S p c u S_l!/� u & r S-[�#�}<����n�& r [�#�%'lwS-`${�&ba>&�g$g�S-`${ � %'& p c�#��"�� u S hmu & p &�g$c]l�c�[;c u � p � h [�akg'[il SVcTSV[�`'l[�nRc u ��l�[�%$# h ��&�` p c]&�#�{��"c � %'& p c�#��"��l"Y

�u �C�'`'&D\7a>&�g$g�S-`${@#���l�%�\-c�S-`${@nt#�[�a c u ��%'lT��[�n &M%$`�S�nt[�#�a {�#�S p #e&�c u �"#c u &�`�& � %'& p c�#��"�CS_lCl u [��`@S-`

���

Page 39: O'3 0D. - cs.umd.edu

lines

nodes

lines

nodes

target quadtree

mapping quadtree

source quadtree

ab

c

d

ef

gi

b d e a f b i a c c g i g h

m o n q u m p s s r s

m

n

p

oq

r

nodes

h

s

t

u

u r r t

1 2 3 4 5 6 7 8 9 10

1 2 3 4 5 6 7 8 9 10

1 2 3 4 5 6 7 8 9 10

��� ��������4 4 ���4��8%6�+-���(��*%/ 6&�(' <�� ��<�".� ��<,+-�.*%�?+-<,� /�*,� + / /�*%� ')/��2� 01�?+ /!+)8%���&�(+:*%/�6��?01/�� ���('1 �/�*�6&�%* 01� 8 " + �%� *%/ 6&�?���%��� �.*� H

�JS-{�%$#�� � =$Y ��u �klwS��"�k[�n�c u �;{�#�S p9h �]\z\_lLS4l p �"g/�"` p �"`ic;%$g/[�`9c u ��\_&�#�{���lTc � lwS��"� p `$[ p ��lCS-`9c u �kl�[�%$# h �>&�` pce&�#m{��"c � %'& p c�#m�"��l��tS�Y���Y-}<`$[ p ��l ��&y` p � S-`9c u �>l�[�%$# h � � %'& p cm#��"��}I&�` p `$[ p � ��S-`9c u �kc]&�#�{��"c � %'& p c�#��"���eY*�[�c��Cc u &�c�����&�#���\-�]noc���S-c u &�a>&�`�( � c�[ � a>&�`�(;a>&�g$g�S-`${�S-`+{�#�S p+h �]\z\ g$#�S-[�#�c�[�c u ��`$[ p �Cak�"#�{ySV`${bg u &�l��

�u ��& h c�%'&D\7g$#m[ h ��l�l�[�n p �"c��"#�a;S-`�S-`${+c u �L\�S-`$�kl��"{�ab�"`ic�S-`�c��"#el�� h cTSV[�`'l!/�"{�S-`'lC��S-c u ��& hmu lT[�%$# h ��`$[ p �!$#�[i& p$h &�l�c�S-`${�c u � �"` p g/[�S-`icel�[�n7&D\z\7&�l�lT[ h S_&�c�� p \zS-`$��l��"{�ak�"`�cel�� S Y ��Y-}i&D\z\<c u �\zS-`$��l��"{�ab�"`icel c u &�c�&�#m�nt[�%$` pS-`+c u � � %'& p cm#��"� `$[ p ���Rc�[;c u ��l��"c�[�n<\�S-`$�;l��"{�ak�"`�celNS-`+c u ��&�l�lT[ h S_&�c�� p ce&�#m{��"c � %'& p c�#��"�C`$[ p ��Y��JS-{�%$#�� �i�u S-{ u \zS-{ u c]l@c u � l�[�%$# h ��c�[sce&�#�{��"cM\�S-`$� h [�aka;%$`�S h &�c�S-[�` nt[�#kc u ���]� &yakg�\-� p &yce&�l��"c�Y ��`�c u �+�'{�%$#���}�c u �l u & p � p `$[ p ��l�&�` p \zS-`$��l�#m�"g$#���l��"`�cCSV`'& h c�S r �;g$#�[ h ��lml�[�#elno[�# � u S hmu `$[ & h cTSV[�`�S_l�`$� h ��l�l�&�#m( &�l�c u �"#��;&�#���]S-c u �"#�`$[+l�[�%$# h ��\zS-`$��l�[�#Cce&�#�{��"c�\zS-`$��l�&�l�lT[ h S_&�c�� p ��S-c u c u �;`$[ p ��l"Y ��u S_l�S4l�& h"h [�akg�\zS_l u � p !i(+c u ���'#]l�c\zS-`$�g$#�[ h ��l�l�[�#�&�lml�[ h S_&�cm� p �SVc u ��& h�u & h c�S r �l�[�%$# h ��`$[ p �C��� u �"#m�&y` � �� ��,-�� \zS-`$�[�#N`$[ p �S4l p �]�'`$� p &�lN[�`$�c u &�cNS_l�g'&�#�cTS h S-g'&�cTSV`${�S-`@c u � h %$#�#��"`�c�[�g'�"#e&�cTSV[�`<�7g'&�l�l SV`${�S-cel �"` p g'[�S-`�cel�c�[�c u ��'#el�cN\zS-`$��g$#�[ h ��lml�[�#RS-`@c u �h [�#�#m��l�g'[�` p S-`${;ce&�#m{��"c�`$[ p ��YR��`+�JS-{�%$#�� �i� }�c u ���'#el�c \zSV`$��g$#m[ h ��l�lT[�#el�&�#�� l u [���`k��S-c u &�#�#�[�� lN�"a>&y`'&�c�S-`${nt#�[�a c u �"a p S-#�� h c�� p &�c�c u � h [�#�#���lTg'[�` p S-`${ lT[�%$# h �k`$[ p ��l"Y ��u �>l�[�%$# h ��\zS-`$�@�"` p g'[�S-`�c h [�[�# p S-`'&�cm��l�&�#��c u �"`;l u &�#�� p &�ak[�`${&D\z\�\�S-`$��g$#�[ h ��l�l�[�#]l/S-` c u ��&�l�l�[ h S_&�c�� p c]&�#�{��"c<`$[ p � r S_&&Cl�� � %$�"` h ��[�n1l h &�`�[�g'�"#e&�cTSV[�`'l"Y

Q�& hmu & h c�S r ��ce&�#�{��"c�\zSV`$�@g$#�[ h ��l�l�[�#Cc u �"`XlwS-a %�\-ce&y`$�"[�%'lw\-( p �"c��"#�a;S-`$��l�� u �"c u �"# [�# `$[�cCc u ��\zS-`$�kc u &�c� �

Page 40: O'3 0D. - cs.umd.edu

�������������������������������������������������������������������������������������������

����������������������������

��������������������������������������������������������������������������������������������������������

�����������������������������������

�������������������������������������������������������������������������������������������

���� �

�� �������� � � ������

�������� ����������������������������������

lines

nodes

lines

nodes

target quadtree

mapping uniform grid

source quadtree

d d e b e a f b i a c c g i g h

m o n q n u m p s p s

m

n

p

oq

r

cells

s

t

u

r s u r r t

����������������������������

ab

c

d

ef

gi

h

1 2 3 4 5 6 7 8 9 10111213141516

1 2 3 4

1 2 3 4 5 6 7 8 9 10111213

��� ��������4 ��� D " + �%�5*�8�+@� )�� ')/���� 01� + /:+)8%���&�(+ � � 8%6&+@���(� � 8& � ���*,� %�<,�%* �%�! �" /�=���*��8���*2� " /��5���� � 69� 8+-<,�%� +-< 8&*G8 � � 8%6&+@�3�(��H

S-c�#��"g$#���l��"`�cel�S-`�c��"#el�� h cel�c u �C!$#�[i& p$h &�l�c�� p l�[�%$# h �C\zS-`$� lT�"{�ak�"`�c�YN�tn7c u �Cce&�#m{��"cR\zS-`$��S-`�c��"#el�� h celc u � !$#m[i& p��h &�l�cm� p lT[�%$# h ��\zS-`$��}�c u �"`;c u �ce&�#m{��"cI\zS-`$�C#�� h [�# p lNc u �S p �"`�c�Sz�'�"#�[yn1c u ��S-`�c��"#el�� h cTSV`${L\zSV`$��Y � [�`�c�S-`�%�SV`${�c u S_lg$#�[ h ��l�l"}�c u � h [�\z\-� h c�S-[�`@[�nPl�� h [�` p \zSV`$��g$#m[ h ��l�lT[�#elR&�l�lT[ h S_&�c�� p ��S-c u ��& hmu & h c�S r � l�[�%$# h �`$[ p �g'&�l�l���lNc u �]SV#h [�[�# p S-`'&�c���l�c�[�c u ��'#]l�c�g$#�[ h ��lml�[�#RS-`+��& hmu & h c�S r ��&�l�l�[ h S_&�c�� p ce&�#�{��"cR`$[ p ��Y � {i&DS-`I}�c u ��\�S-`$� h [i[�# p SV`'&yc���l&�#���c u �"` h [�aka;%$`�S h &�c�� p &�ak[�`${k&D\z\N\zSV`$�;g$#�[ h ��l�l�[�#el�S-`�c u ��c]&�#�{��"c�`$[ p � r S4&@&kl�� � %$�"` h �;[�n�l h &y`�[�g/�"#e& �c�S-[�`'l"}<&�` p ��& h�u ce&�#�{��"c�\zSV`$�;g$#�[ h ��l�l�[�# p �"c��"#ma;S-`$��l�SV`Xg'&�#]&D\z\V�]\R� u �"c u �"#�[�#`$[�c�S-cCS-`icm�"#el�� h cel�c u � lT[�%$# h �\zS-`$��Y�&` h ��&D\z\& h c�S r � lT[�%$# h �b\�S-`$��g$#�[ h ��lml�[�#el u & r �kc�#]&�`'l�a;S-c�c�� p c u �]S-# h [i[�# p S-`'&�c���l�c�[Xc u �+&�l�l�[ h S_&�c�� pce&�#m{��"c\zS-`$�+g$#�[ h ��l�l�[�#]l"}Ic u ��S-`�c��"#el�� h c�S-[�`�[�g/�"#e&�c�S-[�`XS_l h [�akg�\-�"c��>&�` p &D\z\�ce&�#m{��"c\zS-`$��l�S-`�c��"#el�� h c�S-`${X&�`i([�nRc u � lT[�%$# h ��\zS-`$��l h [�`�ce&DS-` & \�S_l�c�[yn�c u �LS p �"`ic�Sz�'�"#elC[yn�c u �LS-`ic��"#]l�� h c�S-`${�l�[�%$# h �L\zSV`$��l Y �JS-{�%$#�� �$� l u [�� lc u �k#m��l�%�\-c�[�nc u �>lT� � %$�"` h �@[�nlT[�%$# h �;\zS-`$�+!$#�[i& p$h &�l�cel"Y;�w`ic��"#]l�� h c�S-`${ l�[�%$# h �;\zS-`$�@S p �"`�c�Sz�'�"#el;&�#��M\�S_l�cm� p!'�"`$��&yc u c u ��&yg$g$#�[�g$#�S_&�c���c]&�#�{��"c�\zS-`$��Y

W�S r �"`>&�` � ��S-a>&�{���} �b\zS-`$��l��"{�ak�"`�cel"}�&�` p &�`>&�l�lT[ h S_&�c�� p � %'& p cm#��"� �SVc u &�!$% h U��"c h &�g'& h S-c�( �&�` pu �]S-{ u c�\-[�{��}�c u � p &�ce& � g'&y#e&D\z\-�]\1!$% h U��"c|�x � � %'& p c�#��"�Ca>&�gMSV`�c��"#elT� h c�S-[�`+[�g'�"#]&�c�S-[�`kce&yU���l#�M���J�7c�S-ak��S-`c u ����[�#el�c h &�lT��Y ��u S_l p �"{��"`$�"#e&yc�� h &�lT� ��[�%�\ p &�#�S_l���Szn�c u ���'`'&D\�a@&�g$g�S-`${ � %'& p cm#��"� h [�`�ce&DS-`$� p &@lwS-`${�\-�`$[ p ��Y �w`Xc u � & r �"#e&y{�� h &�l���� u �"#��;c u ���]�$g'� h cm� p c�#��"� u �]SV{ u cCS_l �;�t\-[�{(�I�]}$Szn����;&�l�l�%$ak��c u &�cCc u �"#��;&�#��

���

Page 41: O'3 0D. - cs.umd.edu

lines

nodes

lines

nodes

target quadtree

source quadtree

ab

c

d

ef

gi

b d e a f b i a c c g i g h

m o n q u m p s s r s

m

n

p

oq

r

h

s

t

u

u r r t

1 2 3 4 5 6 7 8 9 10

1 2 3 4 5 6 7 8 9 10

��� ��������4 ���!��/ �2� 01� +5/ +)8%���&�(+ � � 8%6&+@���(� ".�.*%�9�%* 6 �/��.*%+?01/��9�?��*�� 0(8�+-� /�*!0�<�8&*2*%�%" ' " /��6&�(+5�%�5�9�.*&�.*%����*,+ �%��')�01+@� /�*�H ��<�8%6��6 *%/ 6&�(' 8�*�6 ".��*,�(' 8%�3� *,/�+7+@<%���3�0��. �� �%*%+ /+" 8�*%=01/��9�?��*�� 0(8�+-� /�*%'(H

&�c�ak[il�c � l�[�%$# h ��`$[ p ��l�c u &yc h [�#�#m��l�g'[�` p � p cm[M&�lwS-`${�\-��ce&y#�{��"c�`$[ p ��}�c u �"`@c u � h [�akg�\-�]��SVc�(k[yn7c u �Ca>&�gS-`icm�"#el�� h c�S-[�`�[�g'�"#e&yc�S-[�`kS_l �;�t\-[�{(� � � �D�eY ��u S_l�S_l[�!$ce&DS-`$� p !i(@[�!'l��"# r S-`${kc u &yc���lTce&�!�\zS_l u S-`${>c u ��lT[�%$# h �c�[�ce&�#�{��"c�`$[ p �Ca>&�g$g�S-`${;#�� � %�S-#���l �;� \V[�{��J�R[�g'�"#e&yc�S-[�`'l��tS�Y���Y4}~&q�$�~� p `�%$a;!'�"#�[�n7l h &�`'l�&�` p #���l u %/0>��l�&�c��& hmu \-� r �]\R[�nRc u � � %'& p c�#��"���]}'&�` p c u &�c c u ��& h c�%'&D\IS-`�c��"#el�� h cTSV[�` p �"cm�"#�a;S-`'&�c�S-[�`Xg u &�l���[�nRc u � &D\-{�[�#�S-c u a#�� � %�S-#���l��M��� �D��l h &�`'l"Y

(���� ��� GIHI?$3�24?'* �b?<O1,/F ���<F$0 �

��u � p &�ce& � g'&�#e&D\z\-�]\�!$% h U��"c�|�x � � %'& p c�#��"�kl�g'&�cTS4&�\�#e&y`${�� � %$�"#�(�&D\-{�[�#TSVc u a g$#�[ h �"� p l�S-`9&bn�&�l u S-[�` l SVa �Sz\_&�#�c�[@c u ��SV`�c��"#elT� h c�S-[�`9&D\-{�[�#�S-c u a � u �"#m� c u � � %'& p c�#��"� p � h [�akg/[ilwS-c�S-[�`XS_lC�"akg�\-[�(�� p c�[@a>&D��S-a;S��"�kc u �`�%$a !/�"#[�nRg'&�#e&D\z\-�]\R[�g'�"#e&yc�S-[�`'l"YR�w`+c u ��nt[�\z\-[��SV`${ p ��l h #�S-g$c�S-[�`I}I&�{i&�SV`�&�l�l�%$ak��c u &yc�c u �"#���&�#���c���[�SV`$g$%$cp &�ce& � g'&�#e&D\z\-�]\I!$% h U��"c|�x � � %'& p cm#��"��l�[�nIc u ��l�&�ak��lwS��"��Y6�9�C��Sz\z\7c��"#�a c u � � %'& p c�#��"�Cc u &�c h [�`�ce&DS-`'l�c u �\zS-`$�>l��"{�ak�"`�cel�c�[k!/� �]�$g'&�` p � p c u �kl�[�%$# h � � %'& p c�#��"�b� &D\_l�[@#��]no�"#m#�� p c�[+&�l�c u � ��� � ��� ��� ��� ���� �]}'&�` p c u �

� %'& p c�#��"� h [�`ice&�SV`�S-`${Xc u �;\zS-`$�+l��"{�ak�"`�celCnt#�[�a � u S hmu c�[+c���l�cLno[�#CS-`�c��"#el�� h cTSV[�`���S-c u c u �k�]�$g'&�`'lwS-[�`�l��"cc u ��ce&y#�{��"c � %'& p c�#��"��Y

�u �&�\V{�[�#�S-c u a !'�"{ySV`'l !i(���lTce&�!�\zS_l u S-`${M&Ca@&�g$g�S-`${�!'�"c����"�"`MlT[�%$# h �&�` p ce&�#�{��"c7`$[ p ��lNS-`k&�`�S p �"`ic�S h &D\a>&�`$`$�"#@c�[�c u &�ck�"abg�\V[�(�� p &�cbc u ��!/�"{�S-`$`�SV`${ [�n�c u � SV`�c��"#elT� h c�S-[�` &D\-{�[�#�S-c u a�Y &` h �Xc u ��[�`$� � cm[ � [�`$�

�i

Page 42: O'3 0D. - cs.umd.edu

lines

nodes

lines

intlist

nodes

target quadtree

source quadtree

ab

c

d

ef

gi

b d e a f b i a c c g i g h

m o n q u m p s s r s

m

n

p

oq

r

h

s

t

u

u r r t

1 2 3 4 5 6 7 8 9 10

1 2 3 4 5 6 7 8 9 10

f i c

��� �������64 ��� B �('���" + /!"�+@<%� ')/���� 01� "��.*%� $���/28%6�0(8�' +�/� ��%� 8�+@� /�* %4� +@< �.*%+5�%�3')�01+@�.*%� ')/���� 01�".��*,��� 6��%*%+@� # �%�3' '�<%/+%4* $��%*%�8�+@<?+-<,�?8& � ���/ ��5� 8+ � + 8%�3���(+4"��.*%��H

l�[�%$# h �kc�[+ce&�#m{��"c `$[ p �ka>&yg$g�SV`${�S_l���lTce&�!�\zS_l u � p �w#��]no�"#�cm[��JSV{�%$#�� � �bnt[�#�&�`9�]�'&�akg�\-�>lT[�%$# h �kc�[+c]&�#�{��"c`$[ p � a>&yg$g�SV`${@&�` p &y`k�]� &yakg�\-���]�~g'&�`'l SV[�`>#��"{ySV[�`>� u S hmu S_l p �"`$[�c�� p !�(kc u �C{�#e&D(�#��"{�S-[�`+l�%$g'�"#�S-akg/[il�� p[�`kc u � l�[�%$# h � � %'& p c�#��"���e}�c u �g$#�[ h ��l�l [�n p �"c��"#�a;S-`�S-`${>&D\z\1c]&�#�{��"cN\zS-`$��l�c u &�cNS-`�c��"#el�� h c�c u ��#��"{�S-[�` p �]�'`$� p!�(>c u ��lT[�%$# h ��\zS-`$�;�]�~g'&y`'lwS-[�` l��"cC&�` p c u ���]�$g'&�`'lwS-[�`�#]& p S-%'lg$#�[ h �"� p lSV`X&�`@S-c��"#e&�cTS r ��n�&�l u S-[�`IY

�u ��l�g'&�c�S_&D\ #]&�`${�� � %$�"#�( &�\V{�[�#�S-c u a [�g'�"#e&yc���l;[�` &9l SV`${y\V�9lwS��"�Xl��"ck[�n�`$[ p ��l@&�ck&Xc�S-ak�s�tS�Y���Y-}�&D\z\`$[ p ��lC[�n l S �"��� ���� u �"#���� � ���e} S-c��"#e&�cTSV`${@%$g��&y# p nt#�[�a c u � l�a>&�\�\-��l�c�l S �"� p `$[ p ��lCc�[kc u ��#�[�[�c`$[ p �S-` c u � � %'& p c�#m�"�+#��"g$#���l��"`�ce&�c�S-[�`IY�Q�& h�u `$[ p �+S-`�c u S_l@l��"ck[�n�l�a>&D\z\-��l�c � lwS��"� p `$[ p ��l+� l u [���`�%$`'l u & p � pS-` �JS-{�%$#�� �i� � !$#m[i& p$h &�l�c]l�S-`�g'&�#]&D\z\V�]\c u � h [�[�# p S-`'&�c�� r &D\-%$��l;[�n c u �@�"` p g'[ySV`�cel;[ynq&D\z\ &�l�l�[ h S_&�c�� p \�S-`$�l��"{�ab�"`icel�tS�Y���Y-}�&D\z\<c u ��\zS-`$��l��"{�ak�"`�celRc u &�c�&�#���nt[�%$` p S-`@c u � � %'& p c�#��"��`$[ p ���Rc�[�c u �Cl��"c�[�n<\zS-`$�qlT�"{�ak�"`�celS-` c u �X&�l�l�[ h S_&�c�� p ce&�#�{��"c � %'& p c�#��"��`$[ p ��Y �u S4lMS_l>& h"h [�akg�\zS_l u � p S-` &�lwS-a;Sz\_&�#kn�&�l u S-[�`�&�lb�&�l p [�`$���S-c u c u �@S-`ic��"#]l�� h c�S-[�` &�\V{�[�#�S-c u a�}���S-c u c u � �'#el�c;\zS-`$��g$#�[ h ��l�l�[�#>&�l�l�[ h S_&�c�� p ��S-c u ��& hmu & h c�S r ��lT[�%$# h �`$[ p ��g'&�l�l SV`${ h [�[�# p S-`'&�cm� r &�\V%$��l@[yn S-celb�"` p g'[�S-`�cel@c�[9c u �+�'#el�cM\�S-`$�9g$#m[ h ��l�lT[�#;S-`�c u � h [�#m#���l�g'[�` p SV`${ce&�#m{��"c `$[ p ��Y ��u ��l�� h [i[�# p S-`'&�c�� r &D\-%$��l�&�#��;c u �"`9l u &y#�� p &�ak[�`${+&D\z\R\zSV`$�@g$#�[ h ��l�l�[�#]l�SV`sc u �k&�l�l�[ h S_&�c�� pce&�#m{��"cI`$[ p � r S_&�&Cl�� � %$�"` h �[�n1l h &�`;[�g/�"#e&�c�S-[�`'l Y�Q�& hmu & h c�S r ��ce&y#�{��"cJ\�S-`$�g$#m[ h ��l�lT[�#Rc u �"`klwS-a;%�\Vc]&�`$�"[�%'lw\-(h &D\ h %�\_&�c���lNc u �Q % h \�S p ��&�` p S4lTce&�` h ��!'�"c����"�"`�SVc]l��]\znP&�` p c u � h [�aka;%$`�S h &�c�� p l�[�%$# h � \zSV`$��Y �tn1c u ��l��"g'&�#]&�c�S-[�`p S_l�ce&�` h ��S_l \V��lmlRc u &�`bc u �#e& p S-%'l�[�nI�]�$g'&�`'lwS-[�`I}�c u �"`kc u ��ce&�#�{��"cN\zS-`$��#�� h [�# p lRc u ��S p �"`�c�Sz�'�"#[�nIc u � lT[�%$# h �\zS-`$�M&�l�\-(�S-`${@��S-c u S-`�c u �;l�g'& h � p �]�'`$� p !i(@c u ��l�[�%$# h ���]�~g'&y`'lwS-[�`9l��"c�Y

�'�

Page 43: O'3 0D. - cs.umd.edu

lines

nodes

lines

nodes

target quadtree

source quadtree

ab

c

d

ef

gi

b d e a f b i a c c g i g h

m o n q u m p s s r s

m

n

p

oq

r

h

s

t

u

u r r t

1 2 3 4 5 6 7 8 9 10

1 2 3 4 5 6 7 8 9 10

��� �������64 �����4*%� +5/ /�*%� ')/���� 01� + / +)8%���&�(+�*,/�6��9� 8& � 2��*�!8&*�6 �3�(��� / * " /��5� �6 $=9+@<%��� 2 �8&*,'1� /�*?')�(+48�*�6��� � 8&*%'�� /�*�� 8%6 �.�%' H

� [�`icTSV`�%�S-`${ c u S_l@g$#�[ h ��l�l"}Cc u ��l�� h [�` p \zS-`$��g$#m[ h ��l�lT[�#�&�l�l�[ h S_&�c�� p ��S-c u ��& h�u & h c�S r ��l�[�%$# h �X`$[ p �g'&�l�lT��l�c u � h [�[�# p S-`'&�cm� r &�\V%$��lC[yn7S-cel��"` p g/[�S-`ic]lCc�[kc u �C�'#elTc g$#�[ h ��l�l�[�#�S-`���& hmu & h cTS r ��&�l�l�[ h S_&�c�� p c]&�#�{��"c`$[ p ��Y � {�&DS-`I}<c u � h [i[�# p SV`'&yc�� r &D\-%$��l�[yn�c u ��\�S-`$��� lL�"` p g'[�S-`�cel�&y#���c u �"` h [�aba %$`�S h &�cm� p &�ak[�`${+&D\z\N\�S-`$�g$#�[ h ��l�l�[�#]l�S-` c u �+ce&y#�{��"c;`$[ p � r S_&9&sl�� � %$�"` h �X[�n�l h &�` [�g'�"#e&�cTSV[�`'l"}�&y` p ��& h�u c]&�#�{��"c�\zS-`$� g$#m[ h ��l�lT[�#h &D\ h %�\_&�c���l;c u � p S_l�ce&�` h �+!/�"c ���"�"`sS-cel��]\znq&�` p c u �+l�[�%$# h �b\zSV`$��Y &` h ��&D\z\ & h c�S r �>lT[�%$# h �b\�S-`$�+g$#�[ h ��l�l�[�#elu & r ��c�#e&y`'l�a;S-c�c�� p c u � h [�[�# p S-`'&�c�� r &D\-%$��lC[�nRc u �]S-#��"` p g'[ySV`�celCc�[bc u � &�lml�[ h S_&�cm� p ce&�#m{��"c�\�S-`$�kg$#m[ h ��l�lT[�#el"}c u � h [�aka;%$`�S h &�c�S-[�`9l�ce&�{��Cno[�#�c u � h %$#�#m�"`ic�\-(X& h c�S r � � %'& p c�#m�"��`$[ p � lwS��"��S_l h [�abg�\V�"cm��Y��`X[�%$#��]� &�abg�\V��}[�`�\-(b\�S-`$��l��"{�ak�"`ic � S_l nt[�%$` p c�[�S-`�c��"#el�� h c�c u � �]�$g'&�` p � p #��"{ySV[�`kS-`+c u ���'#el�c�S-c��"#e&�cTSV[�`I}�S-`�c��"#el�� h cTSV`${M\�S-`$��$Y

���]nt[�#���c u �9l�[�%$# h �X`$[ p ��S-c��"#]&�c�S-[�` h [�`�c�S-`i%$��l�&�` p `$[ p ��l@[�n�c���S h �Xc u � h %$#�#��"`�c�& h c�S r �X`$[ p �9lwS��"�&�#��@a>& p ��& h c�S r ��}R��& hmu [�n c u � h %$#m#��"`icT\V(�& h c�S r �+l�[�%$# h ��&�` p ce&�#�{��"c lwS-!�\zS-`${�`$[ p ��l;S_l;ab�"#�{�� p Y � l;&�`[�g$c�S-a;S���&�cTSV[�`+c�[�\V��lml��"`+c u ��`�%$a !/�"#[�n�lT[�%$# h ��\�S-`$�;l��"{�ak�"`�c h [�aka;%$`�S h &�c�S-[�`'l"}'&�\�\7l�[�%$# h �\zS-`$� lT�"{�ak�"`�celS-`9c u � h %$#�#��"`�c�\-(9& h c�S r �kl�[�%$# h � `$[ p ��lC� u [ilT� p S_l�c]&�` h �;nt#�[�a c u �;!'[�# p �"#�[�n�c u �]SV# h [�#�#���l�g/[�` p S-`${�!�\-[ h US_lk{�#���&�c��"#;c u &�`�c u �+�]�~g'&�`'l SV[�` #e& p S-%'l@&�#�� p �]\-�"c�� p Y �tn &9lT[�%$# h �@\zS-`$��\zS-��l@&�c p S_l�ce&�` h � \-��l�lkc u &�`�c u ��]�$g'&�`'lwS-[�`�#e& p S-%'lLno#�[�a c u �k!/[�# p �"#;[�nc u �>lT[�%$# h �k`$[ p ��� l h [�#�#���lTg'[�` p S-`${X!�\-[ h U1} c u �"`9c u �+l�[�%$# h �M\�S-`$�a;%'l�c;!'�+#��"c]&DS-`$� p nt[�#�\_&�c��"#;#��"!$#�[i& p$h &�l�c�Y ��u S_l�S_l;!'� h &y%'l���&Xl�[�%$# h �b\zSV`$��� lk#��"{ySV[�`�[�nC�]�~g'&�`'l SV[�`���c u �&�#���&���S-c u S-` c u �+�]�$g'&�`'lwS-[�` #e& p S-%'lk[ynqc u �@\zS-`$���;a>&D(9S-`�c��"#el�� h ckc]&�#�{��"c�\zS-`$��l@c u &�ck&�#��+`$[�c@&�l�l�[ h S_&�c�� p

�i�

Page 44: O'3 0D. - cs.umd.edu

lines

nodes

lines

intlist

nodes

target quadtree

source quadtree

ab

c

d

ef

gi

b d e a f b i a c c g i g h

m o n q u m p s s r s

m

n

p

oq

r

h

s

t

u

u r r t

1 2 3 4 5 6 7 8 9 10

1 2 3 4 5 6 7 8 9 10

c

��� ������� 4 ��� D 01+-� )���')/���� 01� 8&* 6�+ 8 �����(+C*%/ 6&�(' /+" �9�.*���� 8&")'�� �(� ' %�� +-<4/�+@<%�%� " 8%�3���%���.*�8%01+@� )�*%/ 6&�('?'1<�8,6&�6 * 6 ���5�.*%� +@<%�9# ��')+9� +5�%� 8�+@� / * /+"?"��.*%��01/��9����*�� 0(8+-� /�*%'(H�� <,� �� � 8&*%'1� /�*���(� � /�* � ' '��� ��%�5��� �/�')�6���* 6�8%� ���%� ��� 8 = /�*?+-<,� ' / �2� 01��� � 8%6&+@�3�(��H

r

a bc

A B

��� ������� � ��� �! 8&�9 �" � %4<%�%����/�*%�?')/���� 01�9"��.*%� � � 81= $�� 6��%" �(+5�6 � 8&* 69+-<,��')�01/�*�6 ".��*,�� � 81=7*,/&+�$��!6&�%" �(+5�6 6 �2� �.*%� +@<%� ')/���� 01�9*%/ 6&�9�G�%�3���� 2<�8�')��H ��/2� +-<,� � � )�%* � 8%6 �.�%'/+" �� 2 �8&*,'1� / * ) � "��.*%� � �.'4�� � 8&*%'�� /�*����(��� /�* �9� ��<%+ ��*,+ �%��')�01+�8 + 8 �����(+�".��*,� � �.*G8&*%/�+@<%�%�0����5���%*%+@" =��2*�8�')' /�0�� 8�+ �6 *%/ 6&�5 H

��S-c u c u ��!�\-[ h U h [�#m#���l�g'[�` p SV`${+cm[kc u � lT[�%$# h �C\zS-`$��� lC`$[ p �@�tS�Y���Y4}'&;ce&�#m{��"c�\zS-`$� a@&�(b\zS-� r �"#�( h \-[ilT� cm[kc u �!'[�# p �"#�SV`�&y` & p ��[�S-`�S-`${k`$[ p ���eYR�$[�#��]�'&�akg�\-��} h [�`'lwS p �"#c u ��lwS-c�%'&�c�S-[�` p �"g�S h c�� p S-`��JS-{�%$#��$= [�n7c���[C\�S-`$�l��"{�ab�"`icel � &�` p � S-` &�l�[�%$# h �k`$[ p � h [�#�#���l�g/[�` p S-`${Xc�[+!�\-[ h U �<YRWS r �"`sc u �k�]�'&�akg�\-� l SVcm%'&�c�S-[�` ����S-c uc u ���]�$g'&�`'lwS-[�`�#e& p S-%'l ) �e} � a>&D(k!'�;l�&Dnt�]\V( p �]\-�"c�� p &�l�S-cel��]�$g'&�`'lwS-[�`�#��"{�S-[�` h &�`+`$[�cg'[ilmlwS-!�\V( S-`ic��"#]l�� h c&�`�(+[�c u �"#C!�\-[ h U~lC[�%$celwS p �;[�n �1}/� u Sz\-� � a>&D(+`$[�cC!'� p �]\-�"c�� p &�lSVc]lC�]�~g'&�`'l SV[�` #m�"{�S-[�`�SV`�c��"#elT� h cel[�c u �"#!�\-[ h U$lC�tS�Y���Y-}�!�\-[ h U �eY�*[�cm� c u &yc�c u �"#��CS_l�`$[;`$�"� p c�[ p �]\-�"c���&�`�(>c]&�#�{��"c \�S-`$��lC&�l�&D\z\7c u ��ce&y#�{��"cR\zS-`$��lC&�#��hmu � h U�� p nt[�#�S-`icm�"#el�� h c�S-[�`+��S-c u &;l�[�%$# h �C\zS-`$��S-`+g'&�#]&D\z\V�]\�Y ��u %'l�#��"ak[ r &�\1[�n�&�ce&y#�{��"cR\zS-`$� p [���l�`$[�c&�!I� h c

�i�

Page 45: O'3 0D. - cs.umd.edu

g'�"#Tno[�#ma>&�` h ��Y?&�n h [�%$#el���}/Szn�c u �"#��k&�#���ab[�#��;ce&�#�{��"c�\zSV`$��lLc u &�`Xg$#�[ h ��l�l�[�#]l"}<c u �"`Xc u S_lCa>&D(+!'�k&@%'l��]nt%�\[�g$c�S-a;S���&�cTSV[�`IY

�u �>#���lT%�\Vc;[�nc u �@`$[ p �>ak�"#m{�S-`${�&y` p \zS-`$� p �]\-�"c�S-[�` &Dntc��"#�g$#�[ h ��lmlwS-`${9c u �>l�a@&D\z\V��lTc � lwS��"� p `$[ p ��lLS4lp �"g�S h c�� p no[�#C[�%$#��]�'&�akg�\-� p &�c]&�l��"c�SV`��JSV{�%$#��-= � Y>*�[�c���c u &�c�`$[�l�[�%$# h ��\zS-`$��l����"#�� p �]\-�"c�� p &�l���& h�u [�nc u �]S-#k�]�$g'&�`'lwS-[�`�#��"{ySV[�`'l�S-`�c��"#el�� h cm� p c u �>!/[�# p �"#;[�n c u �>!�\-[ h U$l h [�#�#m��l�g'[�` p S-`${9cm[ c u �]SV#;`$[ p ��l�S-`�c u �S-`�S-c�S_&D\ � %'& p c�#m�"��Y

lines

nodes

lines

intlist

nodes

target quadtree

source quadtree

ab

c

d

ef

gi

b d e a f b i a c g i g h

m o n q u m p s r s u

m

n

p

oq

r

h

s

t

u

r r t

1 2 3 4 5 6 7

1 2 3 4 5 6 7

cgi

��� ������� ����� D 01+@� )�9' / �2� 01�!8&* 6 + 8%�3���(+�*%/ 6&�(' /+" �!��*��.� 8&"2'1� �(� ' %4� +@< /�+-<,�%�;" 8 �����%�4��* 8%01+@� )�9*,/�6&�(' 8&*�6 "��.*%�(':'1<�8,6&�6 * 8 " +5�%� +@<%� # �3' + � + �%� 8�+@� /�* /+";".�.*%�G01/ �!� ��*2� 0(8�+@� / * 8&*�6*%/ 6&���G�%�3��� *%� H�� /&+5�?+-< 8�+ +@<%�G6�8�'1<,�67+ 8 �����(+�".�.*%� � �.*�6 � 0(8�+5�('4+-< 8�+;� +(% 8�' � 8%� �1�6G8�'�.*%+5�%�3')�01+@�.*%�?+-<,� �� � 8&*%'�� /�*?�3�(��� / *:6����5��*,�4+-<,� � +5�%� 8�+@� / *:+@<�8�+ % 8�'��-�%' + 01/��9 �" �(+ �6 H � <%��� 2 �8&*,'1� /�* ���(� � /�*�� '�'��� ��%�5��� �/�')�6���*G6�8%� �1�%� ��� 8 = /�*?+-<,� ')/���� 01� � � 8%6&+@�3�(��H

� ntc��"# &D\z\ h %$#m#��"`icT\V(�& h c�S r ��l�[�%$# h � &�` p ce&�#m{��"c�`$[ p ��l u & r �@!'�"�"`�ak�"#�{�� p }R��� h [�`�c�S-`�%$�+c u � &y!'[ r �g$#�[ h ��l�l"}<a>&yU�S-`${�&D\z\R`$[ p ��lL[�n�c���S h � c u �Ml S �"�k&�lCc u � h %$#�#��"`�c�\-(9& h c�S r �;`$[ p ��l�& h c�S r ��Y���&�lwS h &D\z\-(�}7���;&�#��h \zS-a !�S-`${X[�`$��\-� r �]\�[�n�c u � � %'& p c�#��"�k&�l����;ak[ r ��nt#�[�a c u � p �"�"g/��l�c�`$[ p �kc�[��&�# p c u � #m[i[�c�`$[ p ��Y ��u �#���l�%�\-c[ynPc u �ql�� h [�` p SVcm�"#e&�c�S-[�`bS_ll u [��`bSV`��JS-{�%$#m� = � ��S-c u `$[;`$�"� SV`�c��"#elT� h c�S-`${kce&�#�{��"c�c�#��"��\zS-`$��l!/�]SV`${p �"c�� h c�� p Y:&` h �kc u ��\-� r �]\�[�n�c u �;#�[�[�cC[�n�c u � � %'& p cm#��"��l u &�l�!'�"�"`9g$#�[ h ��l�l�� p }<c u �MlTg'&�c�S_&D\R#e&�`${�� � %$�"#�([�g/�"#e&�c�S-[�` S4l h [�akg�\-�"c���}/��S-c u &D\z\I\zSV`$��lqS-`�c u ��ce&�#�{��"c � %'& p c�#��"��c u &�c�S-`�c��"#el�� h c�c u � l�[�%$# h ���]�$g'&�`'lwS-[�`Xl��"cu & r S-`${9&b\zS_l�ck[�n�S p �"`�c�Sz�'�"#el;[ync u �>l�[�%$# h �b\zS-`$��l;c u &�cC\_&D(9��S-c u S-`�c u �k#e& p S-%'l�[�n�]�$g'&�`'lwS-[�`IY��JS-{�%$#�� = �p �"g�S h cel�c u ��lwS-c�%'&�c�S-[�`@S-akab� p S4&yc��]\-(+g$#�S-[�#c�[;c u �C�'`'&D\I#�[�%$` p [�n�l�[�%$# h ��c�[;ce&�#�{��"c \zSV`$� h [�aba %$`�S h &�cTSV[�`'l"Y

���

Page 46: O'3 0D. - cs.umd.edu

� � � � � � �� � � � � � �� � � � � � �� � � � � � �� � � � � � �� � � � � � �� � � � � � �

lines

nodes

lines

intlist

nodes

target quadtree

source quadtree

ab

c

d

ef

gi

b d e a f b i a c g h i

m o n q u m p s r s t

m

n

p

oq

r

h

s

t

u

u

1 2 3 4

1 2 3 4

i cgi

��� ������� ����� D 01+-� )��' / �2� 01� 8&*�6;+ 8 �����(+ *%/�6��(' 8 " + �%� +@<%� ' �01/ * 6 � +5�%� 8�+@� / *:/+"C".�.*%��01/ �!� � *�� 0(8�+@� /�*!8&* 6 *%/ 6&� ���%������*,��H � <,� �� 2 �8&*,'1� / * ���(��� /�*!� ' '1�2 ��%� �.� �/%')�6 ��*!628 � �1�%� ��� 8(=/�*?+-<,� ')/��2� 01��� ��8,6&+@�3�(��H

*�[�c�S h ��c u &yc p %$#�S-`${@c u �q&�\V{�[�#�S-c u a�}$&�\zS-`$��S-`+c u ��ce&y#�{��"c � %'& p c�#m�"� h [�%�\ p !'��a>&�#mU�� p &�lRS-`�c��"#el�� h cTSV`${c u � � %$�"#�(k#m�"{�S-[�` lT� r �"#e&D\'c�S-ak��l Y�Z[���� r �"#�}�c u �#��"g'[�#�c�S-`${;[�nIc u ��S-`icm�"#el�� h c�S-[�`@[�`�\-( u &�g$g/�"`'l�[�` h � &�c�c u �h [�` h \-%'lwS-[�`�[�n�c u �>&D\-{�[�#�S-c u a�Y��w`9[�# p �"#�c�[�& r [yS p c u S_l p %$g�\�S h &�cTSV[�`I}R[�` h �k&D\z\�g$#�[ h ��l�lwS-`${�[�n�c u �kl�g'&yc�S_&D\#e&�`${�� � %$�"#�(bS_l h [�akg�\-�"c�� p }'c u � l��"c[ynIS-`ic��"#]l�� h c�S-`${+ce&�#�{��"c�\zS-`$��l�S_ll�[�#mc�� p & h"h [�# p S-`${@c�[;S p �"`�c�Sz�'�"#�Y �u S4l#���l�%�\-celS-`9&D\z\7g�S-� h ��l�[�n�&�\zS-`$�;S-`�c u ��[�#�S-{�S-`'&D\Rce&�#�{��"c�a>&�g+[ h"h %$gi(�S-`${�& h [�`�c�S-{�%$[�%'lCl�g'& h ��S-`Xc u �L\�S-`$��&�#[�# p �"#TSV`${@[�nRg$#�[ h ��l�l�[�#el Y � `�%$gi�&�# p SV` h \-%'lwS r �@l��"{�ak�"`�c�� p a@&D�iS-a;%$a l h &y`I}'&�` p & p [���`i�&�# p S-` h \-%'lwS r �l��"{�ab�"`ic�� psh [�gi(9l h &y`9[�g'�"#]&�c�S-[�` h &�`s!'�@%'l�� p c�[�#���l�[�\ r �>&y`i(�S-` h [�`'lwS_l�c��"` h S-��l"} #���l�%�\-c�S-`${�SV`�&D\z\�c]&�#�{��"c\zS-`$��l!/�]SV`${bg$#�[�g'�"#T\V(@a>&�#mU�� p Y7jC%$g�\zS h &�c���ce&�#�{��"cN\zS-`$��l�a>&D( c u �"`>!/��l�&Dnt�]\V( p �]\V�"cm� p � &�l���& hmu S-`'l�ce&y` h � [�n&L\zSV`$��S_l�g$#�[�g'�"#�\-(+a>&�#mU�� p ��&�` p c u ��#���l�%�\-c[�n7c u ��� [�S-`+a>&D(kc u �"`+!'��#m�"g'[�#�cm� p Y ��u S_l�S_l�S-akg'[�#�ce&�`�c&�l�S-c& r [�S p l�c u ��`$�"� p c�[k�]\zS-a;S-`'&�c�� p %$g�\zS h &�c��k&�`'l����"#el � � #��]n ����� Y

W�S r �"`>&�` � ��S-a>&�{���} �b\zS-`$��l��"{�ak�"`�cel"}�&�` p &�`>&�l�lT[ h S_&�c�� p � %'& p cm#��"� �SVc u &�!$% h U��"c h &�g'& h S-c�( �&�` pu �]S-{ u c �;� \V[�{����]}<c u � p &�ce& � g'&�#]&D\z\V�]\�!$% h U��"c;|�x � � %'& p c�#��"�;a>&�g9l�g'&�cTS4&�\�#e&�`${�� � %$�"#�(�[�g/�"#e&�c�S-[�`sce&�U���l�;�/��\V[�{�����c�S-ak��S-`Xc u ����[�#]l�c h &�l���Y ��u S_l p �"{��"`$�"#e&�c���!'� u & r SV[�# ��[�%�\ p [ h"h %$#�S�n�&yc��& hmu [�nRc u � �M�t\-[�{��y�l�ce&y{���lR[�nIc u �Cl�g'&�c�S_&D\<#e&�`${�� � %$�"#m(�}i`$[�`$�[�n7c u �Cl�[�%$# h ��\zSV`$��l���"#m�#��"ak[ r � p nt#�[�a h [�`'lwS p �"#e&�cTSV[�`IY ��u S_l S4lg'[�l�lwS-!�\-�;Szn�c u ��#e& p SV%'lC[yn��]�$g'&�`'lwS-[�`�S_lC� � %'&�\7c�[@c u ��\-�"`${�c u [�n�c u � p S4&y{�[�`'&D\�& h #�[ilml�c u � lTg'& h � l�g'&y`$`$� p!�(>c u � � %'& p c�#m�"��Y

� =

Page 47: O'3 0D. - cs.umd.edu

�w`9c u �+& r �"#e&�{�� h &�l���}R&�l�lT%$ak�kc u &�c���& h�u [�n�c u ����\zS-`$��l��"{�ak�"`�cel�S_l�!$#�[i& p$h &�l�c�&�l�a@&D\z\�`�%$a !/�"#�[�nc�S-ak��lM�tS�Y���Y-} �;���J���[ r �"#�c u �k�"`icTSV#m� l�g'&yc�S_&D\�#e&�`${�� � %$�"#�(s[�g'�"#e&yc�S-[�`IY>Q�& h�u [�nc u ���;� \V[�{�����l�ce&�{���lC��Sz\�\#�� � %�S-#�� �;�t\-[�{#�J��c�S-ak��c�[@l�[�#�c &y` p ak�"#�{���c u �C\zS-`$��l�g$#�S-[�#Cc�[k!$#m[i& p$h &�l�cC&�` p a>&y#�U�S-`${'Y � [�a;!�S-`�S-`${+c u �c�S-ak��#�� � %�S-#�� p c�[;!$#�[i& p$h &�l�c�c u �C\zSV`$�kl��"{�ak�"`ic]l���S-c u c u ��l�[�#�c�S-`${>&�` p ak�"#m{�S-`${ h [ilTcel"}�c u � p &�ce& � g'&�#e&D\z\-�]\!$% h U��"c |�x � lTg'&�c�S_&D\7#e&y`${�� � %$�"#m(>��Sz\z\Rce&�U�� �M��� � \V[�{���\-[�{ ����cTSVab�CSV`�c u � & r �"#]&�{�� h &�l���Y

lines

nodes

lines

intlist

nodes

target quadtree

source quadtree

ab

c

d

ef

gi

a b c g i

m n o p q r s t u

h

m

n

p

oq

rs

t

u

1

1

cgi

��� ������� � ��� D 01+-� )��G')/���� 01��8&* 69+)8%���&�(+:*%/�6��(' ���!�;�6�� 8�+5�%" = �� � /�� + /!+-<,� # * 8&" � + �%� 8�+@� /�*/+" 01/��!����*&� 0(8�+@� /�* H ��/�+5��+@<�8+C+ 8 �����(+$".��*,�(' " 8&* 6 � <�8�)�� $��(�%*G� 8�� �1�648�' �.*%+5�%�3' �01+-�.*%�+@<%�4�� � 8&*%'�� /�* ���(� � /�*4/�* ���� )&� /��%' � +5�%� 8�+-� /�*%'(H D 6�6�� +@� / * 8&"." =��,')/���� 01� "��.*%�(' $ �%� � � � 8&* 6 �% �%��� 6&�%" �(+5�6�6 �2� �.*%�?8 ��5� /�� ')/��2� 01� *%/ 6&� ���%������ 2<�8�' �;8'$+@<%�%�.� �� 2 �8&*,'1� / *?���(� � /�*%' 6�� 6*%/�+ ".� ��/��,+ '1� 6&�G/!"�+@<%� $�" /�0��('?01/2� ���('1 �/�*�6���*,��+ / +@<%�%�.� ')/���� 01�9*%/ 6&�('(H � <,� �� � 8&*%'1� /�*���(� � /�* � ' '��� ��%�5��� �/�')�6���* 6�8%� ���%� ��� 8 = /�*?+-<,� ' / �2� 01��� � 8%6&+@�3�(��H

(���� �kA�3�0DFiF�GIHI?$3�24?'* ���<F~0�24F~8

(���� ��� BC.1*��I,/.IOI2���?$3�24.IO

��u �g/[�\-(i{�[�`�S���&�c�S-[�`@g$#�[ h ��lmlNnt[�#�[�c u �"# p &�ce& � g'&�#]&D\z\V�]\Il�g'&�c�S_&D\Il�c�#�% h cm%$#���lRl�% hmu &�lRc u � ��� c�#��"�S4l�lwS-a;Sz\_&�#�c�[c u &�c p ��l h #�S-!'� p no[�#Rc u �!$% h U��"c�|�x � � %'& p c�#��"��S-` � � h c�S-[�` � Y � Y � YNWS r �"`@& p &�ce& � g'&�#]&D\z\V�]\ ��� c�#��"��}����lTce&�#�c!�( h [�`'l�c�#m% h c�S-`${M&�g'&�#mc�S_&D\1��S-`${�� p�� � p {���#��"g$#���lT�"`ice&yc�S-[�`IY &` h ��c u � g'&y#�c�S_&D\I��S-`${�� p�� � p {���#��"g$#m��l��"`ic]&�c�S-[�`S_l h [�abg�\V�"cm� p }���& hmu \zS-`$��g$#�[ h ��lml�[�#@\-[ h &�\�\-( &�l�lwS-{�`'l+&y` S-`�S-c�S_&D\kg'[y\V(�{�[�` S p �"`�c�Sz�'�"#�no[�#+c u �X!'[�# p �"#TSV`${g'[y\V(�{�[�`'l�[�`+c u �C\-�]ntcq&y` p #�S-{ u cClwS p ��l�� lT�"� � � h c�S-[�` � Y � Y � no[�# p �"c]&DSz\4l �eY

�i�

Page 48: O'3 0D. - cs.umd.edu

ab

cd

ef

g

h

f h a b d g c ef f a a d d c cL L L L L L L Lf f a a d d c cR R R R R R R R

LID

RID

N0

lines

4 5 6 7

N1 2 3

N2 1

45

6 7

2

3

1

� � ������� ��4 �� *�� +-� 8&"� �/�" =��/�*�8')'1� � *2���%*+5'(H

�u ��S-`�S-c�S_&D\Ig'[y\V(�{�[�`@&�l�lwS-{�`$ak�"`�cRS_l�l u [��`�SV`@�JSV{�%$#�� = � nt[�#R[�%$#R�]�'&�akg�\-� p &�ce&�l��"cN� u �"#���c u ��\-�]noc�&�` p#�S-{ u c�g/[�\-(i{�[�`;S p �"`ic�Sz�'�"#el�&�#m� h [�`ice&�SV`$� p S-`kg$#�[ h ��l�l�[�#�l��"cel � ���b&y` p �����;#���l�g'� h cTS r �]\V(�Y'*��]�~c�}�!'�"{�S-`$`�S-`${��S-c u c u �k`$[ p ��l�&�c�c u �;\-��&Dn�\-� r �]\�[�nc u � ��� c�#m�"��}I���kak�"#�{��M&�\�\lwS-!�\zSV`${�\zS-`$��l;c�[�{��"c u �"#CS-`ic�[�c u �;g'&�#��"`�c`$[ p ��l"Y � \z\\zSV`$��lbc u &�c�S-`�c��"#el�� h c>&y`i(9[yn c u �+[ r �"#�\_&�g$g�S-`${9#��"{ySV[�`'l�no[�#�ak� p !i(9c u �+!'[�%$` p S-`${�!'[D�~��l�[�nc u �@`$[ p ��lMc u &�c u & r �@!'�"�"`�ab�"#�{�� p &�#��ka>&y#�U�� p no[�#�#��"!$#�[i& p$h &�l�c�S-`${9&�ak[�`${�c u �b\�S-`$��lMS-`�c u �>ab�"#�{�� p`$[ p ��l"Y ��u S_l;S_l;`$� h ��l�lm&�#�(sSV` [�# p �"#;c�[Xg$#�[�g'&y{i&�c��@c u �+� � %�S r &D\-�"` h �X!'�"c����"�"` c u � p S"!P�"#m�"`ic;S p �"`�c�Sz�'�"#elS-`9c u �;ak�"#�{�� p `$[ p ��l�� u S hmu #��"g$#m��l��"`ic�c u �Mlm&�ak�;g'[�\-(�{�[�`IY;�$[�#��]�'&�akg�\-��} h [�`'lwS p �"# �JS-{�%$#��-=�=�&@� u �"#����� u & r ��c���[ ��� cm#��"�;`$[ p ��l � &�` p� c u &�cq&y#��;c�[>!/�kak�"#�{�� p Y���`9c u S4lC�]�'&�akg�\-��}J`$[ p �6� h [�`ice&�SV`'l�\zS-`$��l� � � � � � � � }�&y` p `$[ p � kh [�`�ce&DS-`'l�\�S-`$��l � � � $ � ��� � � YI�w`>c u ��'{�%$#���}�\zSV`$��l � ��� � � $ � a %'lTc�!'�C#��"!$#�[�& p$h &�l�cc�[kc u ��ak�"#�{�� p l��"c�[�n7\zS-`$��lL�tS�Y���Y-}�\zS-`$��l � ��� � � � � $ � ��� � � � � � �7&�l�c u �"(kS-`�c��"#el�� h cCc u ��[ r �"#�\_&�g$g�S-`${@#��"{�S-[�`nt[�#�ak� p !�( c u �k!'[�%$` p S-`${X!'[D�$��l�[�n�`$[ p ��l �X&�` p Y ��u �kg$%$#�g/[il��@[�n�c u S_lL[�g'�"#e&yc�S-[�`XS_l�c�[�%$g p &�cm�kc u ���S-`${�� p�� � p {��@#��"g$#���lT�"`ice&yc�S-[�`'l�[�n&�`�(X`$� h ��l�l�&�#m(�\zS-`$��l@�tS�Y���Y4}<\zS-`$��l � &�` p � S-` �JS-{�%$#�� =�=�&��eY?� u �"`�c u ���S-`${�� p�� � p {���#m�"g$#���l��"`�ce&�c�S-[�`bS_l�%$g p &�cm� p }$���`$[�c���&�`�(kg'[�\-(�{�[�`@S p �"`�c�Sz�'�"#el�c u &�c�a;%'l�c&D\_l�[;!'�C%$g p &�c�� p Y��`sc u �;�]� &�abg�\V�MSV`��JSV{�%$#���=�=$}/\zS-`$� � u &�lC!/[�c u S-celC\-�]ntc�&�` p #�S-{ u c�g'[�\-(�{�[�`XS p �"`�c�Sz�'�"#el�%$g p &�c�� p � � � S-`�JS-{�%$#��-=�=�&b!'� h [�ak��l � � S-`��JS-{�%$#��-=�=y!I}1&�` p lwS-a;Sz\_&�#�\-(�} � � !/� h [�ak��l � � Y � S-`$� �+p [i��lC`$[�c u & r ���]S-c u �"#[�n<S-cel�g'[�\-(�{�[�`bS p �"`ic�Sz�'�"#el%$g p &�c�� p !/� h &�%'l���S-cel \V�]ntc&�` p #�S-{ u c�g'[�\-(�{�[�`@S p �"`�c�Sz�'�"#el&�#��\V�]��S h [�{�#e&yg u S h &�\�\-(a;S-`�S-a>&D\�Y

� [�#�&�\�\7l�% hmu g'[�\-(�{�[�`@S p �"`icTS��'�"#�%$g p &�c���lq����Y�{'Y-} � � c�[ � � &�` p � � c�[ � � S-`��JS-{�%$#��$=�=��e}���� !$#�[�& p$h &�l�cc u �;%$g p &yc���lCc�[>&D\z\�[�c u �"#\zS-`$��lCS-`Xc u �;ak�"#�{�� p `$[ p � r S_&+l h &�`X[�g'�"#]&�c�S-[�`'l"Y � [ h &D\z\-(�}<Szn�c u ��c�#e&�`'lTa;S-c�c�� pg'[y\V(�{�[�`;%$g p &�c���a>&�c hmu ��lJ�]SVc u �"#Rc u �R\-�]ntcR[�#7#TSV{ u cNg'[�\-(�{�[�`�S p �"`icTS��'�"#]lN[�n'c u ��\-[ h &D\�\zS-`$��}ic u �R\-[ h &�\~g/[�\-(i{�[�`S p �"`icTS��'�"#�S_l�%$g p &�c�� p c�[+#��1J'� h c�c u �;g'[�\-(�{�[�`XS p �"`�c�Sz�'�"#el�c u &�c u & r �;!'�"�"`�!$#�[i& p$h &�l�c�Yk�$[�# �]�'&�akg�\-��}JS-`

�$�

Page 49: O'3 0D. - cs.umd.edu

ag

c

h eb

f

d

aL

aLaL

aR

aR

aRcL

cL

bLbR

bL

bL

bR

dR

dR

dR

AB

(a) (b)

ag

c

h eb

f

d

aL

aLaL

aR

aR

aRcR

cR

aLaR

aL

aL

aR

dR

dR

dR

��� ������� � ��� ' 8�* �! �8��9 �" � /+" + % /7*,/�6&�(' �G�%�3���.*� 8&* 6 %4<�� 0�<�".��*,�('��!��' + $��?�3�+$���/28%6�0(8�' ++5/98�"�"2+-<,�����%�����6 ".��*,�('�� 8&* 6 ' $ * ��+-<,���3�('���" +$/+" +@<%���G�%�3��� /� ��%� 8�+@� /�*�H

�JS-{�%$#�� =,=�&$}Dc u �#�S-{ u cRg'[�\-(�{�[�`;S p �"`�c�Sz�'�"#�[�n'\zS-`$� � S_lN%$g p &yc�� p cm[�#��1J'� h cRc u ��n�& h cRc u &�cNg'[y\V(�{�[�`MS p �"`�c�Sz�'�"#� � !'� h [�ab��l � � Y � S-a;Sz\_&�#�\-(�}Rc u ��\-�]ntc�lwS p �kg'[�\-(�{�[�`XS p �"`�c�Sz�'�"#el�[�nR\zS-`$��l $�&�` p � &�#m� %$g p &�c�� p cm[+#��1J'� h cc u ��n�& h c�c u &�cRg'[y\V(�{�[�`bS p �"`icTS��'�"# � � !/� h [�ak��l � � Y ��u �#���lT%�\VcTSV`${;g/[�\-(i{�[�`kS p �"`�c�Sz�'�"#el�&�` p ak�"#�{�� p `$[ p ��l&�#�� p �"g�S h cm� p S-` �JS-{�%$#m�>=�=�!IY ��u S_l�g$#�[ h ��lml h [�`ic�S-`�%$��l�%$g+c u ��"`�c�S-#�� ��� c�#��"�C%$`�c�Sz\J&�\�\<\zS-`$��l&�#�� h [�`ic]&DS-`$� pS-`9&>lwS-`${�\-�;`$[ p �M&y` p &�\�\R`$� h ��l�l�&y#�(+!$#�[i& p$h &�l�cel u & r ��!'�"�"` h [�abg�\V�"cm� p Y �u ���'#el�cC#�[�%$` p #���l�%�\-cel�S-`Xc u �ak�"#�{ySV`${;[�n<\-��&DnI`$[ p ��l } �'} � }�&�` p ��S-`+�JS-{�%$#��$= � S-`�c�[�\-��&Dn7`$[ p ��l � &�` p �LS-`+�JSV{�%$#�� = � }�� u S hmu p �"g�S h celc u ��#���l�%�\-c�[�n�c u ���'#el�cC#�[�%$` p [�nN\-��&Dn�`$[ p �;ak�"#�{�S-`${'Y ��u ���'`'&D\ h [�`��'{�%$#]&�c�S-[�`X[�nR[�%$#�[�#�S-{�S-`'&D\R�]� &yakg�\-�p &�ce&�l��"cS_l p �"g�S h cm� p S-`��JS-{�%$#�� = � Y ��u ��S p �"`�c�Sz�'�"#el;&�l�lwS-{�`$� p cm[+c u �;c u #��"�;g'[�\-(�{�[�`'l�&�#��kl u [��`�S-`9c u ��'{�%$#���!�(+�"` h \-[ilwS-`${@c u ��S p �"`�c�Sz�'�"#el�SVc u SV` h S-# h \-��l"Y

ab

cd

ef

g

h

a b f h c d e ga a a a c d c dL L R R L L L La a a a c d c cR R L L R R R L

LID

RID

lines

N1 2 3

N2 1

2

3

1

� � ������� � ���4A�/�" =��/ *2� �8+-� /�* 8 " + �%� # ��')+;��/���* 6 /+" " �8 " *,/�6&�?���%����� *%� H

�u � �� c�#��"��� lCl�g'&�c�S_&D\�l�[�#mc {�#m��&�c�\-(+\zS-a;S-cel�c u � &�ak[�%$`icC[�n�S-`�c��"# � l��"{�ak�"`ic h [�aka;%$`�S h &�c�S-[�`s`$� h ��l�l�&�#�(&�l h [�akg'&�#m� p ��S-c u &b`$[�` � l�g'&�c�S_&D\z\-(9l�[�#�cm� p�p &�ce&�l��"c� u �"#��k&D\z\N\zSV`$��lL��[�%�\ p�u & r ��c�[ h [�aka;%$`�S h &�c���c u �]SV#�"` p g'[ySV`�cel@&�` p g'[�\-(�{�[�`�S p �"`icTS��'�"#]l@c�[ &D\z\ [�c u �"#el"Y9Z�[���� r �"#�}Rc u �@`$[�` ��p S_lE��[�S-`ic p � h [�akg/[ilwS-c�S-[�` [yn c u ���� c�#m�"� h &y%'l���lCS-` h #���&�lT� p9h [�akg$%$ce&yc�S-[�`'&D\ h [�akg�\-�]�iS-c�S-��lLS-`9c u ��\-[ h &�\�!$#�[i& p$h &�lTc�S-`${+g u &�l��;[�n�c u �Ml SV!�\zS-`${

� �

Page 50: O'3 0D. - cs.umd.edu

ab

cd

ef

g

ha b c d e f g ha a c a c a a aL L L R L R R Ra a a a a a c aR R L L L L L L

LID

RID

lines

N2 11

aR cL

aL

��� ������� � ��� � /��9 �" �(+-� /�* /!" +@<%�; �/�" =���/�*�� �8�+@� /�* /� ��%� 8�+@� /�*(%4� +-<:+-<,� # *�8�"& �/�" =���/�*;" 8�$��%" '�%*�0��.� 0�" �6 H

ak�"#�{��R[�g'�"#e&yc�S-[�`�S-` h [�akg'&�#TS4lT[�`�c�[C&�`�&�`'&D\-[�{�[�%'l p S_lE� [ySV`�c p � h [�akg/[ilwS-c�S-[�`kl�g'&�cTS4&�\ p &�ce&lTc�#�% h c�%$#���lT% h�u &�lc u � |�x � � %'& p cm#��"�>� *��]\_l � � }%*��]\_l � ��� [�#Rc u � � � � c�#��"�?� �'&D\-[%� � � Y ��u S_lNS_l !'� h &�%'l���S-cNS_lR[�ntc��"`kc u � h &�lT�c u &�ca>&�`�(@\zS-`$��lCn�&D\z\7S-`Xc u ��S-`ic��"#]l�� h c�S-`${�&�#���&�l�� u �"`Xc u � ��� c�#��"�;`$[ p ��l�&�#���ab�"#�{�� p Y � S-c u #��"g$#���lT�"`ice&yc�S-[�`'l!'&�l�� p [�`X& p S_lE� [ySV`�c p � h [�akg/[ilwS-c�S-[�`9[yn�l�g'& h ��}<[�`�\-(�c u [il���\zS-`$��l�c u &�cS-`�c��"#el�� h c�c u �MlTg�\�S-c�cTSV`${@\zS-`$��lb�tS�Y���Y-}h �]\z\�!/[�%$` p &�#�S-��l]����[�%�\ p `$�"� p c�[;!'��\-[ h &D\z\-(�!$#�[i& p$h &�l�c p %$#�S-`${>c u � lwS-!�\zS-`${+ak�"#�{���[�g/�"#e&�c�S-[�`IY

*�[���}�\-�"c+%'l@��l�c�S-a>&�cm� c u � `�%$a;!'�"#+[�n;!$#�[i& p$h &�l�celb`$� h ��l�l�&�#�( p %$#�S-`${ c u �Xg/[�\-(i{�[�` S p �"`�c�Sz� h &�c�S-[�`g$#�[ h ��l�l p %$�+c�[�c u �k\zS-`$��l�S-`icm�"#el�� h c�S-`${9[ r �"#�\_&�g$g�S-`${X#��"{�S-[�`'l Y��w`�c u �+& r �"#e&�{�� h &�l���}R&�l�lT%$ak�>c u &�c���& hmu��� c�#m�"� `$[ p � u &�lC&;n�&�`$[�%$c[yn � Y � �"c������ u �"#�� ��� � � ��!'�;c u �Lno#]& h c�S-[�`�[yn�c u ��\zS-`$��lCS-`X��& hmu `$[ p �c u &�c�S-`icm�"#el�� h c�[�`$�;[�#Cak[�#���[�n�c u �;[ r �"#�\_&�g$g�S-`${�#m�"{�S-[�`'l�nt[�#�ab� p !�(�c u ��!'[�%$` p SV`${X!/[��$��l�[�n�c u ��`$[ p ��lc u &�c u & r �@!'�"�"` ak�"#�{�� p Y � \_l�['}�\V�"c�� p �"`$[�c��+c u � u �]SV{ u ck[yn c u � ��� c�#��"�X���SVc u [�%$c;\-[il�l�[�n�{��"`$�"#e&D\zS-c�(�}��� \-[�{�� �N}J� u �"#����sS_l�c u �k`i%$a;!/�"#�[�n�\zS-`$��l�S-`�c u �;c�#��"���eYkvClwS-`${Xc u ��n & h c�c u &�c ��� �N}PSVc h &�`9!/�l u [��`Xc u &�cCc u �;`�%$a !/�"#�[�n�\-[ h &D\�!$#�[i& p$h &�l�cel � c u &�cCa;%'l�c�!'�;a>& p � p %$#TSV`${�c u �;ak�"#�{�S-`${+g u &�lT��l p %$�c�[kc u �CSV`�c��"#elT� h c�S-[�`�[�nN\zS-`$��l��S-c u c u ��[ r �"#�\_&�g$g�S-`${@#��"{�S-[�`'lS4l

��� ���� d ��� � � ��� �� ����� �

��u S_l�S_l�S-` c u ����[�#el�c h &�l�� �;���J�eYCZ[���� r �"#�} c u �k& r �"#e&�{�� ��h &�lT� h [�akg�\-�]�iS-c�(+S_lC�]�$g'� h c�� p c�[k!'��\-[����"#�Y�w`g'&�#�cTS h %�\_&�#D}$c u ��& r �"#e&�{�� ��h &�l�� h [�akg�\-�]�iS-c�(@[�n�c u �\zS-`$�;!$#�[i& p$h &�lTc�S-`${MlTc��"g@S_l p �"g'�"` p �"`�c�%$g'[�`+c u ��&�!�Sz\�S-c�([�n7c u � `$[ p �qlTg�\�S-c�cTSV`${+&D\-{�[�#TSVc u a cm[�g'&�#�cTSVcTSV[�`>c u �C!$% h U��"cel�&�l�a;% h�u &�l�g'[ilmlwS-!�\V�;�wc u �"#��]nt[�#���\V[����"#�S-`${;c u �nt#e& h c�S-[�`���[�n�\zS-`$��lCS-`�c��"#el�� h cTSV`${�c u �k[ r �"#�\_&�g$g�S-`${�#��"{�S-[�`'l]�eY � ab[�#�� p �"c]&DSz\V� p &�`'&D\-($lwS_lCS_l�&+lT%$!$� � h cCnt[�#nt%$#�c u �"##���lT��&�# hmu Y

�i�

Page 51: O'3 0D. - cs.umd.edu

(���� ��� � ?'H � O/3"F~0�8"F$��3�24.IO

WS r �"` p &�ce& � g'&y#e&D\z\-�]\�l�[�%$# h �;&�` p ce&�#m{��"c ��� c�#��"��l"}<& h [�#m#���l�g'[�` p �"` h ��!'�"c����"�"`�c u ��l�[�%$# h �;&�` p ce&�#�{��"c ��c�#��"��`$[ p ��l a %'lTcR!'�C��l�ce&�!�\zS_l u � p � u S h�u ��Sz\z\P!/�%'l�� p cm[ p �"c��"#�aMSV`$�Cg'&�c�cm�"#�`'lN[�n1g'&y#e&D\z\-�]\ h [�aka;%$`�S h &yc�S-[�`IY��&�lwS h &D\z\-(�}$nt[�#��& h�u l�[�%$# h � ��� c�#��"�C\-��&DnR`$[ p � ��} ����a;%'l�c p �"c��"#ma;S-`$��c u �CS-`�c��"#el�� h c�S-`${@ce&�#�{��"cR\-��&Dn�`$[ p ��l"Y� `i( l�[�%$# h �+\zS-`$�XS-` �XaMSV{ u c;S-`�c��"#el�� h c�&y`$[�c u �"#kce&y#�{��"c;\zS-`$� h [�`�ce&DS-`$� p S-` &sce&�#�{��"c�\-��&Dn;`$[ p ���kc u &�cS-`icm�"#el�� h cel ��Y�� [�#�]�'&�akg�\-��} SV`X�JS-{�%$#��>=��$}/l�[�%$# h �C\zS-`$�kl��"{�ak�"`�c �@� h [�`�ce&DS-`$� p S-` lT[�%$# h ��`$[ p � �e}�a;S-{ u cS-`icm�"#el�� h c�c]&�#�{��"cJ\zSV`$� � � h [�`ic]&DS-`$� p S-`kce&�#�{��"cR`$[ p � �/�7&�lN`$[ p ��l &�` p ��S-`�c��"#el�� h cDY7� n7&�l�[�%$# h � &y` p c]&�#�{��"c\-��&DnR`$[ p � p [k`$[�c�S-`�c��"#el�� h c�} c u �"`@S-c�S_l`$[�c�g/[il�lwS-!�\-��no[�#�c u ��&�l�l�[ h S4&yc�� p�h [�`�ce&DS-`$� p \zS-`$��lCc�[�S-`ic��"#]l�� h c�YR�w`�JS-{�%$#��?=��$}$l�[�%$# h �L\zSV`$� � h &�`$`$[�c�S-`ic��"#]l�� h cce&�#m{��"c�\zS-`$� ) � h [�`�ce&DS-`$� p SV`�ce&�#�{��"c�`$[ p � �/��&�l`$[ p ��l &�` p� p [k`$[�c�S-`�c��"#el�� h c�Y

lines

leafnodes

source R-tree

d e b c i g h a f

ab

c

d

e f

gi

h

lines

leafnodes

target R-tree

m o p s n q u r t

m

n

p

o q

rs

t

u

A

B

C

D

A B C D

K

L

M

N

K L M N

1 2 3 4

��� ������� � ���(�+ �8&�! �" � 628�+)8�) �8%� 8&"." �%"2B +@�3�(�('#" /�� +@<%�4'@8&�G� ')�(+ /+" ')/���� 01�48&* 6 + 8 �����(+$".��*,�('8�'4��*���� ���2�3� 4 ��H����8 " *,/�6&��$�/���* 6 �.*%�?�3�01+ 8&*%��" �(' 8%����'�<%/+%4* " /2�1$�/�+-< ')/���� 01� ' � � � � �8&* 6 �* 8&* 6 + 8%�3���(+ '�� � � ��� � 8&* 6 � * 628�+)8�) �8%� 8&"." �%" B +@���(�('(H � *%+5�%�5*�8&" B +@�3�(� *%/ 6&�('�8&*�6$�/���* 6 �.*%� $�/� ,�('48%�3� /�� � +5+5�6 " /�� 0�" 8%� � + =(H

� [�#���& h�u l�[�%$# h �M\V��&�nq`$[ p ��}Nc u �>g$#m[ h ��l�l�[�n p �"c��"#�a;S-`�S-`${9� u S hmu ce&y#�{��"c�\-��&DnC`$[ p ��lLS-c�SV`�c��"#elT� h celLS4lp �"c��"#�aMSV`$� p S-`+&�c�[�g ��p [���`ka>&�`$`$�"#C�tS-`@c u �qlT� � %$�"`�c�S_&D\ p [�a>&DS-`I}�c u S_l�g$#m[�!�\-�"a u &�l�!/�"�"` lTc�% p S-� p no[�#�c u �� � � c�#��"� � ��#TSV` ��� � �eY �9���'#elTc h�u � h U�Szn'c u ��!'[�%$` p S-`${�#�� h ce&�`${�\-��lJ[�n'c u ��c ��[#m[i[�cJ`$[ p ��l p [C`$[�cJSV`�c��"#elT� h c�YI�w`c u S_l h &�l���}�`$[�\-��&Dn7`$[ p ��l h &�`;S-`icm�"#el�� h c�Y'&c u �"#���S_l���}�!'�"{�S-`$`�S-`${>&�c�c u �#�[�[�c�`$[ p ��\-� r �]\1[�nIc u �Cl�[�%$# h ��&�` pce&�#m{��"c ��� c�#m�"��l"}$c u � h�u Sz\ p #��"`9[�nRc u �;l�[�%$# h ��#�[i[�c`$[ p �;&�#��LSV`�c��"#elT� h c�� p ��S-c u c u � hmu Sz\ p #��"`9[�nRc u ��c]&�#�{��"c

=

Page 52: O'3 0D. - cs.umd.edu

#�[�[�cR`$[ p ��Y �u �#���l�%�\-c�S-`${�S-`ic��"#]l�� h c�S-[�`'l�&y#��c u �"` h [�aka;%$`�S h &yc�� p c�[�c u � h�u Sz\ p [yn1c u ��l�� h�u Sz\ p `$[ p ��l��tS�Y���Y-}c u �@{�#e&�` p$hmu Sz\ p #��"` [�nc u �@#�[�[�c�`$[ p ��l]��S-`���& hmu a>&�gIY ��u �>{�#e&�` p$hmu S�\ p #��"` S-`�c u �@ce&�#m{��"c ��� cm#��"�+c u �"`l��]\-� h c�S r �]\-( h [�aka;%$`�S h &�c��;c u �]S-#�!'[�%$` p SV`${�#�� h ce&�`${y\V��lCcm[>c u �;&�g$g$#�[�g$#TS4&yc��;{�#e&�` p$hmu Sz\ p #m�"`XS-` c u �MlT[�%$# h �a>&�g �tS�Y���Y-}Nc u [�l�� lT[�%$# h � ��� c�#��"�@{�#e&�` p$hmu Sz\ p #��"`�� u [il��@g'&�#��"`�c;�&�l�g$#�� r S-[�%'lw\-(sno[�%$` p c�[�S-`icm�"#el�� h c;c u �g'&�#��"`�cC[�n�c u ��ce&�#m{��"c ��� c�#m�"��{�#e&y` p$h�u Sz\ p #��"`<�eY ��u S_lCg$#�[ h ��lml h [�`�c�S-`�%$��l[�` p [��`�c u ��c�#��"��%$`ic�Sz\Rc u ��\-��&Dn`$[ p ��l�S-`���& h�u���� cm#��"� u & r � p �"c��"#ma;S-`$� p &D\z\IS-`�c��"#el�� h c�S-`${b\-��&Dn�`$[ p ��lS-`�c u ��[�c u �"# p &�ce& � g'&�#e&D\z\-�]\ ��� c�#m�"��Y

1 2 3

4 5 6 7 8 9

0

S0

S1

S2

B C D

E F G H I J

A

T0

T1

T2

��� ������� � ��� �! �8��9 �" �:/+" # ��')+ " � )�%" *%/�6�����*,+ �%��')�01+@� /�*!6��(+ �%�5�9�.*�8�+@� / *?�.* +-<,��+ /� 56&/+%4*8&" ��/�� � +@<�� %4<%�%��� +-<2�3�(� ')/��2� 01� *,/�6&�('G')��� �,�%*%+@� 8&"." = $&��/28%6�0(8')+ + /�+-<,� 01/��5�3�('1 �/�* 6 �.*%�+ 8 �����(+�*,/�6&�(' H

� [�#��]� &yakg�\-��} h [�`'lwS p �"# �JS-{�%$#��>= � � u �"#���c u #��"��l�[�%$# h � `$[ p ��l�S-`�g$#m[ h ��l�lT[�#�{�#�[�%$g�� � a;%'l�cl�� � %$�"` �c�S_&D\z\-( p �"c��"#�a;S-`$��� u S hmu ce&�#�{��"c�`$[ p ��l�S-`+g$#�[ h ��lml�[�#�{�#�[�%$g�� � c u �"(MSV`�c��"#elT� h c�Y���� h &�%'l���`$[ p ��l ��} � }$&�` p��&y#��k&�c�c��"akg$cTSV`${+cm[ h [�aka;%$`�S h &�c��k��S-c u c u �kl�&�ak�;ce&�#m{��"c�`$[ p �@l��"{�ak�"`�c�}<c u � h [�aka;%$`�S h &�c�S-[�`'l�a;%'l�c!'� p [�`$��l�� � %$�"`icTS4&�\�\-(s�tS�Y���Y-}$`$[ p � �Ccm[k`$[ p � }�nt[�\z\-[���� p !i(@`$[ p � � cm[ `$[ p � }��"c h Yz�eY ��`��JS-{�%$#��?= � }�c u �p &�l u � p &y#�#�[�� !/�"`$��&�c u g$#m[ h ��l�lT[�#�{�#�[�%$g�����lwS-{�`�Sz�'��l�c u &�c&kl h &�`@[�g/�"#e&�c�S-[�`+��Sz\z\R!'��%'l�� p c�[kl u &y#���c u �h [�aka;%$`�S h &�c�� p S-`�nt[�#�a>&yc�S-[�`@no#m[�a c u ��`$[ p ��l�S-`+g$#�[ h ��l�l�[�#�{�#m[�%$g�� � �tS�Y���Y-}�cm[ `$[ p ��l �k&y` p �eY ��u %'l"}�S-cS_l`$[�c`$� h ��l�l�&�#m(knt[�#�`$[ p ��l ��} � }/&�` p �kcm[�S-` p �"g/�"` p �"`$c�\-( h [�aka;%$`�S h &yc�����S-c u c]&�#�{��"c�`$[ p ��l �>&y` p Y

&` h �@c u �k�]�'&�akg�\-�@�'#elTc�\-� r �]\`$[ p �bS-`icm�"#el�� h c�S-[�` p �"c��"#�a;S-`'&�cTSV[�`9S_l h [�akg�\-�"c�� p S-`��JSV{�%$#��A= � }I��& hmul�[�%$# h �`$[ p ��S-`>g$#m[ h ��l�lT[�#�l��"c�� � ��Sz\z\ u & r ���l�ce&y!�\�S_l u � p &q\zS4lTc�[yn'S-`icm�"#el�� h c�S-`${;ce&�#�{��"cR`$[ p ��l S-`>g$#m[ h ��l�lT[�#l��"c�� � Y ��u S_l�S-`�c��"#el�� h cTSV[�`�S-`�nt[�#�a>&yc�S-[�`@S_lc u �"`�g'&�l�l�� p &�\V[�`${>c�[bc u �]S-# h�u Sz\ p #��"`�� S Y ��Y-}�c u � l�[�%$# h ��`$[ p ��lS-`�g$#�[ h ��l�l�[�#lT�"c�� � �eYR��`+c u S4l�]� &�abg�\V��} ����&�l�l�%$ak�Cc u &�cl�[�%$# h ��`$[ p ���qS-`ic��"#]l�� h cel�ce&y#�{��"c�`$[ p ��l &�` p�/}'l�[�%$# h ��`$[ p � � &D\_l�[bS-`icm�"#el�� h cel�ce&�#�{��"c�`$[ p ��l &�` p �'}'&y` p l�[�%$# h ��`$[ p � �bS-`�c��"#el�� h c]lce&y#�{��"c`$[ p ��l��&�` p� Y ��u ��S-c��"#e&yc�S r � g$#m[ h ��l�l�c u �"` h [�`�c�S-`i%$��l }i�SVc u c u �Cl�[�%$# h �C`$[ p ��l S-`+g$#�[ h ��l�l�[�#�l��"c�� �;p �"c��"#�a;S-`�S-`${� u S hmu ce&�#m{��"c�`$[ p ��lS-`�g$#�[ h ��l�l�[�#Cl��"c�� �;c u �"(@S-`icm�"#el�� h c�YR�w` �JS-{�%$#�� �� }$l�[�%$# h ��`$[ p ��l } � }$&�` p � a>&D(h [�aka;%$`�S h &�c��MSV`�g'&�#e&�\�\-�]\���S-c u ce&�#m{��"c `$[ p ��l � }/}I&�` p�� }<#���l�g/� h c�S r �]\-(�}NS-`9g$#�[ h ��l�l�[�#;l��"c � �9�w� u [@S-`c�%$#�`kl u &y#���c u � h [�aka;%$`�S h &�c�� p S-`�nt[�#�a>&�cTSV[�` �SVc u ce&�#�{��"c7`$[ p ��l � }��<}�&�` p�� }�#���lTg'� h c�S r �]\-(�} r S_&�l��"{�ak�"`�c�� pl h &�`'l �eYN��`�c u ��`$�]�~c�S-c��"#]&�c�S-[�`X��� u S hmu S_l`$[�cl u [��`<�]}~lT[�%$# h ��`$[ p ��l �/} �'}$&�` p �;��Sz\z\ &D\_l�[ h [�aka;%$`�S h &�c��

= �

Page 53: O'3 0D. - cs.umd.edu

4 5 6 7 8 9B B CC C D

1 2 3

0

S0intersect

list

S1

S2

B C D

E F G H I J

A

T0

T1

T2

��� ������� � ���(�! 8&�! &" �C/+" ')�01/�* 6 " � )�%"%*%/ 6&�4��*,+ �%��')�01+@� /�*:6��(+ �%�5�9�.*�8(+-� /�* �.*4+-<,� + /� 56&/+%4*8&" ��/�� � +@<�� %4<%�%���$+@<����(�$' / �2� 01�4*%/ 6&�(' $��3/28%620(8�')+ ��*: �8%� 8�"�" �%"@+ / +@<%��01/��5�3�('� �/ * 6 �.*%� +)8%���&�(+*%/ 6&�('(H

S-`�g'&�#]&D\z\V�]\R��S-c u ce&y#�{��"c�`$[ p ��l � } '}$&�` p � }�#���lTg'� h c�S r �]\-(�Y

� \-c��"#�`'&�cTS r �]\V(�}���� h [�%�\ p �"akg�\-[�(>&�ak[�#�� l�c�#]&DS-{ u cTno[�#m�&y# p c u [�%${ u \-��l�l��]\-�"{i&�`�c�!'[�c�c�[�a � %$g@&�g$g$#�[i& hmuc�[+c u �bg$#�[�!�\-�"a [�n p �"c��"#�a;S-`�S-`${9&D\z\l�[�%$# h �>&�` p ce&�#m{��"cC\-��&Dn`$[ p �;S-`�c��"#el�� h cTSV[�`'l"Y>Q�& h�u ce&y#�{��"c�`$[ p �;S-`c�%$#�`;c�#]&�`'l�a;S-celPS-celN!'[�%$` p S-`${�#�� h ce&�`${�\-� h [�[�# p S-`'&�c���lNc�[�c u �R�'#el�c�lT[�%$# h ��\-��&Dn1`$[ p ��SV`bc u �&�#�!�S-c�#e&�#m(C\�S-`$��&�#[�# p �"#TSV`${s�tS�Y���Y-}Il�[�%$# h ��\V��&�n`$[ p ��� SV`��JSV{�%$#���=����]Y ��u ��l�� h [�[�# p S-`'&�cm��lC��Sz\�\�c u �"`9!/�>l u &�#�� p &�ab[�`${�&D\z\l�[�%$# h �\-��&Dn7`$[ p ��l r S_&k&�l��"#�S-��l�[�n7l h &y`>[�g/�"#e&�c�S-[�`'l Y &` h ����& h�u l�[�%$# h ��\-��&Dn7`$[ p � U�`$[�� l�c u � h [i[�# p SV`'&yc���l[�n�c u � h [�aba %$`�S h &�cm� p c]&�#�{��"c�\-��&Dn�`$[ p ��}/S-` g'&y#e&D\z\-�]\ }J��& hmu lT[�%$# h ��\-��&Dn�`$[ p �;c u �"` p �"c��"#�a;S-`$��l�� u �"c u �"#[�#C`$[�cCS-cCS-`ic��"#]l�� h cel�c u � c]&�#�{��"c`$[ p ��Y��tnc u �"#���S_l�&�`�S-`ic��"#]l�� h c�S-[�`I}Ic u �"` c u �;S-` p �]��[yn�c u �kce&�#m{��"c`$[ p �S_l�&�g$g/�"` p � p c�[+c u �>lT[�%$# h ��\-��&Dn `$[ p ��� l�\zS4lTc [yn�ce&�#m{��"c�`$[ p �MSV`�c��"#elT� h c�S-[�`'l"Y ��u S_l�lwS-c�%'&yc�S-[�`XS_l p �"g�S h c�� pS-`9�JSV{�%$#��-=��$}/� u �"#���c u � h [�aka;%$`�S h &yc�S-[�`Xg'&�c u !/�"c����"�"`��'#elTc ce&y#�{��"c�\V��&�n�`$[ p �@��`$[ p � � �&�` p c u ���'#]l�cl�[�%$# h �\-��&Dn7`$[ p ����`$[ p �5�/�7S_l�l u [��`IY ��u � p &�l u � p &�#�#�[�� !'�"`$��&�c u c u ��l�[�%$# h ��\-��&Dn7`$[ p ��l�#��"g$#���l��"`�cel�c u �l h &�`b[�g'�"#e&yc�S-[�`>c u &�cNS_l��"abg�\V[�(�� p c�[�l u &y#��c u �Cce&�#�{��"cR`$[ p �C!'[�%$` p S-`${;#�� h ce&y`${�\-� h [�[�# p S-`'&�c���l�&�ab[�`${�&D\z\[�n�c u �kl�[�%$# h ��\V��&�n`$[ p ��l"Y �u S4l�S_lLak[�#���[�n&b!$#�%$c���nt[�# h �k&�g$g$#�[i& h�u � u �"#��;c u �kl�g'&�c�S_&D\ p � h [�akg'[il SVcTSV[�`S-` p % h � p !i(@c u � p &yce& � g'&�#e&�\�\-�]\ �� c�#��"��S_l�[�`�\V(+%'lT� p &�c�c u �L\V��&�n7\-� r �]\�Y

�JS-{�%$#m� � � #��"g$#���l��"`�celCc u �klwS-c�%'&�cTSV[�`�nt[�%$` p &�noc��"#�&D\z\�[�n�c u �;ce&�#�{��"c�\-��&Dn`$[ p ��l u & r � h [�aba %$`�S h &�cm� pc u �]S-#C!'[�%$` p S-`${+#�� h ce&y`${�\-� h [�[�# p S-`'&�c���l�c�[kc u ��lT[�%$# h ��\-��&Dn�`$[ p ��l"}<&�` p ��& hmu l�[�%$# h ��\-��&DnR`$[ p � u &�l h [�a �g�Sz\-� p S-celqSV`�c��"#elT� h c�S-[�`X\zS_l�c�Y ��u �;S-`�c��"#el�� h cTSV[�`X\zS4lTcelCnt[�#���& hmu l�[�%$# h ��\-��&Dn`$[ p �@&�#�� p �"g�S h c�� p &�lCc u � h [�\ �\-� h c�S-[�`�[yn�!/[��$��l�!/�"`$��&�c u ��& hmu l�[�%$# h ��`$[ p ��S p �"`�c�Sz�'�"#��w��Y�{'Y-}$l�[�%$# h ��`$[ p � � l S-`ic��"#]l�� h c�S-[�`+\zS_l�c h [�`�ce&DS-`'lce&�#m{��"c�`$[ p �LS p �"`�c�Sz�'�"#el � &�` p �/�eY

&` h ��&D\z\7l�[�%$# h � � ce&�#�{��"cR`$[ p �CS-`icm�"#el�� h c�S-[�`'l u & r �!/�"�"` p �"c��"#�a;S-`$� p }$c u ��l�[�%$# h �\-��&Dn7`$[ p ��l���Sz\z\7c u �"`c�#e&y`'l�a;S-c�c u �C�"` p g'[ySV`�c h [�[�# p S-`'&�c���l�[�n7&D\z\ h [�`�ce&DS-`$� p \zS-`$��l��"{�ak�"`�celRcm[ &D\z\<S-`ic��"#]l�� h c�S-`${kce&�#m{��"cN\-��&Dn7`$[ p �

= �

Page 54: O'3 0D. - cs.umd.edu

lines

leafnodes

source R-tree

d e b c i g h a f

ab

c

d

e f

gi

h

lines

leafnodes

target R-tree

m o p s n q u r t

m

n

p

o q

rs

t

u

A

B

C

D

A B C D

K

L

M

N

K L M N

K K L LL M

N

intersectlist

��� ����������&� ��/ �2� 01� 8&*�6?+)8%�3���(+:B +-���(�(':8 " +5�%� 8&"."�')/���� 01� 8&* 6 +)8%���&�(+ " �8 " *%/ 6&�?��*,+ �%��')�0�+@� /�*%':<�8�)� $��(�%*G6&�(+5�%� �!��*,�6 8&* 69�3�01/�� 6&�6 ��*?+@<%�G8& � ���/ �� � 8�+5��' / �2� 01�?*%/ 6&�('(H

\zS-`$� l��"{�ak�"`�cel"YNQ�& hmu c]&�#�{��"c<\zS-`$�c u �"` p �"c��"#ma;S-`$��lN� u �"c u �"#R[�#I`$[�cIS-cNS-`icm�"#el�� h celN&�`�(�l�[�%$# h ��\zS-`$� l��"{�ak�"`�c�Y

v�`�\zS-U��>c u � p &yce& � g'&�#e&�\�\-�]\�!$% h U��"c;|�x � � %'& p c�#m�"�MlT[�%$# h �kc�[+c]&�#�{��"cC`$[ p � h [�aka;%$`�S h &�c�S-[�`sg$#�[ h ��lml"}c u �;`$[�` ��p S_lE��[�S-`icCS-#�#m�"{�%�\_&�#�g'&�#�c�S-c�S-[�`�S-`${+[�n�lTg'& h ��SV` p % h � p !i(�c u � p &�c]& � g'&�#e&D\z\-�]\ ��� c�#m�"� p � h [�akg'[il SVcTSV[�`h #���&�cm��lk& p$p S-c�S-[�`'&D\ h [�aka;%$`�S h &yc�S-[�` p Sz� h %�\-c�S-��l"Y �w`'l�c���& p [�nq&D\z\q& h c�S r ��l�[�%$# h �+`$[ p ��l h [�aba %$`�S h &�cTSV`${S-`�g'&�#e&D\z\-�]\��S-c u c u �+&�l�l�[ h S_&�c�� p ce&�#�{��"c�`$[ p �kS-`�c u �@[�`$� � c�[ � [�`$�>a>&yg$g�SV`${sg$#�[ r S p � p !i(9c u �>a>&yg$g�SV`${

� %'& p c�#��"�LSV`sc u � p &�c]& � g'&�#e&D\z\-�]\�!$% h U��"cq|�x � � %'& p cm#��"��}'c u � p &yce& � g'&�#e&�\�\-�]\ ��� c�#��"�kl�[�%$# h �;c�[kce&�#m{��"c\-��&Dn`$[ p � h [�aka;%$`�S h &�c�S-[�`'l�&�#���l hmu � p %�\-� p &y` p a>& p ��S-`�&�`@S-c��"#]&�c�S r ��g$#m[ h ��l�l Y ��u S_l�S_l p %$��c�[;c u � l SVcm%'&�c�S-[�`&�#�S_lwS-`${+� u �"`�a;%�\VcTSVg�\-�>lT[�%$# h ��`$[ p ��l�S-`icm�"#el�� h c�&>lwS-`${�\-�;ce&�#m{��"c`$[ p �k����Y�{/Y-}�S-`9�JSV{�%$#�� �$� }'l�[�%$# h ��`$[ p ��l } �'}$&�` p ��& h�u S-`�c��"#el�� h cc]&�#�{��"c�`$[ p � �/�eY

�u � l hmu � p %�\�S-`${kg$#m[�!�\-�"a S_l�&�`'&D\-[�{�[�%'lNc�[�c u � ��u #�[�a@&�c�S h ��` p �]�@g$#�[�!�\-�"a �zWq&�#m� ���� � u �"#��c u ��l��"cR[�nl�[�%$# h � &�` p ce&�#�{��"c\V��&�n�`$[ p ��l�a>&D(>!/�;c u [�%${ u c[�n�&�lC&kl��"cC[�n r �"#�c�S h ��l"}<&�` p c u �LS-`ic��"#]l�� h c�S-[�`'lC!'�"c����"�"`c u �+`$[ p ��lk&�l�� p {���l;!/�"c����"�"`�c u � r �"#�c�S h ��l"Y ��u ��l��+� p {���lk&�` p�r �"#�cTS h ��l no[�#ma &�!�S-g'&�#�cTSVcm��{�#e&yg u }�&�` pS-c u &�l@!/�"�"` l u [��`�c u &�c+c u �"#��X�]�iS_l�cel�&�g'[�\-(�`$[�a;S_&D\;c�S-ak�9&D\-{�[�#�S-c u a nt[�#�l hmu � p %�\zSV`${�c u �s`$� h ��l�l�&�#�(h [�aka;%$`�S h &�c�S-[�`'l:�zW�&�!'[ ����� Y

�w` l�[y\ r S-`${�c u � h [�aka;%$`�S h &�c�S-[�` l hmu � p %�\zS-`${�g$#�[�!�\-�"a�} &�`$[�` � [�g$c�S-a>&D\�l�[�\-%$c�S-[�` �&�l hmu [il��"` %'l SV`${&�{�#��"� p (�&yg$g$#�[i& hmu Y � c;��& hmu S-c��"#e&yc�S-[�`�[�nql�[�%$# h �>cm[ c]&�#�{��"c h [�aka;%$`�S h &�c�S-[�`'l"}�c u �b�'#el�ckl�[�%$# h �@`$[ p �

= �

Page 55: O'3 0D. - cs.umd.edu

lines

leafnodes

source R-tree

d e b c i g h a f

ab

c

d

e f

gi

h

� �� �

��� �� �� �� �

lines

intlist

leafnodes

target R-tree

m o p s �� n ��q� �� �u r t

m

n

p

o q

rs

t

u

A

B

C

D

A B C D

K

L

M

N

� �� �K L M N

K K L LL M

N

intersectlist

ci

f

��� ����������� � ��/��2� 01�!8&* 6 +)8%���&�(+?628�+ 8�) �8%� 8�"�" �%" B +@�3�(�(' %4� +@< # ��')+��3/��2*�6 /!" 01/��9�?��*�� 0(8�+@� /�* '@0�<,�6 ��".�.*%� <�� � <2"�� ��<%+5�6 �,'1�.*%� 0���� 0�" �(' H � *�8,01+-� )�� "��.*%�('G8&* 6 *,/�6��('�8%�3� '1< 8%6&�6 H� 8%�3���(+4"��.*%�(' 8 ��� � 8 � ���6 %4� +-<G+-<,��*�8&�G�(' /!" +@<%� ��*,+ �%��')�01+@��*,� ')/���� 01� ".��*,�('(H

#�� � %�S-#�S-`${ h [�aka;%$`�S h &�c�S-[�` lT�]\V� h c]l@c u �@�'#el�ckc]&�#�{��"ck`$[ p �+S-` S-cel�S-`�c��"#el�� h c�S-[�` \zS_l�c�����Y�{'Y-} S-` �JS-{�%$#�� ��� }l�[�%$# h � `$[ p �6� l��]\-� h celCc]&�#�{��"cC`$[ p � � �eY ��u �;`$�]�~c�l�[�%$# h ��`$[ p �k#�� � %�S-#�S-`${ h [�aka;%$`�S h &�c�S-[�`Xc u �"`9l��]\-� h celc u � �'#el�cNce&�#�{��"cJ`$[ p ��c u &�c u &�lI`$[�c7!/�"�"` g$#m� r S-[�%'lw\-(;l��]\-� h c�� p !�(�c u �R�'#elTc7l�[�%$# h ��`$[ p �����Y {'Y-} SV`k�JS-{�%$#�� ��� }l�[�%$# h �`$[ p � l��]\-� h cel�ce&�#m{��"c7`$[ p � �/�eY � [�`�c�S-`�%�SV`${LS-`>c u S_l�n &�l u SV[�`I}i&D\z\'nt[�\z\-[���S-`${ l�[�%$# h �`$[ p ��l #�� � %�SV#TSV`${h [�aka;%$`�S h &�c�S-[�`�l��]\-� h c�c u ���'#el�c�ce&�#m{��"c`$[ p �;S-`9c u �]S-#CS-`ic��"#]l�� h c�S-[�`X\zS_l�celCc u &yc u &�lC`$[�c�!'�"�"`9g$#�� r S-[�%'lw\-(l��]\-� h c�� p !i(�&�`$[�c u �"#l�[�%$# h ��`$[ p � p %$#�S-`${+c u � h %$#m#��"`ic h [�aka;%$`�S h &�c�S-[�`+S-c��"#]&�c�S-[�`IY

&` h �k&D\z\Rg'[ilmlwS-!�\V� h [�aka;%$`�S h &�c�S-[�`'l u & r ��!'�"�"` p �"c��"#�aMSV`$� p no[�#Cc u � h %$#�#��"`�cCSVcm�"#e&�c�S-[�`I}/��& hmu lT[�%$# h �\-��&Dn `$[ p �>c u &�c u &�l�&Xl h�u � p %�\-� p�h [�aba %$`�S h &�cTSV[�`9S_l�a>& p �+& h c�S r ���tS-` �JS-{�%$#m� ��� }Nc u S_l h [�#�#���lTg'[�` p l�c�[l�[�%$# h � `$[ p ��l5�<} }1&y` p �eY1vClwS-`${�&bc�� h�u `�S � %$�>lwS-a;Sz\_&�#�cm[>c u &yc�"akg�\-[�(�� p SV`sc u � p &�c]& � g'&�#e&D\z\-�]\�!$% h U��"c|�x � � %'& p c�#��"��S-`�c��"#el�� h c�S-[�` &D\-{�[�#�S-c u a�}���& hmu & h c�S r �9l�[�%$# h �X`$[ p �9!$#�[i& p$h &�l�celbc u �X�"` p g'[�S-`�cel+[�nk&D\z\&�l�lT[ h S_&�c�� p \zS-`$� lT�"{�ak�"`�cel��tS�Y���Y-}$&D\z\Ic u �C\zSV`$�;l��"{�ak�"`�cel�c u &�c&�#m�nt[�%$` p S-`+c u � ��� c�#m�"��`$[ p ����cm[ c u �ql��"c�[�n\zS-`$� l��"{�ab�"`icel S-`+c u ��&�lml�[ h S_&�cm� p ce&y#�{��"c ��� c�#��"��`$[ p ��Y ��u S_l�S_l& h"h [�akg�\zS_l u � p !�(kc u �C�'#elTc�\zS-`$��g$#m[ h ��l�lT[�#&�l�lT[ h S_&�c�� p ��S-c u ��& hmu & h c�S r �Xl�[�%$# h ��`$[ p �Xg'&�lmlwS-`${9S-cel@�"` p g/[�S-`icel@cm[9c u ���'#el�c;\zS-`$�9g$#�[ h ��l�l�[�#kS-`�c u �h [�#�#m��l�g'[�` p S-`${kc]&�#�{��"c ��� c�#��"��`$[ p ��YR��`��JS-{�%$#m� ��� }ic u ��'#elTc�\zS-`$��g$#�[ h ��l�l�[�#]l� S Y ��Y-}$l�[�%$# h ��\zSV`$��l5$/} � }$&�` p� ��&�#���l u [��`+��S-c u &�#m#�[�� l��"a>&�`'&�c�S-`${;nt#�[�a c u �"a p S-#�� h c�� p &�c�c u � h [�#�#���lTg'[�` p S-`${+l�[�%$# h ��`$[ p ��l"Y &` h �c u �l�[�%$# h ��\zS-`$��"` p g/[�S-`ic h [i[�# p SV`'&yc�� r &�\V%$��l u & r ��!/�"�"` h [�aka;%$`�S h &�c�� p c�[�c u ���'#elTc7ce&y#�{��"cJ\�S-`$�g$#m[ h ��l�lT[�#

= �

Page 56: O'3 0D. - cs.umd.edu

S-`Xc u � &�lml�[ h S_&�cm� p c]&�#�{��"c �� c�#��"�;`$[ p ��}<c u �"(�&�#���c u �"`�l u &�#�� p &yak[�`${+&D\z\�ce&y#�{��"c�\zS-`$�kg$#�[ h ��l�l�[�#]l�S-`Xc u �l�&�ab��ce&�#�{��"c�`$[ p � r S_&k&kl�� � %$�"` h ��[�n�l h &�`+[�g'�"#e&�cTSV[�`'l"Y

Q�& hmu & h c�S r �kce&�#m{��"cC\zSV`$�@g$#�[ h ��l�l�[�#�c u �"`�lwS-a;%�\-ce&�`$�"[�%'l \V( p �"c��"#�a;S-`$��l�� u �"c u �"#�[�#�`$[�c�S-cLSV`�c��"#elT� h celc u �@!$#�[i& p$h &�l�c�� p l�[�%$# h � ��� cm#��"�k\zS-`$� lT�"{�ak�"`�c�YX�tn c u �>ce&y#�{��"c�\zS-`$�+S-`�c��"#el�� h c]l;c u �@!$#�[i& p$h &�lTc�� p lT[�%$# h �\zS-`$��}<c u �"`�c u �;l�[�%$# h �L\zSV`$�MS p �"`�c�Sz�'�"#CS_l�S-` h \-% p � p SV`9&�\zS_l�c�[�nNS-`icm�"#el�� h c�S-`${@\zS-`$��lCc u &�c�S_l�&�l�lT[ h S_&�c�� p ��S-c uc u �@ce&�#�{��"cC\�S-`$��Y � [�`ic�S-`�%�S-`${9c u S_l�g$#�[ h ��lml"}Nc u � h [y\�\-� h c�S-[�`�[ynql�� h [�` p \zSV`$�+g$#m[ h ��l�lT[�#el;&�l�l�[ h S_&�c�� p ��S-c u��& hmu & h c�S r �>l�[�%$# h � ��� cm#��"�>`$[ p ������Y�{'Y-}PS-` �JS-{�%$#�� ��� }Nl�[�%$# h �b\zS-`$��l � } �$}R&�` p �/� g'&�l�l���lCS-cel��"` p g/[�S-`icelc�[Xc u �@�'#elTc g$#m[ h ��l�lT[�#;S-`���& hmu & h c�S r ��&�l�lT[ h S_&�c�� p c]&�#�{��"c�`$[ p ��Y � {i&DS-`I}�c u �@\�S-`$���"` p g'[�S-`�cel>&y#��+c u �"`h [�aka;%$`�S h &�c�� p &�ak[�`${k&D\z\I\zS-`$�;g$#�[ h ��l�l�[�#el�SV`�c u ��ce&�#m{��"c�`$[ p � r S_&@& lT� � %$�"` h �;[�n�l h &�`+[�g/�"#e&�c�S-[�`'l }'&�` p��& hmu ce&�#�{��"c�\zS-`$�>g$#�[ h ��l�l�[�#CSV`sg'&�#e&D\z\-�]\ p �"c��"#ma;S-`$��l�� u �"c u �"#�[�#�`$[�c�S-c�S-`icm�"#el�� h celCc u �@l�[�%$# h ��\zS-`$��Yk�tn&ce&�#m{��"cR\zS-`$��S-`�c��"#el�� h celc u � !$#m[i& p$h &�l�cl�[�%$# h �C\zSV`$��} c u �"`+c u ��l�[�%$# h �\zS-`$��S p �"`�c�Sz�'�"#S_l�S-` h \-% p � p SV`�c u ��\�S_l�c[�n�SV`�c��"#elT� h c�S-`${+\zS-`$��l�c u &�cCS_l�&�l�l�[ h S_&�c�� p ��S-c u c u �kce&y#�{��"c�\zS-`$��Y &` h �>&�\�\�& h c�S r �kl�[�%$# h ��\zS-`$�>g$#�[ h ��l�l�[�#elu & r �kc�#]&�`'l�a;S-c�c�� p c u �]S-# h [i[�# p S-`'&�c���l�c�[�c u �>&�l�l�[ h S_&�c�� p ce&�#�{��"cC\�S-`$��g$#�[ h ��lml�[�#el"}Jc u � h %$#�#��"`�c�S-c��"#]&�c�S-[�`[�n h [�aka;%$`�S h &yc�S-[�`'l�S_l h [�akg�\-�"c���}�&�` p &�\�\ & h cTS r ��l�[�%$# h �@`$[ p ��l p �]\V�"cm�+c u �>c]&�#�{��"c�`$[ p �+c u &yc �&�lLc u �#�� h S-g�S-�"`ic�[�nIc u �]S-# h [�aka;%$`�S h &yc�S-[�`'l no#�[�a c u �]S-#�S-`�c��"#el�� h cTSV[�`k\zS_l�cel"Y ��u �c]&�#�{��"cR`$[ p ��l�c�[�!/� p �]\-�"c�� p nt#�[�ac u �CS-`�c��"#el�� h c�S-[�` \zS4lTcel &ycc u S_l�g'[ySV`�c�&�#���c u � h S-# h \-� p S p �"`ic�Sz�'�"#el�S-`X�JSV{�%$#�� ��� Y

� [�`icTSV`�%�S-`${>�SVc u c u S_l�g$#�[ h ��lml"}$c u �;l�� h [�` p #m[�%$` p [�n�l�[�%$# h ��`$[ p ��c�[kc]&�#�{��"c�`$[ p � h [�aka;%$`�S h &�c�S-[�`'la;%'l�cN!'� l hmu � p %�\-� p Y��$[y\�\-[���S-`${ &y`�S p �"`icTS h &�\Pl��]\-� h c�S-[�`kg$#m[ h ��l�lR&�lI!/�]no[�#m��}�c u ���'#el�c�l�[�%$# h ��`$[ p �#�� � %�SV#TSV`${& h [�aka;%$`�S h &�c�S-[�`�a>&�U���l SVc]l+l��]\-� h c�S-[�`IY Q�& hmu nt[�\z\-[��SV`${�`$[ p ���tS-`�[�%$# &y#�!�S-c�#e&�#�(s\zS-`$��&�#�[�# p �"#�S-`${�[�nl�[�%$# h �C\V��&�n�`$[ p ��l]��#�� � %�S-#�S-`${�& h [�aka;%$`�S h &�c�S-[�` �'#el�c p �"cm�"#�a;S-`$��l� u �"c u �"# [�#�`$[�c &�`�(>[�nNS-cel�#��"a@&DS-`�SV`${S-`icm�"#el�� h c�S-`${@ce&�#�{��"c�`$[ p ��l u &�l�`$[�c!/�"�"`�lT�]\V� h cm� p !�(+&;g$#�� h � p S-`${�l�[�%$# h ��`$[ p ��Y��tn�c u S_lS4lc u � h &�lT��}$c u �l��]\-� h c�S-[�`sS_l�a@& p ��}7&�` p c u �;nt[�\z\-[���S-`${�lT[�%$# h �k`$[ p ��l�#�� � %�S-#�S-`${ h [�aka;%$`�S h &�c�S-[�`sa>&�U��kc u �]SV#kl��]\-� h c�S-[�`'l��g$#�[ r S p � p &y`�%$`'l��]\-� h c�� p c]&�#�{��"cI`$[ p ��S-` c u �]SV#NS-`�c��"#el�� h cTSV[�`�\zS_l�celJS_lR& r &�S�\_&�!�\-���eY ��`k�JS-{�%$#�� ��� }�c u �lT�]\V� h cm� pce&�#m{��"c�`$[ p ��lC&�#���l u [��`@S-`�c u �CS-`ic��"#]l�� h c�S-[�`+\zS_l�cel��"` h \-[il�� p SV` h S-# h \-��l"Y

&` h ��&�\�\�l�[�%$# h �+`$[ p ��l u & r � h [�aka;%$`�S h &�c�� p c u �]SV#b�"` h \V[�lwS-`${ l�[�%$# h �@\zS-`$��lk�SVc u &D\z\ [�n c u �+c]&�#�{��"c`$[ p ��l�S-`�c u �]S-#�S-`�c��"#el�� h c�S-[�`@\zS_l�cel }'&�` p &D\z\<S-`ic��"#]l�� h c�S-`${>c]&�#�{��"c \�S-`$��l u & r � !/�"�"`�a>&y#�U�� p S�nRc u �"(bS-`ic��"#]l�� h c&+!$#m[i& p$h &�l�cm� p l�[�%$# h �M\�S-`$��}Rc u �kS-`�c��"#el�� h c�S-[�`�[�g/�"#e&�c�S-[�`XS_l h [�akg�\-�"c���Y+� [�#�[�%$#��]� &yakg�\-� p &�c]&�l��"c�}Jc u �c u S-# p &�` p �'`'&D\$#�[�%$` p [�n h [�aka;%$`�S h &�c�S-[�`'lPS_l7l u [���`�S-`k�JSV{�%$#�� ��� }"��S-c u [�`�\-(�l�[�%$# h ��`$[ p � !$#�[i& p$h &�l�c�S-`${l�[�%$# h �C\�S-`$��l � &�` p �@c�[kc u ��ce&y#�{��"c�\zSV`$��l ' &�` p � h [�`�ce&DS-`$� p S-`�c]&�#�{��"c�`$[ p � �<Y

W�S r �"`��b\zS-`$��l��"{�ak�"`�celR&�` p &�`>&�lml�[ h S_&�cm� pk��� c�#��"����S-c u &C`$[ p � h &�g'& h S-c�( � &�` pMu �]SV{ u c�\-[�{����w#�� h &D\z\nt#�[�a c u � p S_l h %'l�l SV[�`�[�n c u � ��� c�#��"�@!$%�Sz\ p SV`${�g$#�[ h ��l�l�c u &�c;&�` �� c�#��"� h [�`ic]&DS-`�SV`${ ��\zS-`$��l�S_l;[�n��[�#el�c �h &�l�� u �]S-{ u c��M�t\-[�{��J���e} c u � p &�ce& � g'&y#e&D\z\-�]\ ��� c�#��"�+a@&�g�S-`ic��"#]l�� h c�S-[�`�[�g/�"#e&�c�S-[�`�ce&yU���l �;�/� � � \V[�{��J�

=�=

Page 57: O'3 0D. - cs.umd.edu

lines

leafnodes

source R-tree

d e b c i g h a f

ab

c

d

e f

gi

h

lines

intlist

leafnodes

target R-tree

m o p s n q u r t

m

n

p

o q

rs

t

u

A

B

C

D

A B C D

K

L

M

N

K L M N

� �� �K L L

intersectlist

N

c fi

��� ������� � ��� ��/���� 01� 8&*�6 + 8 �����(+ 6�8+)8�) 8 � 8&"." �%" B +@�3�(�(' %�� +@< ')�01/�*�6 �3/��2*�6 /+" 01/��9�?��*�� 0(8�+@� /�*?'@0�<%�6���".��*,��<�� ��<�".� ��<%+5�6 �%'���*,��0��.� 0�" �('(H ��<�8,6 �.*%���.*�6 � 0(8�+5�('�*,/�6��('�*,/&+ �8%�3+@� 0��� 8�+-�.*%��.* +-<,�!0����5�3�%*,+ ��/���* 69/!"�01/ �!� �2*�� 0(8�+@� / * H ��/�+5�9+@<�8�+:')/���� 01� *%/�6�� ��*,+ �%��')�01+@� /�* ".� ' + '<�8�)���$��(�%* ��/ 6 � #��6 " /�"." /&%��.*%� +@<%�4# ��')+ �3/��2*�6?01/ �!� �2*�� 0(8�+@� / *:6��% �� 01+ �6 ��*!��� � �2�3�����H� 8%�3���(+4"��.*%�(' 8 ��� � 8 � ���6 %4� +-<G+-<,��*�8&�G�(' /!" +@<%� ��*,+ �%��')�01+@��*,� ')/���� 01� ".��*,�('(H

c�S-ak��Y ��u S_l�S_lC[�!$ce&DS-`$� p !�(+[�!'l��"# r S-`${+c u &�cC��l�ce&�!�\zS_l u S-`${�c u �kl�[�%$# h ��c�[@ce&�#m{��"c`$[ p � a@&�g$g�S-`${+#�� � %�S-#���l�;� � \-[�{ �J��[�g'�"#]&�c�S-[�`'lC�tS�Y���Y4}��;��� ��l h &y`'l&�c��& hmu \-� r �]\R[�nRc u � p &�ce& � g'&�#e&D\z\-�]\ �� c�#��"���eY �u ��ce&�#m{��"c�\�S-`$�a>&�#mU�S-`${�g u &�l��k[�nc u �>&�\V{�[�#�S-c u a #m� � %�S-#���l;&�c�ak[�l�c �;���J��l h &�`'l"Y ��u S_l�S_lLc u � h &�l��b� u �"`���& h�u lT[�%$# h �\-��&Dn�`$[ p �@S-`�c��"#el�� h celM��& h�u c]&�#�{��"cL\V��&�nq`$[ p ��} h &y%'lwS-`${9��& hmu [�n c u � �M��� $�� ��l�[�%$# h �@\V��&�nq`$[ p ��l;� u S hmuh [�`�ce&DS-`'l � \zSV`$��lCcm[ h [�aka;%$`�S h &yc�����S-c u ��& h�u [�nNc u � �;��� $�� ��ce&�#m{��"c�\V��&�n�`$[ p ��l"Y � � h &D\z\7c u &�c���� u & r �&;a>&��iS-a;%$a [�n � \zS-`$��l�S-`���& hmu l�[�%$# h �C\V��&�n�`$[ p ��}'&y` p c u &�c�c u �"#m��S_l&;c�[�ce&D\I[�n ��\zS-`$��l"Y

(���� ��� GIHI?$3�24?'* �b?<O1,/F ���<F$0 �

��u �+&D\-{�[�#�S-c u a no[�#�g'�"#Tno[�#ma;S-`${�c u �+l�g'&�c�S_&D\�#e&�`${�� � %$�"#�(�nt[�# p &yce& � g'&�#e&�\�\-�]\ ��� c�#��"��lLS_l r �"#�(9lwS-a;Sz\_&�#kc�[c u &�c��"akg�\-[�(�� p � u �"` h [�akg$%$c�S-`${kc u �CS-`�c��"#el�� h c�S-[�`X&�l p ��l h #�S-!'� p S-` � � h c�S-[�` � Y � Y � Y ��u �"#���&y#�� c���[ lTa>&D\z\ak[ p Sz� h &�c�S-[�`'l;c u &yc�&�#��@`$� h ��l�l�&�#�(�S-` & p &�g$cTSV`${�c u � p &�ce& � g'&�#]&D\z\V�]\ ��� cm#��"�kS-`�c��"#el�� h cTSV[�` &D\-{�[�#�S-c u a c�[X&l�g'&�cTS4&�\7#e&�`${�� � %$�"#�(+&D\-{�[�#�S-c u a�Y

�u �k�'#elTckak[ p S�� h &yc�S-[�`�S-` r [�\ r ��l;c u �+g$#m[ h ��l�l�[�n p �"c��"#�aMSV`�S-`${�c u �+ce&�#m{��"c�`$[ p ��l;��S-c u � u S hmu ��& hmul�[�%$# h ��`$[ p ��a;%'l�c h [�aba %$`�S h &�cm��YI��`�c u �RS-`�c��"#el�� h cTSV[�` &D\-{�[�#TSVc u a�}�c u S_l<#�� � %�S-#�� p �'` p SV`${�&�\�\$l�[�%$# h � � c]&�#�{��"c

= �

Page 58: O'3 0D. - cs.umd.edu

lines

leafnodes

source R-tree

d e b c i g h a f

ab

c

d

e f

gi

h

lines

intlist

leafnodes

target R-tree

m o p s n q u r t

m

n

p

o q

rs

t

u

A

B

C

D

A B C D

K

L

M

N

K L M N

� � � �L

intersectlist

c fi

��� ������� ��4 � ��/���� 01� 8�*�6�+)8%���&�(+�6�8+)8�) 8 � 8&"." �%" B +@�3�(�(' %4� +@< # *�8&" ��/ �2*�6 /+" 01/��9�?��*�� 0(8�+@� /�* '@0�<,�6 ��".�.*%� <�� ��<�".� ��<%+5�6 $=9�%')�G/!"�0��.� 0�" �('(H � * 8%01+@� )�7".�.*%�(' 8�*�6 *,/�6��(' 8%�3� '1< 8%6&�6 H��/�+5�7+@<�8+;/�*�" = ')/���� 01�9*%/ 6&�� *%�(�6�' + / 01/��9�?�&*2� 0(8+ ��%4� +@< 8 +)8%�3���(+?*%/�6���H � 8%���&�(+".��*,�('48 ��� � 8 � ���6 %�� +-<G+-<,�7* 8&�?�(' /+" +@<%���.*%+5�%�3')�01+@�.*%� ')/���� 01��"��.*%�(' H

`$[ p ��S-`�c��"#el�� h cTSV[�`'l"YC�tn�c u �;!'[�%$` p SV`${�#�� h ce&�`${y\V��lnt[�# ��& h�u l�[�%$# h �;`$[ p �M&y#����]�$c��"` p � p !i(+c u � #]& p S-%'l[�n�]�$g'&�`'lwS-[�`bSV`b��& h�u@p SVab�"`'lwS-[�`+g$#�S-[�#�cm[ h &D\ h %�\4&yc�S-`${>&D\z\'`$[ p ��S-`icm�"#el�� h c�S-[�`'l"}������"`'l�%$#��Cc u &�cR`$[�`$� h ��l�l�&�#�(l�[�%$# h �C\�S-`$�;c�[kc]&�#�{��"c�\zS-`$� h [�aka;%$`�S h &yc�S-[�`'l&�#���[ r �"#T\V[�[�U�� p Y

�u �>l�� h [�` p &y` p �'`'&D\�ab[ p Sz� h &�c�S-[�`�c�[+c u � p &�ce& � g'&�#]&D\z\V�]\ ��� c�#��"�MSV`�c��"#elT� h c�S-[�` &�\V{�[�#�S-c u a h [�` h �"#�`'lc u ��l�[�%$# h �C\zS-`$��cm[�ce&�#m{��"cR\zS-`$��S-`�c��"#el�� h c�S-[�` h &�\ h %�\_&�cTSV[�`IY � &yc u �"#c u &�` p �"c��"#�aMSV`�S-`${k� u �"c u �"#[�#�`$[�c�c ��[\zS-`$��l;S-`�c��"#el�� h c�} ��� h &D\ h %�\_&�c���c u � p S_l�c]&�` h �+!'�"c����"�"`�c u �+l�[�%$# h �+&�` p ce&�#m{��"c�\zS-`$��l"Y9� nqc u � p S_l�ce&y` h �@S4l\-��l�lCc u &�cCc u �;#e& p S-%'lC[�n��]�$g'&�`'lwS-[�`I}Jc u �;ce&�#�{��"c�\zSV`$�b��Sz\�\ h \-��&�#�\-(+S-`�c��"#el�� h c�c u �;�]�$g'&�`'lwS-[�`9#m�"{�S-[�`X[�n�c u �&�l�lT[ h S_&�c�� p l�[�%$# h �\zS-`$��&�` p l u [�%�\ p c u %'l�!/� a@&�#�U�� p Y &` h ��c u ��l��Cc���[ l�a>&�\�\<ak[ p S�� h &yc�S-[�`'l&�#��Ca>& p �Cc�[c u � p &yce& � g'&�#e&�\�\-�]\ ��� c�#m�"��S-`ic��"#]l�� h c�S-[�`+&D\-{�[�#�S-c u a�}�S-c�&�\4lT[�nt%$` h c�S-[�`'l�&�l�&�l�g'&�c�S_&D\<#e&�`${�� � %$�"#�(k&D\-{�[�#TSVc u a�Y

�u � p &�c]& � g'&�#e&D\z\-�]\ ��� cm#��"�>a@&�g l�g'&�c�S_&D\#e&y`${�� � %$�"#�(9[�g'�"#e&�cTSV[�` &D\_l�[Xce&�U���l �;�/� � � \-[�{ �J��c�S-ak��}��S-c u c u � h [�abg�\V�]��S-c�(�&�`'&D\-($lwS_l;!'�]S-`${�S p �"`ic�S h &D\Cc�[+c u &�c�[�nc u � p &yce& � g'&�#e&�\�\-�]\ ��� c�#��"�@a>&�gXS-`�c��"#el�� h cTSV[�`[�g/�"#e&�c�S-[�`�&�c�c u ���"` p [�n � � h c�S-[�` � Y � Y � Y

= �

Page 59: O'3 0D. - cs.umd.edu

r

a b

A

c

B

A'

r

r

r

��� ������� � ���#�! 8&�9 2" ��%�<,�%�3� +@<%� �%*�" 8 �����%�?�%*�+2/+"�+@<%� ')/���� 01� 6�8�+ 8�) �8%� 8&"�" �%",B +@���(� $�/���* 6 �.*%�9���01+)8�*%��" � � $�= +@<%�:�� � 8&*%'�� /�*�� 8%6 �.�%' ) ' 0��3�8�+@�.*%� $�/ �2*�6���*,���3�01+ 8&*%��" � � � *� &�5� /�� + /*%/ 6&� ��*,+ �%��')�01+@� /�*�6&�(+5�01+-� /�* � '�*%�01�(' '@8 ��=(H � <,��628�'1<%�6 $�/��2*�6 �.*%� ���01+)8�*%��" � �3�% ���� ')�%*,+ ':8 + 8 �����(+ 628�+ 8�) �8%� 8�"�" �%" B +-���(�7*,/�6�� +-< 8�+ 01/�*,+)8&�.*%' + 8 �����(+�".��*,� � H

(���� � � A�3�0DFiFsGPHJ?$3�24?'* � �1F$0�2-F$8

WS r ��c u &�c�c u � � � � c�#��"��a>&�U���l�%'lT��[�n�&�`bS-#�#��"{�%�\_&�# p � h [�akg'[il SVcTSV[�`+\zS-U���c u � �� c�#��"��}�c u � � � � c�#m�"�ql�g'&yc�S_&D\

� %$�"#�(�&D\-{�[�#�S-c u a@l &�#m� � %�SVcm�Ml SVaMS�\_&�#�cm[kc u [il�� p ��l h #�S-!'� p SV` � � h c�S-[�` � Y � no[�#c u � �� c�#��"��Y �u � � � � c�#m�"��� lp S_lE��[�S-`ic p � h [�abg'[ilwS-c�S-[�` p [���l u [���� r �"#@�"`'&�!�\-��\�S-`$��lT�"{�ak�"`�cel;c�[��]�iS_l�cbS-` p S !I�"#��"`�cb\V��&�n `$[ p ��l;S-` &�`&�`'&D\-[�{�[�%'l n &�l u SV[�`+c�[;c u ��!$% h U��"c|�x � � %'& p c�#��"��Y ��u S_llTa>&D\z\ p S !I�"#��"` h �Lno#m[�a c u � �� c�#��"�k�w� u S h�u�p [���lg'�"#ma;S-c &b\zS-`$� l��"{�ak�"`ic�cm[k\zS-�kS-`9ab[�#��;c u &�`X[�`$��\-��&Dn`$[ p ���C#���l�%�\-cel�S-`�l�[�ak�k& p$p S-c�S-[�`'&D\�g$#m[ h ��l�l SV`${ S-`c u � � � � cm#��"� &�\V{�[�#�S-c u a>lk&�l h [�akg'&�#�� p ��S-c u c u � h [�#m#���l�g'[�` p SV`${ ��� c�#��"��&D\-{�[�#�S-c u a>l p %$�+c�[�S-` h #���&�lT� p`�%$a !/�"#el�[�nN\zS-`$��l�&�` p `$[ p ��l Y

(���� ��� BC.1*��I,/.IOI2���?$3�24.IO

��u � � � � c�#��"�bg'[�\-(�{�[�`�S���&�c�S-[�` &D\-{�[�#�S-c u a S_l r �"#�(9lwS-a;Sz\_&�#;c�[�c u &�c�nt[�#�c u � ��� c�#��"�+&�l p ��l h #�S-!'� p S-` � � h]�c�S-[�` � Y � Y � YN��� h &y%'l���c u � � � � c�#m�"���"akg�\-[�($l& p S_lE��[�S-`ic p � h [�akg/[ilwS-c�S-[�`I}'&kl SV`${y\V�L\zSV`$��a>&D(k#���lwS p �LSV`+ab[�#��c u &�`�[�`$��\-��&Dn�`$[ p �@� l SVaMS�\_&�#�cm[kc u ��!$% h U��"c�|�x � � %'& p c�#��"���eY��w`X[�# p �"#Cc�[ u &�` p \-�kc u S_l p S"!P�"#m�"` h �k��S-c u#���l�g/� h c;c�[+c u � ��� cm#��"��}Nc u �kg'[y\V(�{�[�`�S���&�cTSV[�` &D\-{�[�#�S-c u a a;%'l�c�!'� h�u &�`${�� p l�[�ak�"� u &�c p %$#�S-`${Xc u �k`$[ p �ak�"#�{ySV`${bg u &�l���Y

� &�c u �"#+c u &�`�a>&y#�U�S-`${�&D\z\�\�S-`$��l�c u &�c@S-`�c��"#el�� h c�&y`i( [�n c u �s[ r �"#�\_&�g$g�S-`${ #��"{�S-[�`'lbnt[�#�ab� p !i( c u �!'[�%$` p SV`${�!'[D�$��lC[�n�c u �;`$[ p ��lCc u &�c�&�#��;ak�"#�{ySV`${X��&�lc u �"#��k&�#��;`$[�`$�;��S-c u & p S_lE� [ySV`�c p � h [�akg/[ilwS-c�S-[�`<�e}c u ��%$g p &�c���g$#m[ h � p %$#��Lno[y\�\-[�� l�c u ��c�� h�u `�S � %$� p ��l h #TSV!/� p SV`�c u ��!$% h U��"c |�x � � %'& p c�#m�"��g'[y\V(�{�[�`�S���&�cTSV[�`&D\-{�[�#TSVc u a S-` � � h cTSV[�` � Y � Y � Y � \z\�c u �;\zS-`$��l�S-`�c u �kak�"#�{�� p lwS-!�\zSV`${s`$[ p �+&�#��;�'#]l�c�l�[�#�cm� p & h"h [�# p S-`${Xc�[S p �"`icTS��'�"#D} &�` p &D\z\ p %$g�\zS h &�c���\zS-`$��l+&�#��+a>&�#mU�� p nt[�#k#��"!$#m[i& p$h &�l�cTSV`${�&�ak[�`${9c u �+\zS-`$��lbSV` c u ��ab�"#�{�� p

=��

Page 60: O'3 0D. - cs.umd.edu

`$[ p ��l"Y ��u S_l��"`'&y!�\V��lMc u � h [�#�#m� h c�%$g p &yc�S-`${ [yn p %$g�\zS h &�c��@\zS-`$��l�S-`�c u �kak�"#�{�� p `$[ p ��l Y ��u � p %$g�\zS h &�c��`$[ p �k#��"!$#�[i& p$h &�l�c�S-`${+[�g/�"#e&�c�S-[�`XS_lC%'l�� p c�[+%$g p &�cm�kc u �;��S-`${�� p�� � p {��@#��"g$#���l��"`�ce&�cTSV[�`'lC[�n&D\z\ p %$g�\zS h &�c��\zS-`$��l &�` p a@&DS-`ice&�SV` h [�`'lwS_l�c��"` h (�Y�jC%$#�S-`${kc u ��%$g p &�c���}$����`$[�cm�q&�`�(@g'[�\-(�{�[�`@S p �"`icTS��'�"#]lCc u &�c�a;%'l�c&D\_l�[!'�@%$g p &yc�� p � S Y ��Y-}7&�ab[�`${ p %$g�\zS h &yc��@\zSV`$��l }NSzn[�`$�;\zSV`$� u &�l�g'[y\V(�{�[�`sS p �"`icTS��'�"#]l�c u &�c &�#m��\-��l�l�c u &y`9c u �g'[y\V(�{�[�`�S p �"`�c�Sz�'�"#elb[�nc u ��l�� h [�` p \zSV`$���]Y��w` & p$p S-c�S-[�`I}�&D\z\�\zS-`$��lb� u [il��@�"` p g'[�S-`�cel�n�&D\z\[�` & h [�abak[�``$[ p �k!'[�# p �"#�&�#��;a>&�#�U�� p nt[�#Cc u �;#��"!$#�[i& p$h &�l�c�[�n�c u �]S-#��"` p g'[�S-`�c h [�[�# p S-`'&�c���lqSV`s[�# p �"#�c�[@%$g p &�cm�kc u ���S-`${�� p�� � p {���#��"g$#���l��"`�ce&�cTSV[�`'l�&y` p g/[�\-(i{�[�`@S p �"`�c�Sz�'�"#el�[�n�&�`�(;\zS-`$��c u &yc�a@&�(kl u &y#��q&y`+�"` p g'[�S-`�c!$%$c�\zS-�S-` &�`$[�c u �"#`$[ p ��Y

� n7&�`i(�\zS-`$� u &�l�S-cel�g'[�\-(�{�[�`bS p �"`�c�Sz�'�"#el�%$g p &�c�� p@p %$#�S-`${;c u ��'#]l�c�#�[�%$` p [�nI#��"!$#m[i& p$h &�l�cTSV`${/}�c u �"`@c u �g'[y\V(�{�[�`sS p �"`icTS��'�"#b%$g p &�c��@a;%'l�c�!/� h [�aka;%$`�S h &�c�� p S-` &�l�� h [�` p #�[�%$` p [�n!$#�[i& p$h &�lTc�S-`${ cm[ &D\z\�[�c u �"#\zS-`$��l;S-`�c u �>ab�"#�{�� p `$[ p ��Y � [ h &D\z\-(�}RSzn�c u �@c�#e&�`'l�aMSVcmc�� p g'[y\V(�{�[�`�%$g p &�c��@a>&�c hmu ��l��]S-c u �"#;c u �k\-�]ntc;[�##�S-{ u cg'[y\V(�{�[�`@S p �"`�c�Sz�'�"#el�[�n7c u �C\-[ h &D\I\zS-`$��}'c u �"`+c u �C\V[ h &D\7g/[�\-(i{�[�`@S p �"`ic�Sz�'�"#CS_l�%$g p &�c�� p cm[ #m�1J'� h cc u �g'[y\V(�{�[�` S p �"`ic�Sz�'�"#el�c u &�c u & r ��!'�"�"`�!$#m[i& p$h &�l�cDY

� lPS4lNc u � h &�l�����S-c u c u ��!$% h U��"c�|�x � � %'& p c�#��"�&�` p���� c�#��"��g'[y\V(�{�[�`�S���&�cTSV[�`>&D\-{�[�#�S-c u a@l"}�c u ��ab�"#�{�S-`${&�` p %$g p &�c�S-`${+g$#�[ h ��l�l h [�`�c�S-`i%$��l�%$g�c u ���"`ic�S-#�� � � � c�#��"��%$`�c�Sz\�&D\z\I\zSV`$��l�&y#�� h [�`�ce&DS-`$� p S-` &blwS-`${�\-��`$[ p �&�` p &D\z\R`$� h ��l�l�&�#m(>!$#�[�& p$h &�l�cel u & r ��!/�"�"`�a>& p ��Y

(���� ��� GIHI?$3�24?'* *<.12 O

��u � � � � c�#m�"� l�g'&�cTS4&�\� [�S-` &D\-{�[�#TSVc u a>l+� SV`�c��"#elT� h c�S-[�` &�` p l�g'&�c�S_&D\�#e&�`${�� � %$�"#�(/�M&�#m�+S p �"`icTS h &�\ c�[�c u �[�`$��lC%'l�� p ��S-c u c u � ��� c�#m�"�;S-` � � h c�S-[�` � Y � Y � }'��S-c u [�`$�@l�a>&D\z\�ak[ p Sz� h &�c�S-[�`�&�c�c u �k�"` p [�n�g$#�[ h ��l�lwS-`${'Y��� h &�%'l���c u � p S_lE��[�S-`ic p � h [�akg'[il SVcTSV[�`+[�n7c u � ��N� c�#��"�Ca>&D( h &�%'l���l�[�ak�\zS-`$��l�c�[;!/��l�g�\zSVcC& h #�[il�l a;%�\VcTSVg�\-�\-��&Dn`$[ p ��l }IS-c�a>&D(�!'�@c u � h &�l��;c u &�c &b\zS-`$�@S-`9c u �>lT[�%$# h �ka>&ygXS_l�[�`�\-(X��S-c u S-` & {�S r �"` p S_l�ce&y` h �>[�n&g'[�#�c�S-[�`�[�n &+\zS-`$�+c u &�c u &�l�!'�"�"` l�g�\zS-c�S-`�c u �>c]&�#�{��"c�a>&ygIY ��u %'l"}R&@\zS-`$�+S-`�c u �@ce&�#�{��"c�a>&�g9a@&�(X!/�a>&�#mU�� p &�l���S-c u S-` &�{�S r �"` p S4lTce&�` h ��ak[�#m��c u &�`@[�` h ��Y �u S4l�S4l�&�`'&D\-[�{�[�%'lc�[;c u ��lwS-c�%'&�c�S-[�`+�"` h [�%$`ic��"#m� p&�cCc u ���"` p [�n�c u � |�x � � %'& p cm#��"� l�g'&yc�S_&D\1��[�S-`�� l��"� � � h c�S-[�` � Y � Y � �eY��w`�&+l SVaMS�\_&�#Cn�&�l u S-[�`I}<c]&�#�{��"c�\zS-`$��l&�#����'#el�cl�[�#�c�� p !i(bS p �"`ic�Sz�'�"#�} c u �"`�&�`@%$gi�&�# p S-` h \-%'lwS r �kl��"{�ak�"`�c�� p a>&D��S-a;%$a l h &�`I}$&�` p & p [���`i�&�# pS-` h \-%'lwS r � l��"{�ak�"`icm� p�h [�gi(9l h &y`�[�g'�"#e&yc�S-[�` &y#��>%'lT� p c�[X#��"ab[ r �>&�`�( p %$g�\zS h &yc���l>&y` p n�&D\_l��@`$�"{i&�c�S r �]\-(a>&�#mU�� p \zS-`$��l"Y � S-`$��l�&�#�� h [�`'lwS p �"#�� p n�&D\_l���`$�"{i&�c�S r �]\-(Xa>&�#�U�� p Szn&�`$[�c u �"#S-`'l�c]&�` h �;[�n�c u �kl�&�ak�L\zSV`$�MS4la>&�#mU�� p &�lJS-`�c��"#el�� h c�S-`${'}$&�` p c u �"(k&�#��`$[�cRa@&�#�U�� p Y ��u �#m�"ak[ r &D\'[�nIc u � p %$g�\�S h &�cm��l&�` p n�&D\_l��`$�"{i&yc�S r ��l#���l�%�\-celS-` &D\z\7c]&�#�{��"c�\zS-`$��l!/�]SV`${+g$#m[�g'�"#�\-(+a>&y#�U�� p Y

= �

Page 61: O'3 0D. - cs.umd.edu

� BCF$0D:�.10�6X?<OP�yF ��.I69HI?'0�2E8".JO

��u �Cg'�"#�nt[�#�a@&�` h �[�nIc u �c u #��"�qlTg'&�c�S_&D\PlTc�#�% h c�%$#���l�S-`>c u � p &�ce& � g'&�#]&D\z\V�]\<�"` r S-#�[�`$ak�"`�c�S_l h [�akg'&�#�� p %'l SV`${c u ����%$#m��&�%;[�n'c u � � �"`'l�%'l � ��W�Q �C��� S-`$� �JSz\V��a>&yg�[�n1| #�S-` h � WC�"[�#�{���l � [�%$`�c�(�}�xXj � h [�`�ce&DS-`�S-`${q&�g$g$#m[�� �S-a>&�c��]\-( � =$} � � \zSV`$�@l��"{�ak�"`�cel"}<l u [��`+S-`��JS-{�%$#m� ��� �eY$&%$# p &yce& � g'&�#e&�\�\-�]\�&D\-{�[�#�S-c u a@l�&�l�l�%$ak��c u &�cCc u ��"`�c�S-#�� p &�ce&�l�c�#�% h cm%$#��#���lwS p ��l S-`ka>&DS-`@ak�"ak[�#m(�[�nIc u � �u SV`$U�S-`${>xX& hmu SV`$��l � x � =;� ��� g$#�[ h ��lml�[�#el"} � Wq���� xs�eY ��u %'lab��&�l�%$#��"ak�"`�cel�[�nR� � & g'�"#Tno[�#ma>&�` h � &y#���ak��&y`�SV`${y\V��lml�SV`Xc u S_l h [�`�c��]�~c���c u � p � r �]\V[�g$ak�"`ic[�n p S_l�U � !'&�l�� p�p &�c]& � g'&�#e&D\z\-�]\�&�`'&D\-[�{il�c�[kc u � p ��l h #�S-!'� p &D\-{�[�#TSVc u a>l�S_l &bl�%$!$��� h c�no[�#�no%$cm%$#���#���l���&�# h�u �eY

��� ���2�3� � ���4E�8� �/+" A �5��* 01��� �(/��3���('�� /���*%+ = � E�� H

� ��� =@?$3"? G<3�0,�P��3 �I0DF ���I2_* � BCF$0�:w.10�6X?<OP��F

�JS-{�%$#�� ��� g$#���lT�"`icelCc u � !$%�Sz\ p c�S-ak��l�nt[�#�c u �;c u #��"� p &�c]&+l�c�#�% h c�%$#m��l�no[�#C`$[ p � h &�g'& h S-c�S-��l�#]&�`${�S-`${+nt#�[�a=bc�[�= Y �u � � � � c�#m�"���&�l�!$%�S�\-c���S-c u & ��� Y = � aMSV`�S-a>&�\�[ h"h %$g'&�` h ( \-� r �]\���l��"��c u � p S_l h %'l�lwS-[�`9!/�]\-[��L�eY�$#m[�a c u ��'{�%$#���}'&D\z\Ic u #��"��l�cm#�% h c�%$#���l��]� u SV!�S-c p � h #���&�lwS-`${k!$%�Sz\ p cTSVab��l&�l�c u ��`$[ p � h &�g'& h S-c�S-��l�S-` h #���&�l���Y��u S_l�!'� u & r SV[�#�S_l p %$��cm[�c u � p � h #���&�l�� p &yak[�%$`�c�[�n7l�g'&�cTS4&�\JlT[�#�c�S-`${�c u &�c�ce&�U���l g�\4& h ����S-c u c u �S-` h #���&�lT� p

��

Page 62: O'3 0D. - cs.umd.edu

10

50

100

250

500

1000

15002000

0 10 20 30 40 50

CPU Seconds (log scale)

Node Capacity

R+-treeR-tree

bucket PMR quadtree

��� �������� � � �����." 6�+@���G�('1" /�� +-<,� +-<2�3�(� 6�8�+ 8 ')+@� � 01+-�2�3�('#" /�� +-<,��� 8& 4/+" A �5��* 01� � �(/������('� /��2*%+ =�� E�� ' � � � � � ��"��.*%�('�*�H

`$[ p � lwS��"��l"YR��%�S�\ p S-`${kc�S-ak��lJnt[�#Nc u ��c u #��"� p &�ce&Cl�c�#m% h c�%$#���lN�]� u SV!�S-c�&�`'&D\-[�{�[�%'lN!/� u & r S-[�#NS-`kc u �l�� � %$�"`�c�S_&D\�"` r S-#�[�`$ab�"`ic$� Z�[i�]\ ��� � YN��cRS_l�&D\_l�[k&�g$g'&�#m�"`ic�c u &�c�!$%�Sz\ p S-`${>c u �!$% h U��"c|�x � � %'& p c�#��"��S_l�&yg$g$#�[D�iS-a>&�cm�]\V(� � � c�S-ak��l n &�l�c��"#�c u &�`>c u � ��� cm#��"�nt[�#�lwS-a;Sz\4&y#`$[ p � h &yg'& h S-c�S-��l"Y ��u �C#��]\_&�c�S r � p S"!P�"#m�"` h �CSV`+!$%�Sz\ p g/�"#�nt[�# �a>&�` h �S4l�&�c�c�#TSV!$%$c]&�!�\-�c�[�c u �%'lT�[�nP&L#��"{�%�\_&�# p � h [�abg'[ilwS-c�S-[�`bS-`>c u � h &�l���[�nIc u �!$% h U��"c�|�x � � %'& p c�#��"�� u S hmu a@&�U���l�S-c r �"#�(+��&�l�(+c�[>l�g�\zS-c�&�`�[ r �"#)J'[���S-`${>`$[ p � &�l�c u �"#��LS_l�� %'l�cC[�`$� h�u [�S h ��Y���` h [�`�c�#e&�l�cD}$c u ���� c�#m�"�q&�` p c u � � � � cm#��"�a>&�U�� %'l��C[�nIS-#�#m�"{�%�\_&�# p � h [�akg'[�lwS-c�S-[�`+� u S h�u #m� � %�S-#���l�cm��l�c�S-`${k&�g'[�l�lwS-!�\-(@\4&y#�{��`�%$a !/�"#el�[�n�l�g�\zS-cq&��iS_l ��h [�[�# p S-`'&�cm��g'&DS-#elS-` p �"c��"#�aMSV`�S-`${+&�\-[ h &�\�\-(�[�g$c�S-a>&D\7`$[ p � lTg�\�S-c�Y

�JS-{�%$#m� ��� l u [�� l;c u ��!$%�Sz\ p c�S-ak��lMno[�#bc u � � � � c�#��"��[�n�c u � � #�� p �"#�S h U$l�!$%$#�{/}(0 � a>&yg h [�`ic]&DS-`�SV`${&�g$g$#�[D��S-a>&�c��]\-( ���� � \zSV`$�9l��"{�ak�"`ic]l+� lT�"� �JS-{�%$#�� � ��nt[�#>&sa>&�g�[�n � #�� p �"#�S h U$l�!$%$#�{ �eY���` & p$p S-c�S-[�`�c�[r &y#�(�S-`${;c u �`$[ p � h &�g'& h S-c�( !/�"c����"�"` �� &�` p = }���� &�\4lT[ r &�#�S-� p c u �a;S-`�S-a>&D\I[ h"h %$g'&�` h (;\-� r �]\_l�!'�"c����"�"`� = � &�` p = �� � &�lk&9g/[�S-`ic+[ynq#��]nt�"#��"` h ��}�c u ��!/��l�c+g'�"#�nt[�#�a@&�` h �+nt[�#>&�` ��� c�#��"��}�c��"#�ak� p &�` � � � c�#��"�� ��� h U �� �� } u &�l;!'�"�"`�[�!'l��"# r � p c�[X!/� �i �� &�` p S_l;c u �+[�`$�@c u &�c;���@%'l��@S-` [�%$#;�]�$g'�"#�S-ak�"`�cel]�eY�� u �"`l�g�\zS-c�c�S-`${k&�`$[ p ��}$&�a;S-`�S-a>&D\<[ h"h %$g'&�` h (M\V� r �]\P[yn � � �"`'l�%$#���l c u &�c���& h�u [yn1c u �c���[�#���l�%�\-c�S-`${;`$[ p ��lRS_l�&�c\-��&�l�c � � nt%�\z\ Y�Z��"` h ��}$� u �"`+c u ��a;S-`�S-a>&D\N[ h"h %$g'&�` h (b\-� r �]\IS_l�#e&�S4lT� p }�no�"���"#l�g�\zS-cq&��iS_l ��h [�[�# p S-`'&�cm��g'&DS-#el&�#��Cc���l�cm� p � u �"` hmu [�[ilwS-`${;c u � !/��l�c l�g�\zS-c�Y �u S4l#���l�%�\-cel�S-`@S-` h #���&�lwS-`${kc u ��l�g'�"� p [�nN[�nIc u ��!$%�Sz\ p g$#�[ h ��l�l&�l h &�`@!'��l��"�"`bS-`��JS-{�%$#�� ��� Y � l S4l�c u � h &�l��nt[�#�c u �q| #�S-` h �kWC�"[�#�{���l a>&�gbSV`��JS-{�%$#m� ��� }�S-` h #���&�lwS-`${@c u �`$[ p � h &�g'& h S-c�(+&D\_l�[k#���l�%�\-celS-` p � h #���&�l�� p !$%�Sz\ p c�S-ak��l"Y

�wc@S_lbSVabg'[�#�c]&�`ic+cm[�`$[�cm� c u &�c &�\Vc u [�%${ u c u � p &�ce&s[�nM�JS-{�%$#m� ����h [�#m#���l�g'[�` p l+c�[�&9a@&�g�c u &�cbS4l

�$�

Page 63: O'3 0D. - cs.umd.edu

��� ���2�3�� ���;E�8� /+"��&�3�6��%� � 0��('�$2����� ��� D4H

25

30

35

40

45

50

0

100

200

300

400

minimal occpancy level (%)

node capacity

CPUseconds

10

20

30

40

50

��� �������� � � �! %�0��,+-� /�*�+@���G�('$�.*?')�01/�*�6&'#" /�� +@<%� B � +@�3�(� $2���." 6�8�" ��/��5� +@<�� " /�� +@<%��� 8& /+":�&���6&�%�5� 0�� '�$��2�3� ��� D ' ��� � � "��.*%�('�*�H

&�g$g$#�[D��S-a>&�c��]\-(;= � [�nCc u � l S �"�+[yn c u &�cLSV` �JS-{�%$#m� ��� �tS�Y���Y4} ���� � \zSV`$��l r �"#el�%'l � =$} � � \zS-`$��l]�e}�c u � � � �c�#��"�+c]&�U���l ��� �$Y ��lT� h [�` p lkcm[9!$%�Sz\ p � u Sz\-�Xc u � ��� c�#m�"�9��%'lwS-`${�&X`$[ p � h &�g'& h S-c�(�[�n = &�` p &Xa;S-`�S-a>&D\[ h"h %$g'&�` h (�\-� r �]\ [�n �� �� �Cno[�# c u ��l�&�ak�@a>&�g�#�� � %�S-#���l ��� Y �Xl�� h [�` p l;c�[X!$%�Sz\ p &�` p c u �+!$% h U��"c@|�x �

� %'& p c�#��"�@#�� � %�SV#m��l���%'l�c ��� Y l�� h [�` p l"YB�s�@no[�%$` p c u &�c p ��l�g�S-c���c u � ��� c�#��"��&�` p�� � � c�#m�"�+!'�]S-`${ � %�SVcm�lwS-a;Sz\_&�#CS-` l�cm#�% h c�%$#���}$c u � � � � c�#m�"��ce&�U���l&yg$g$#�[D�iS-a>&�cm�]\V(+c���[;[�# p �"#el[�n�a@&�{�`�S-c�% p ��\-[�`${��"# c�[b!$%�S�\ p g'�"#\zS-`$� l��"{�ak�"`ic�S-`9c u � p &�ce&�l��"c��w��Y�{'Y-}'lT�"�M�JS-{�%$#m� �~� �eY ��u S_l p S"!I�"#��"` h �;S_l�&�c�cm#�S-!$%$ce&�!�\-�kc�[+& h [�a !�S-`'&�cTSV[�`

���

Page 64: O'3 0D. - cs.umd.edu

� 8�$2" �!����� 8�+ 8�')+@� � 01+-�2�3� $��2��" 67')+ 8�+@� ' +-� 01' " /�� +@<%��B +@�3�(�!8&* 6 B�� +-���(� $�/&+@< �%'���*,� 8&*8%�3+@� # 0�� 8�"�" = <2� ��< 4 ��H ��� �9�.*���� 8&"�/ 0(0��� 8&*�01= " � )�%" " /���+-<,� A � �.*�01��� �(/������('7� 8& �H D "�"+@���G�(' 8 ������*?')�01/�* 6&'(H

" � $ � ��� . )0� � � � � . )0� �� � ' � � . � . +!� � � � " � . +!� � � � " �� � � �

�� � � � � � � �

�� � � � � � �

� � � ��� � � � � � �

�� � � � � �

� � � ��� � � � � � � �

�� � � � ��� �

� � �� � � � � � �

�� � � � � � �

� � ��� � � � � � �

�� � � � � �

� � � ��� � � � � �

�� � ��� � � �

[�n7c u � %'l��C[�n7c u �ql h &y`>ak[ p �]\7&�` p c u �n�& h c�c u &�c�c u � ��� c�#��"� p [i��l�`$[�c��"akg�\-[�(>& p S_lE��[�S-`ic p � h [�akg'[il SVcTSV[�`[�n�l�g'& h �X��c u %'l;g$#m� r �"`icTSV`${sc u � h�u Sz\ p #��"`�[�n�&Xl�g�\zSVcmc�S-`${�`$[ p � no#�[�a c u �"a>l��]\ r ��l@l�g�\zSVcmc�S-`${$�e}�a>&�U�SV`${sS-cg'[�l�lwS-!�\-�kc�[ p �"c��"#�a;S-`$�;c u ��\-[ h &D\z\-( [�g$c�S-a %$a `$[ p �kl�g�\zS-c���S-c u & h [�`'lTce&�`�c`i%$a;!/�"#;� &�g$g$#�[D��SVa@&�c��]\-( �� �[�n�%$g��&�# p &y` p p [��`��&�# p l h &y` [�g'�"#e&�cTSV[�`'l"YC��` h [�`�c�#e&�l�cD}'c u ��`$[ p �@l�g�\zSVcmc�S-`${+g$#�[ h ��lml�SV`sc u � � � � cm#��"��}��S-c u S-cel p S_lE��[�S-`�c p � h [�akg/[ilwS-c�S-[�`9[ynl�g'& h ��}/S_l�&�`�SVcm�"#e&�c�S r �;g$#�[ h ��l�lC� u �"#��bc u �;`i%$a;!'�"#�[yn�S-c��"#e&�cTSV[�`'l�S4lp S-#�� h c�\-(+g$#�[�g/[�#�c�S-[�`'&�\7c�[;c u ��`�%$a !/�"# [ynIS-c��"a>l�S-`�c u ��`$[ p ��c u &�c�S_l!/�]SV`${+l�g�\zS-c�Y ��u S_lc���lTc�S-`${;no[�#lTg�\�S-celak��&�`'lNc u &�c�&�\_&�#m{���`i%$a;!'�"#R[yn h \zS-g$g�SV`${b[�g'�"#e&yc�S-[�`'lNa;%'l�c7!/�g'�"#Tno[�#mak� p &�lN����`$�"� p c�[ p �"cm�"#�a;S-`$�� u S hmug'&�#�cL��[�#�g'&�#�cel ��[yn�c u �C\zS-`$��S_l &�lml�[ h S_&�cm� p ��S-c u c u ��c���[;`$[ p ��l�#���l�%�\-c�S-`${bno#m[�a c u � l�g�\zS-c�Y

*�[�c��bc u &�c�&D\-c u [�%${ u c u �b!$% h U��"ck|�x � � %'& p c�#��"�+���SVc u S-cel p S4lo� [�S-`�c p � h [�akg/[ilwS-c�S-[�`<��&D\_l�[�#�� � %�S-#���l\zS-`$� h \zSVg$g�S-`${'}J��& hmu \zS-`$��S_l h \zSVg$g/� p S-`Xg'&�#e&�\�\-�]\�&ka@&D�iS-a;%$a [�nRnt[�%$#cTSVab��lc u � u �]S-{ u c�[yn�c u ��c�#��"��Y � \_l�[c u �Cn�& h c�c u &�cc u ��!$% h U��"c|�x � � %'& p cm#��"���"akg�\-[�(~lC&�#��"{�%�\_&�# p � h [�abg'[ilwS-c�S-[�`�ak��&�`'l�c u &�c�� u �"` &�`$[ p �S_l lTg�\�S-c�}/c u �"#���&y#����(!I� h c�S r �]\-(+[�`�\-(+c ��[ h &�` p S p &�c��kl�g�\zS-cq&D��S_l ��h [�[�# p S-`'&�c���g'&�SV#]l"Y

�wcS_lS-`ic��"#m��l�c�S-`${+c�[@[�!'l��"# r ��c u &�c c u � � � � c�#m�"��lc u &yc����!$%�Sz\-c�nt[�#c u �;|R#�S-` h �@W �"[�#m{���la@&�g�%'l�� p &a;S-`�S-a>&D\7[ h"h %$g'&�` h (@\-� r �]\7[yn �i� Y = � ��#���lT%�\VcTSV`${MSV`X&�g$g$#�[D��SVa@&�c��]\-( �� � � \zS-`$� h \zS-g'l]�&�` p &;`$[ p � h &yg'& h S-c (r &y#�(�S-`${9!/�"c����"�"` � =�&�` p = Y ��u S_l;c�[�[�UX!'�"c����"�"` ���� �� Y � l�� h [�` p lk&�` p��D���i� Y � lT� h [�` p lk&�l;l u [��`sS-`� &�!�\-� � Y ��u � &�`'&�\V[�{�[�%'l �� c�#��"�����"abg�\V[�(�S-`${ c u � l�&�ak��`$[ p � h &yg'& h S-c�S-��l�&y` p a;S-`�S-a>&D\1[ h"h %$g'&�` h (;\-� r �]\_l]�c�[�[�U+!'�"c����"�"` ��� Y � l�� h [�` p l�&�` pX� �$Y+=>l�� h [�` p l"Y$*[�cm��c u &�c�Szn����;��[�%�\ p�u & r ��%'l�� p &�` � � � c�#��"����S-c u &a;S-`�S-a>&D\[ h"h %$g'&�` h (X\-� r �]\�[yn �� �� � &�l�SV`�c u � �� c�#��"���e}Nc u ��l��b`i%$a;!'�"#]l���[�%�\ pXu & r �b!'�"�"`�&�c�\-��&�l�c�[�`$�[�# p �"#�[�n�a@&�{�`�S-c�% p � u S-{ u �"#DY�v�`�no[�#�c�%$`'&�c��]\-(�} p %$��c�[ u &�# p �&y#��q&y` p c�S-ak�L\�S-a;S-ce&yc�S-[�`'l�������"#���`$[�cC&�!�\-�c�[kg/�"#�nt[�#�a c u ��lT��c���l�cel"Y

���

Page 65: O'3 0D. - cs.umd.edu

50

100

250

500

1000

1500

2000

0 10 20 30 40 50

CPU Seconds (log scale)

Node Capacity

R+-treeR-tree

bucket PMR quadtree

��� ���2�3��� ���4A�/�" =���/�*�� �8�+@� /�* �� ,�0��%+@� /�*?+@���G�(' " /�� +-<,� +-<2�3�(� ' +-�5��01+@�����('(H

� ��� BC.1*��I,'.JOP2���?$3�24.IO BCF~0D:�.<0�6 ?<OI��F

�JS-{�%$#�� �� l u [�� l;c u ���]�$� h %$c�S-[�`�c�S-ak��l;nt[�#ka@&�g�g'[�\-(�{�[�`�S���&�c�S-[�` no[�#b��& h�u [yn�c u ��c u #m�"��l�g'&�c�S_&D\ p &�ce&l�c�#m% h c�%$#���lN%'lwS-`${�c u �| #�S-` h ��W �"[�#�{���lNa>&�g'lN!$%�Sz\-cRS-` � � h cTSV[�`�=$Y � YNjC%$�c�[Cc u ��g'�"#�nt[�#�a@&�` h ��S-`$�]� h S-�"` h S-��l[�n;c u � � � � c�#��"��}C&�a;S-`�SVa@&D\ [ h"h %$g'&�` h ( \-� r �]\ [�n ��� Y = � �&�l@�"akg�\-[�(�� p }C� u Sz\V�sc u � ��� c�#m�"� %'lT� p c u �l�ce&y` p &�# p@�i �� \-� r �]\�Y � #�[�a c u �L�'{�%$#��LSVcCS_l h \-��&�# c u &�cnt[�#g/[�\-(i{�[�`�S���&�c�S-[�`I}<c u ��!$% h U��"c�|�x � � %'& p c�#��"�[ !I�"#el;lwS-{�`�Sz� h &�`�ckg'�"#Tno[�#ma>&�` h ��& p�r &�`ic]&�{���l�[ r �"#;!'[�c u c u � ��� c�#��"��&�` p c u � � � � c�#��"��Y ��u � p S"!P�"#m�"` h �S_l@#�[�%${ u \-( [�`$�X[�# p �"#@[�n�a>&�{�`�S-c�% p ��Y ��c@S_l+&�c�c�#TSV!$%$c]&�!�\-� g$#TSVa@&�#�Sz\-( cm[�c u � h [�`'lwS p �"#e&�!�\-��&�ak[�%$`�ck[�nc�S-ak��c u &�cc u � ��� c�#��"�k&�` p c u � � � � c�#m�"��a;%'l�c�l�g'�"` p SV` p �"c��"#ma;S-`�SV`${+� u S hmu `$[ p ��l�&y#��CS-`ic��"#]l�� h c�S-`${X��[�#& p ��[�S-`�S-`${@SV`Xc u � h &�l���[�n�c u � � � � c�#m�"����� u �"`�ak�"#�{�S-`${+lwS-!�\zSV`${�`$[ p ��l Y �$[�#c u ��!$% h U��"c�|�x � � %'& p cm#��"��}c u S_l h [�akg$%$c]&�c�S-[�`�S_l�SVabak� p S_&�c��>&�lC&b#���l�%�\-c�[�n�#��"{�%�\_&�# p � h [�akg'[il SVcTSV[�`IY��w`�& p$p SVcTSV[�`I}7&�cC��& hmu lTce&�{���[�nc u ��g'[�\-(�{�[�`�S���&�c�S-[�`�g$#�[ h ��lml"}'c u � ��� c�#��"�;&�` p�� � � cm#��"��ak�"#�{���a@&�`i(@ak[�#m��`$[ p ��l � \�S-`$��lLc�[�{��"c u �"#C�tS�Y���Y4}'&`$[ p � [ h"h %$g'&�` h (�[�n � S-akg�\zSV��l�&;n�&�`$[�%$cC[�n � �]}'� u Sz\-�;nt[�#c u ��!$% h U��"cq|�x � � %'& p c�#m�"��nt[�%$# `$[ p ��lC&�#��ak�"#�{�� p c�[�{��"c u �"#�&�c���& h�u l�ce&y{���[�nIc u � h [�akg$%$ce&�c�S-[�`IYRQ�l�l��"`�c�S_&D\z\V(�} c u � !$% h U��"c�|�x � � %'& p cm#��"�g'�"#Tno[�#ma>l&\4&y#�{��"#R`�%$a !/�"#���� � %'&D\~cm[ c u � u �]S-{ u cR[�n1c u ��cm#��"���1[yn1l�a>&D\z\-�"#�`$[ p ��ak�"#�{���l����SVc u #���l�g/� h c�c�[Cc u ��`�%$a !/�"#[�nR`$[ p ��l�!'�]S-`${@ak�"#�{�� p � SV`�g'&�#e&D\z\-�]\Rc u &�`+c u � ��� cm#��"� &�` p c u � � � � c�#��"��Y

���

Page 66: O'3 0D. - cs.umd.edu

� ��� GPHJ?$3�2-?'*+*<.12 O BCF~0D:�.<0�6 ?<OI��F

��u �+U��"(sS_l�l�%$� SV` c u ��l�g'&�cTS4&�\�� [ySV`�g/�"#�nt[�#�a>&�` h �+[ynqc u �+!$% h U��"c>|�x � � %'& p c�#��"� r S4l � & �tr S_lbc u � �� c�#��"�&�` p c u � � � � c�#��"�;S_l�c u �k%'l��k[�n�#��"{�%�\_&�# p � h [�akg'[�lwS-c�S-[�`IY ��u %'l�l SV` h �@c u � p &�ce& � g'&�#e&D\z\-�]\&D\-{�[�#�S-c u a>lCnt[�#c u � �� c�#��"�+&�` p c u � � � � c�#��"�>&�#m�>l�[�lwS-a;Sz\_&�#�}R���k[�`�\V( h [�` p % h cm� p \zS-a;S-c�� p c���l�c]lC[�`9c u � � � � c�#��"��Y ��u �g'�"#Tno[�#ma>&�` h �@[�n c u � � � � c�#��"�+�S�\z\!'�+��[�#]l��>c u &�`�c u &�c�[�nCc u � �� c�#��"�+!'� h &y%'l��+[�n c u �@%'l��+[�n p S_lE��[�S-`icp � h [�akg/[ilwS-c�S-[�` SV`X& p$p S-c�S-[�`+c�[;!'�]S-`${bS-#�#��"{�%�\_&�#�Y ��u %'l \�S-`$��l�&�#m� !$#�[�U��"`@S-`ic�[kl�a@&D\z\V�"#Cg'[�#�c�S-[�`'l�#���lT%�\VcTSV`${S-` h [�#�#���l�g/[�` p S-`${�\-(9ak[�#���\-��&Dn`$[ p ��l"Y ��u S_lL\-��& p l�cm[�&�`XS-` h #���&�l��MSV`�c u �>l S �"�b[�nc u �;S-`icm�"#el�� h c�S-[�`X\zS_l�cel!'�"c����"�"` lT[�%$# h ��&�` p ce&y#�{��"c�`$[ p ��lC&�` p S-akg�\zS-��l�{�#m��&�c��"#��]�~� h %$cTSV[�`�c�S-ak��l"Y

�w` c u � S-`ic��"#m��l�c>[yn�[�!$ce&DS-`�S-`${ &s!'�"cmc��"#>%$` p �"#]l�ce&�` p S-`${�[�n�c u � ��� c�#��"�Xl�g'&�c�S_&D\���[�S-` [�g/�"#e&�c�S-[�`I}����c���l�cm� p !'[�c u &+c�[�g ��p [���`�&�` p !/[�c�c�[�a � %$g &D\-{�[�#�S-c u a�}I� u S�\-�+[�`�\-(�&@!/[�c�c�[�a � %$g�&D\-{�[�#TSVc u a �&�lCcm��l�c�� pnt[�#c u ��!$% h U��"c�|�x � � %'& p c�#��"� &�lc u S_lS_lCc u ��ak[�l�c�\-[�{�S h &D\�&�g$g$#�[i& h�u c�[;S-akg�\-�"ak�"`�c�S-`${�c u ��[�g'�"#e&yc�S-[�`IY� S-a;Sz\_&�#�\-(�}����9[�`�\V(�c���lTc�� p c u �9c�[�g ��p [��` &D\-{�[�#�S-c u a no[�#+c u � � � � c�#m�"��Y �$[�#�& p$p S-c�S-[�`'&�\ h [�akg'&y#�S_l�[�`g$%$#�g/[il���l"}<&;!$#�%$c�� � nt[�# h �;l�[�\-%$c�S-[�`Xc u &�c p [i��l�`$[�c�"akg�\-[�(�&�`�(�l�g'&�c�S_&D\ p � h [�akg'[�lwS-c�S-[�`��tS�Y���Y-}$��& hmu lT[�%$# h �\zS-`$�CS4l!$#�[i& p$h &�lTcRc�[���& hmu ce&�#�{��"c \zSV`$�����&�lJSVabg�\V�"ab�"`ic�� p &�lR���]\z\�Y *�[�c��Cc u &�c�c u � �]�$� h %$c�S-[�`@c�S-ak� [yn7c u S_l!$#�%$c�� � nt[�# h �@&�g$g$#�[i& hmu S_lLS-` p �"g'�"` p �"`�ck[�nc u �>l�g'&yc�S_&D\7��[�S-` h [�` p S-c�S-[�` �tS�Y���Y-}Nc u � p S_l�c]&�` h �>�SVc u SV`�� u S hmuc u � p ��lwS-#�� p \zS-`$��l &y#��Cno[�%$` p �eY

� [�#C��& h�u [�n�c u �MlTg'&�c�S_&D\I��[�S-`'l"}<c u �kl��"c�[�nR\zS-`$��l h [�#�#���l�g/[�` p S-`${�c�[@#e&DSz\-#�[i& p l�SV`sc u �k|R#�S-` h �+WC�"[�#�{���la>&�gX� ����� \zSV`$�;l��"{�ak�"`�cel]�R�&�l hmu [il��"`�&�l�c u � l�[�%$# h ��a>&�gI}�� u Sz\-� c u ��l��"c�[�n7\zS-`$��l h [�#�#m��l�g'[�` p S-`${@c�[;c u �#�[i& p `$�"c���[�#�U;S-`�c u �q| #�S-` h �kWC�"[�#�{���l�a>&�gX� � �$} = � � \�S-`$�kl��"{�ab�"`icel S-` h [�`ic�#]&�l�c�cm[M&Mc�[�ce&D\<[�n � = } � � \�S-`$�l��"{�ab�"`icelPS-`kc u ��[�#�S-{�S-`'&D\'a@&�g�� u S hmu S-` h \-% p ��l�&�\�\'[yn'c u ��\�S-`$��&�# no��&yc�%$#���lN#e&�c u �"#7c u &y`��%'l�cRc u ��#�[i& p l �1�&�lhmu [il��"`�&�l�c u ��ce&�#�{��"c�a>&ygIY7�w`�c u S_l h &�l���}$c u ��l�g'&yc�S_&D\'��[�S-` � %$�"#�(bS_l[�`$��c u &�cl��"�"U$lc�[ p �"c��"#ma;S-`$��� u S hmu#�[i& p l &y#��>�SVc u SV`�&Xl�g'� h Sz�'� p�p S_l�ce&�` h �+[�n�&�#]&DSz\V#m[i& p \zS-`$��Y �u � p S4lTce&�` h �X�tS�Y���Y-} #e& p S-%'l;[�n �]�$g'&�`'lwS-[�`<�r &y#�S-� p !'�"c����"�"` &�` p = � u �"#�� c u �a>&�g@�&�lR`$[�#ma>&D\zS��"� p [�` &�l h &D\-��[�n ��� } � � � ��� } � � � YI�w` & p$p S-c�S-[�`I}c u �!$% h U��"c h &�g'& h S-c�(�nt[�#Rc u ��!$% h U��"c�|�x � � %'& p c�#m�"� r &�#TSV� p !'�"c����"�"`���&�` pk��� }�� u S�\-�Cc u �`$[ p � h &yg'& h S-c (#e&�`${�� p !'�"c����"�"` �� &�` p = no[�#�c u � ��� c�#��"�;&�` p+�� cm[ = no[�#�c u � � � � c�#m�"��Y

�JS-{�%$#m� �i� g$#���l��"`�celbc u � h g$% cTSVab��l;nt[�#@c u �X!$% h U��"c+|�x � � %'& p c�#��"�9l�g'&�c�S_&D\���[�S-` [�g'�"#e&�cTSV[�` &�l@&nt%$` h c�S-[�`+[�n7c u �C#e& p S-%'l�[�n7�]�$g'&�`'lwS-[�`�&y` p c u �C!$% h U��"c h &�g'& h S-c�(�Y6�9�C[�!'l��"# r �Cc u &�c�nt[�#�c u S4l�a>&yg>c u �C�]�$� �h %$c�S-[�`@c�S-ak��S4l�&�cNS-cel�a;S-`�S-a;%$a no[�#�&�!$% h U��"c h &yg'& h S-c (b[�nI#�[�%${ u \-( �"� cm[ ��� Y � l�c u ��#e& p S-%'l�[�nI�]�~g'&�`'l SV[�`S-` h #���&�l���lMc�[��&y# p = } c u ��l��@!$% h U��"c h &�g'& h S-c�S-��l h [�`�c�S-`i%$�+cm[ �]� u S-!�S-c>{�[�[ p g'�"#�nt[�#�a>&y` h � &D\-c u [�%${ u c u �& p�r &�`ic]&�{��CS_l�`$[�c &�l�{�#���&�cDY

� ��[�!'&�l S h no[�# h ��lI��[�#mU &�{i&DS-`'l�cJ��& h�u [�c u �"#7&�l<c u ��#]& p S-%'lI[�n$�]�$g'&�`'lwS-[�`k&�` p !$% h U��"c h &yg'& h S-c (�S-` h #���&�l���Y

� =

Page 67: O'3 0D. - cs.umd.edu

5

20

40

12

16

20

32

30

40

50

50

30

10

0

8

24

28

radius of expansion

bucket capacity

CPUseconds

��� ���������������! %�0��,+-� /�* +@���G�(' �.* ')�01/�* 6&' " /2�$+@<%� $�� 0��1�(+ ACE B�����8%6�+-���(��'1 8�+-� 8&" � /���*8&" ��/�� � +@<�� H

�JS-#el�c�}<�SVc u &b\_&�#�{��"#�#e& p SV%'lL[�n��]�$g'&�`'lwS-[�`I}Jno�"���"#�l�[�%$# h ��\�S-`$��l;&�#��;#��"ab[ r � p nt#�[�a h [�`'lwS p �"#e&yc�S-[�`�&�lC���S-c��"#e&�cm��&�c;\-� r �]\_l+l�% h"h ��l�lwS r �]\-( h \-[il��"#@c�[9c u &yc [yn�c u �+#�[�[�ck`$[ p ��}�c u %'lM#���l�%�\-c�S-`${�S-` ab[�#���l�[�%$# h �@\�S-`$�c�[+ce&y#�{��"c�\zS-`$�>�"` p g/[�S-`ic;c�#]&�`'l�a;S_l�lwS-[�`'l Y � � h [�` p }N&�lCc u �;!$% h U��"c h &�g'& h S-c�(+S-` h #���&�lT��lCnt[�#�&b�$�~� p #e& p SV%'l[�n �]�$g'&�`'lwS-[�`I}���� u & r �bnt�"���"#;`$[ p ��l;!$%$c;[�n\_&�#�{��"# h &yg'& h S-c (�Y ��u �b\V��lml��"`$� p `$[ p � h [�%$`�c #m��l�%�\-cel�S-` &

� %'& p c�#��"��[�nRl u &D\z\-[����"# p �"g$c u ��� u S hmu #���l�%�\-cel�S-` no�"���"#�S-c��"#e&�c�S-[�`'l[�n�c u ��&D\-{�[�#�S-c u a+�]}i!$%$c���& h�u S-c��"#]&�c�S-[�`ce&�U���lJ\V[�`${��"#&�lRak[�#��l�[�%$# h ��\zSV`$��lT�"{�ak�"`�celN`$�"� p cm[�c�#e&y`'l�a;S-c�c u �]S-#��"` p g'[�S-`�c h [i[�# p S-`'&�c���lRcm[�c u �c]&�#�{��"c\zS-`$��l"Y

�JS-{�%$#m� ��� l u [��Cl�c u � h g$%Xc�S-ak��lnt[�#c u ��c�[�g ��p [��` ��� c�#m�"�MlTg'&�c�S_&D\'��[�S-` &�lC&�nt%$` h c�S-[�`X[�nRc u ��#e& p SV%'l[�n �]�$g'&�`'lwS-[�` &y` p c u �+`$[ p � h &�g'& h S-c�(�Y;*�[�c��@c u &�c �� c�#��"��l;��S-c u l�a>&�\�\-�"#k`$[ p � h &�g'& h S-c�S-��l@� S Y ��Y-} �� [�#� =��C�]� u S-!�S-ck�]�$� h %$c�S-[�`�c�S-ak��l�c u &�c�&�#�� h [�`'lwS p �"#e&�!�\-(s\V��lml;c u &�`9c u [il��;nt[�#�\_&�#m{��"#�`$[ p � h &yg'& h S-c�S-��l@�tS�Y���Y-}� =�[�# = �]Y �u ��#���&�l�[�`bnt[�#�c u S_l l�%$!'lTce&�`�c�S_&D\ p S !I�"#��"` h �CS-`�g'�"#�nt[�#�a>&y` h �CS4lc u &�cl�a>&D\z\-�"#`$[ p � h &�g'& h SVcTSV��l#���l�%�\-cCS-`9&��'`$�"# p � h [�akg/[ilwS-c�S-[�`9[yn l�g'& h ��Y��`Xg'&�#mc�S h %�\4&y#�}<��& hmu [�n�c u �;l�a>&D\z\-�"#�l�[�%$# h ��`$[ p ��l�SV`�c��"#elT� h cel&+l�a>&�\�\-�"#;`�%$a !/�"#�[�n�ce&�#�{��"c�`$[ p ��l"Y�� SVc u c u S_lC�'`$�"#�{�#e&�`�%�\_&�#�S-c�(�}Ic u �"#��MS4lqS-` h #���&�l�� p [�g$g'[�#�c�%$`�S-c�(�nt[�#g'&�#e&�\�\-�]\ h [�aka;%$`�S h &�c�S-[�`�� u �"`+!$#�[i& p$h &�l�c�S-`${kc u �;l�[�%$# h �C\zS-`$��lCc�[;c u � &yg$g$#�[�g$#�S_&�c���c]&�#�{��"c�`$[ p ��l"Y

*�[�cl�%$#�g$#TS4l SV`${y\V(�}/c u ���]�$� h %$c�S-[�`+c�S-ak��l�nt[�# ��� c�#m�"��l���S-c u &��$�$� p `$[ p � h &yg'& h S-c (@c��"` p c�[�S-` h #���&�lT��&�lc u �;#e& p S-%'lL[�n��]�~g'&y`'lwS-[�`XS-` h #���&�l���l Y � SVaMS�\_&�#�c�[+� u &�cC�&�l�[�!'l��"# r � p ��S-c u c u �;!$% h U��"c�|�x � � %'& p cm#��"��}c u ��S-` h #���&�l�� p #e& p SV%'lC[yn��]�$g'&�`'lwS-[�`X#���l�%�\-cel�S-`9&@{�#���&�cm�"#`i%$a;!/�"#�[�n�l�[�%$# h � � ce&�#�{��"c�`$[ p �;S-`�c��"#el�� h cTSV[�`'l"}&�l�c u ��#��"{�S-[�` &y#�[�%$` p ��& hmu l�[�%$# h ��`$[ p ��c u &�c u &�l&Mg'[�c��"`�c�S_&D\7[yn�!/�]SV`${@��S-c u S-`�c u ��{�S r �"` p S_l�ce&y` h ��[�n�&

���

Page 68: O'3 0D. - cs.umd.edu

5

20

4015

25

35

45

200

300

400

radius of expansion

node capacity

CPUseconds

0

10

30

50 10

20

30

40

50

100

��� ���������������! %�0��,+-� /�* +@���G�(' �.* ')�01/�* 6&' " /2�$+@<%�!+ /� 56&/+%4* B +@�3�(�!'1 �8+-� 8&" �5/ �.* 8&" ��/ �5� +@<��!H

ce&�#m{��"c�`$[ p �LS4l\_&�#�{��"#DY

�JS-{�%$#m� ��� l u [��Cl�c u ��g/�"# h �"`�ce&�{���[�n & p$p SVcTSV[�`'&D\��]�$� h %$c�S-[�`Xc�S-ak��#�� � %�S-#�� p !�(+c u ��`$[ p ��S-`�c��"#el�� h cTSV[�`g u &�l���[yn7c u ��!'[�c�c�[�a � %$g �� c�#��"��l�g'&�cTS4&�\~��[�S-`�&D\-{�[�#TSVc u a #��]\_&�c�S r ��c�[;c u � `$[ p ��S-`�c��"#el�� h cTSV[�`+g u &�l���[yn7c u �c�[�g ��p [��` ��� c�#��"�kl�g'&yc�S_&D\1��[�S-`9&D\-{�[�#�S-c u a�Y �$[�# c u ��{�S r �"`X`$[ p � h &�g'& h SVcTSV��l�&�` p #]& p SzS�[�n��]�~g'&y`'lwS-[�`I}<c u �!'[�c�c�[�a � %$gbg$#�[ h � p %$#m� #�� � %�S-#���lR!/�"c����"�"` �i � ��� = � ak[�#�� h g$%kc�S-ak�Cc�[ p �"c��"#�a;S-`$��&D\z\1`$[ p �S-`�c��"#el�� h cTSV[�`'l"Y��cl u [�%�\ p !'� h \-��&�#c u &�c�c u ��cm[�g ��p [��` &�\V{�[�#�S-c u a ��� u S hmu a>&�U���l�no%�\z\7%'l���[yn7c u � ��� c�#��"� p � h [�abg'[ilwS-c�S-[�`<�[ !I�"#el�lwS-{�`�Sz� h &�`ic�g'�"#�nt[�#�a>&y` h �q& p�r &�`�ce&�{���l�&�l h [�akg'&�#�� p ��S-c u c u ��lwS-akg�\-�"#!'[�cmc�[�a � %$g+&D\-{�[�#�S-c u a�Y ��u �& p�r &�`ic]&�{��X[�n c u � cm[�g ��p [��` &D\-{�[�#�S-c u a �&�lkg$#�[�`$[�%$` h � p � u �"` c u �9`$[ p � h &�g'& h S-c�S-��l+���"#��9l�a>&�\�\-��l�c�tS�Y���Y-} �� � � =�� &�` p c u � h [�#�#���lTg'[�` p S-`${9c�#m�"� u �]S-{ u c;�&�lL{�#���&�c���lTc�Y�x�[�#��"[ r �"#�}Jc u �@c�[�g ��p [��`�&D\-{�[�#�S-c u ag'�"#Tno[�#mak� p #��]\_&�cTS r �]\V(+!/�"c�c��"#�SVc u &kl�a@&D\z\7#e& p S-%'l�[�n��]�$g'&�`'lwS-[�`IY�v�`�no[�#mc�%$`'&�c��]\-(�}$c u ��`$[ p ��S-`�c��"#el�� h cTSV[�`p �"c��"#�aMSV`'&yc�S-[�` g u &�lT��[�n c u � l�g'&�cTS4&�\���[�S-` [�g'�"#e&�cTSV[�`�[�`�\-( h [�`'l�%$ak��l � � � = � [�n�c u �+�"`�c�S-#�� &D\-{�[�#�S-c u a����S-c u c u ��{�#���&�c���lTc�no#]& h c�S-[�`+[ h"h %$#�#�S-`${>� u �"`+c u ��`$[ p � h &�g'& h S-c�(�&�` p #e& p S-%'l�[�nR�]�~g'&�`'l SV[�` &�#���lTa>&D\z\t�eY

�JS-{�%$#m� �D� g$#���l��"`�celNc u � h g$%kcTSVab��lNnt[�#7c u � ��N� c�#��"�l�g'&yc�S_&D\�� [ySV`b[�g'�"#e&yc�S-[�`IY �9�[�!'l��"# r ��c u &�cNnt[�#Rc u S_la>&�gI}�&�l<c u ��`$[ p � h &�g'& h SVc�(CS-` h #���&�lT��l"}�c u ���]�~� h %$cTSV[�` cTSVab��n�&D\z\_l�� p %$��c�[�nt�"���"#I\-��&Dn<`$[ p ��l]����!$%$cRc u �"`;#�S_l���lh [�`'lwS p �"#e&y!�\V(@nt[�#�`$[ p � h &�g'& h S-c�S-��l � =;&�` p = Y ��u S_l�S_l�!'� h &�%'lT��c u �C`i%$a;!/�"# [�nJ\V��&�n�`$[ p ��l�S-`�c u ��lT[�%$# h �a>&�g p � h #���&�lT��lk�wc u �"#��"!�( !/� h [�a;S-`${X\_&�#�{��"#�}Nc u %'lLS-`�c��"#el�� h c�S-`${Xak[�#m�>ce&y#�{��"c�`$[ p ��lk&�` p9h #���&yc�S-`${ ab[�#��h [�aka;%$`�S h &�c�S-[�` h [�`�J$S h cel]�eY *[�cm� c u &�c��]�~� h %$cTSV[�`9c�S-ak��l�&y#���\4&y#�{��"#�c u &�`Xc u [il���nt[�#�c u � h [�#m#���l�g'[�` p SV`${��� c�#m�"��� lT�"� �JS-{�%$#�� ��� �7&�lRc u � p S4lo� [�S-`�c p � h [�akg'[�lwS-c�S-[�`+#���l�%�\-cel�SV`+&�!/[�%$c�c���S h � &�l a>&�`�(�\V��&�nP`$[ p ��l"}�c u %'l

���

Page 69: O'3 0D. - cs.umd.edu

5

20

4015

25

35

45

50%75%

100%

125%

radius of expansion

node capacity

10

20

30

40

50

0

10

30

50

percentageadditionalcpu time

��� ������� � � ��A��%� 01�%*,+)8�&�:/+" 8,6�6 � +@� /�*�8�"��� ,�0��%+@� / * +-�.���;����� �2�����6 $�=:+-<,� " �8 " *%/ 6&� ��*,+ �%� ')�01+@� /�*G6&�(+5�%�5�9�.*%8+-� /�*; �< 8�')�:/!" +-<,� $�/�+ +5/�� )�2 ?B +@���(� '1 �8�+@� 8&" � /��.*?8&" ��/�� � +@<�� �3�%" 8�+@� )�+5/7+@<%�?+5/ 56&/+%4*?8&" ��/��5� +@<�� H

2

4

6

2

4

6

1000

1500

2000

� � �� � �� � �� � �� � � �� � � �� � �� � �

� � � �� � � �� � � �� � �� � �

� � �� � �� � �� � �

� � �� � �� � �� � �� � �

� � �� � �� � �� � �

� � � �� � � �� � � �� � � �� � � �

� � �� � � � � �� � � �� � � �� � �� � �

� � � �� � � �� � �� � �� � � �

� � �� � �� � � �� � �� � � � � �� � �� � �� � �� � � �� � � �

� � �� � �� � � �� � � �� � � �� � � �� � � �

� � �� � �� � �� � �� � �� � �

� � � �� � � �� � � �

! ! !! ! !! ! !

" " " "" " " "" " " "" " " "

# # # ## # # ## # # #5

20

4025

35

45

30

40

50

20

0

10

30

50

radius of expansion

CPUseconds

node capacity

� � ������� ��4 � �! ,�0��%+@� /�*�+@�.���;�.*�')�01/�* 6&' " /�� +-<,�!B � +@�3�(�?'1 8�+-� 8&" � /���*G8&" ��/��5� +@<�� H

S-` h #���&�lwS-`${kc u � &�ak[�%$`�c�[ynJlT[�%$# h �Cc�[�ce&y#�{��"cR`$[ p � h [�aba %$`�S h &�cTSV[�`�� &�lR���]\z\J&�lNS-` h #���&�lwS-`${kc u � lwS��"��[�nIc u �S-`icm�"#el�� h c�S-[�`s\zS4lTcel]�eY+�JS-`'&D\z\-(�}�&�lCS_lL[�!'l��"# r � p ��S-c u c u �k!$% h U��"c |�x � � %'& p cm#��"�>&�` p c u � ��� c�#��"��}R&�lLc u �#e& p S-%'l�[�nR�]�~g'&�`'l SV[�`+S-` h #���&�l���l�c�[��&�# p = }$c u ���]�$� h %$c�S-[�`�cTSVab��S-` h #���&�l���l Y

� u �"` h [�akg'&�#�S-`${�c u �k�]�~� h %$cTSV[�`�c�S-ak��lL[�n�c u �k!$% h U��"c |�x � � %'& p cm#��"�>&�` p cm[�g ��p [��` ��� c�#��"�+&�` p� � � c�#m�"� l�g'&�cTS4&�\�� [ySV`�&D\-{�[�#�S-c u a@l"}RS-cbS_l>&�g$g'&y#��"`ic@c u &�cbc u �+!$% h U��"c |�x � � %'& p c�#��"�+[ !I�"#elblwS-{�`�Sz� h &�`ic

� �

Page 70: O'3 0D. - cs.umd.edu

� 8�$2" � � � �� �8+-� 8&" � /���*:�� ,�0��%+@� /�*:+-�.���(' " /�� +-<,� +@<����(�;628�+ 8�')+@� � 01+-�2�3�(' " /�� *,/�6&��0(8& 8%0�� + =� ��H

��& ' � " � � " ����� � � ��� "-$ �) � $% , � � � � ��� . )%� � � � � . )%� �

� � �� � �

�� � � � �

��

� � �� � � �

�� � � � �

� � � �� � � �

�� � � �

� � � ��� � � �

�� � � � �

��

��� � ��� � � �

�� � � �

� � ��� � � �

�� �

��

��� ��� � � �

� �� � �

��

g'�"#Tno[�#ma>&�` h � & p�r &�`�ce&�{���l Y �$[�#b�]� &�abg�\V��} h [�`'lwS p �"# � &�!�\-� � � u S h�u ce&y!$%�\4&yc���l;c u � h g$% c�S-ak��lMno[�#kc u �|R#TSV` h �bW �"[�#m{���l�a>&�g�� lRnt[�#c u ��c u #��"� p &�ce&bl�c�#�% h c�%$#m��lC����& hmu ��S-c u &;`$[ p � h &�g'& h SVc�(@[�n � =��Nno[�# & r &y#�S-�"c ([�nl�[�%$# h �;a>&�gX�]�$g'&�`'lwS-[�`'l"Yk� [�#C��& h�u [�n�c u �;\zS_l�c�� p �]�$g'&�`'lwS-[�`'l }Ic u � ��� c�#m�"�kce&�U���lC&�g$g$#�[D��S-a>&�c��]\-()=� �c�S-ak��l\-[�`${��"#�c u &�`�c u � h [�#�#���l�g/[�` p S-`${+!$% h U��"c�|�x � � %'& p c�#��"��}<&�` p c u � � � � cm#��"��ce&yU���l &yg$g$#�[D�iS-a>&�cm�]\V(� cTSVab��l�\-[�`${��"#�c u &�`�c u � h [�#�#���l�g/[�` p S-`${ �� c�#��"��Y ��u S_l�g'�"#Tno[�#ma>&�` h �+& p�r &�`�ce&�{���S_l�g$#�S-a>&�#TS�\-(�!'� h &�%'lT�c u ��!$% h U��"c�|�x � � %'& p c�#��"��a>&yU���l�%'l���[�n�&;#��"{�%�\4&y# p S_lE��[�S-`ic p � h [�akg/[ilwS-c�S-[�`�[�n lTg'& h ��� u S hmu }$S-`X& p &�ce&g'&�#e&�\�\-�]\��"` r S-#�[�`$ak�"`icD}$n�& h Sz\zSVc]&�c���l�S-` h #���&�l�� p &�ab[�%$`ic]l�[�n�g'&�#e&�\�\-�]\ h [�aka;%$`�S h &�c�S-[�`X!'�"c����"�"`9l�[�%$# h �;&�` pce&�#m{��"c a@&�g'l�S-` h [�akg'&�#TS4lT[�`9c�[@c u � ��� cm#��"�k&�` p9� � � c�#m�"��Y ��u S_l p #e&D�!'& h U+[�n�c u � ��� c�#��"�k&�` p9� � � c�#��"�h &�`$`$[�c�!'��[ r �"# h [�ak�C!i(@%'lwS-`${ h \_&�lmlwS h &D\ �� c�#��"��S-akg$#m[ r �"ak�"`ic]l�lT% h�u &�l�c u � ���D� c�#��"�-� ��� h U �� � Y

&%$#��'`'&D\ h [�abg'&�#�S_l�[�`+�&�l p ��lwS-{�`$� p c�[;&�`'l����"#�c u � � %$��l�cTSV[�`+[�n7� u �"c u �"#�%'lwS-`${>&;l�g'&�c�S_&D\ p � h [�akg'[ �lwS-c�S-[�`kab�"c u [ p S4l ��[�#�c u � u Sz\-��Y �u S4l �&�l7& h�u S-� r � p !i(�a>&�U�S-`${�%'l��[�nI&Cc�#�%$��!$#�%$c�� � nt[�# h � &yg$g$#�[i& hmu � u �"#��&+l�g'&�cTS4&�\ p � h [�akg'[�lwS-c�S-[�`XS_l�`$[�c��"abg�\V[�(�� p �tS�Y���Y-}<��& hmu l�[�%$# h ��\zS-`$�>!$#�[�& p$h &�l�celCcm[>��& hmu ce&y#�{��"c�\�S-`$���eY;�wcg$#�[ r � p lT%$g'�"#�S-[�#�c�[�!'[�c u+��� c�#m�"�q&D\-{�[�#�S-c u a>lNS-`@c��"#�a>l [�nIc u �C�]�~� h %$c�S-[�`@c�S-ak�C#�� � %�SV#m� p Y ��u �C!$#�%$c�� � nt[�# h �&�g$g$#�[�& h�u nt[�#�c u ��| #�S-` h �kW �"[�#�{���l�a>&�g@#�� � %�SV#m� p = � Y � h g$%Xl�� h [�` p l"} � � ��� ��� � � � � [�nRc u ��#e& p S-%'l�[yn7�]�~g'&y` �lwS-[�`IYR�w` h [�`�c�#e&�l�cD}�c u ��c�[�g ��p [���` ��� cm#��"��l�g'&�c�S_&D\$��[�S-`�&D\-{�[�#�S-c u a #�� � %�S-#�� p &Ma;S-`�SVa;%$a [yn ��� �$Y+� lT� h [�` p lnt[�#�&D\z\ h [�a;!�SV`'&yc�S-[�`'l�[�n1`$[ p � h &yg'& h S-c (@&�` p #e& p S-%'l�[�nI�]�$g'&�`'lwS-[�`I}�� u Sz\-��c u �!'[�c�c�[�a � %$g ��� c�#��"�C#�� � %�SV#m� p&�aMSV`�S-a;%$a [�n � = � Y � l�� h [�` p l Y &`@c u �C[�c u �"# u &�` p }�[�%$#�!$% h U��"c�|�x � � %'& p c�#m�"� l�g'&�c�S_&D\�� [ySV`+&D\-{�[�#TSVc u a>lg$#�[ r � p l�%$g'�"#�S-[�#�c�[@c u ��!$#�%$cm� � no[�# h �M&yg$g$#�[i& hmu S-`9&D\z\�!$%$c�[�`$� h [�a !�S-`'&�cTSV[�` [ynl�g�\zS-c�c�S-`${�c u #���l u [�\ p &�` p#e& p S-%'l�[�n��]�$g'&�`'lwS-[�`9�wc u � p &�c]&;g'&�#e&D\z\-�]\R!$% h U��"c�|�x � � %'& p c�#��"��nt[�#c u � |R#TSV` h �bW �"[�#m{���l�a>&�g�#�� � %�SV#m� p!'�"c����"�"` ��� Y � &y` p =�=$Y � lT� h [�` p l]�eY

&�n h [�%$#el���}J��� a;%'l�cC!'��&y#�S-`9a;S-` p c u &yc�c u ��l��;�]�~� h %$cTSV[�`9c�S-ak��l�&y#���no[�#�c���[ � a>&yg�l�g'&�c�S_&D\I��[�S-`'l"Y;�tn���;���"#m�kc�[@S-akg�\-�"ak�"`�cMl SV`${y\V� � a@&�g r �"#el SV[�`'l�[�n�c u � � %$�"#�S-��lk� S Y ��Y-}<{�S r �"`�&�lwS-`${�\-�>a>&yg h [�`ice&�SV`�S-`${ \�S-`$�

���

Page 71: O'3 0D. - cs.umd.edu

l��"{�ab�"`icel�#��"g$#m��l��"`icTSV`${;!/[�c u #�[i& p l�&�` p #e&�S�\-�&D(~l�!/�]SV`${ p S4lTc�S-`${�%�S_l u � p !i(>&yg$g$#�[�g$#�S_&�c���&�c�cm#�S-!$%$c��4J1&y{il]�e}c u �@g'�"#�nt[�#�a@&�` h �>[ync u � ��� cm#��"��&�` p���N� c�#��"�@��[�%�\ p S-` h #���&�lT� h [�`'lwS p �"#e&�!�\-(�}�g'�"# u &�g'lM� r �"`�cm[ & \-� r �]\h [�akg'&y#e&�!�\-� cm[ c u &�c p S_l�g�\_&D(�� p !�(kc u �C!$% h U��"c|�x � � %'& p c�#��"��Y � SV`${y\V��a>&�g>lTg'&�c�S_&D\$� [ySV`+&D\-{�[�#TSVc u a>l�&�#��&;c�[�g�S h no[�#�nt%$c�%$#���#m��l���&�# hmu Y

� ��.JOP��*����72 O<,8�kF/6 ?'0��I8

j�&�ce& � g'&�#e&D\z\-�]\ &�\V{�[�#�S-c u a>l�nt[�# p &�ce&klTc�#�% h c�%$#�� h [�`'l�c�#m% h c�S-[�`I}'g/[�\-(i{�[�`�S���&�c�S-[�`I}I&�` p�h [�akg$%$c�S-`${�&kl�g'&yc�S_&D\��[�S-`;no[�#7c u ��!$% h U��"c�|�x � � %'& p cm#��"��} ��� c�#��"��}�&�` pk� � � cm#��"�l�g'&�c�S_&D\ p &�ce&�l�cm#�% h c�%$#���l u & r ��!'�"�"`bg$#���l��"`�c�� p Y� ��l�celC���"#�� h [�` p % h c�� p no[�#���& h�u &D\-{�[�#�S-c u a � u S hmu #�� r ��&�\V� p !'�"c�c��"#�g'�"#�nt[�#�a@&�` h ��no[�#�c u � !$% h U��"c;|�x �

� %'& p c�#��"��Y ��u ��a@&DS-` #m��&�l�[�`�nt[�#kc u S_lb!'� u & r SV[�#kS_lbc u �+n�& h ckc u &yckc u ��!$% h U��"c+|�x � � %'& p cm#��"�+(�S-�]\ p l&�#��"{�%�\_&�# p S_lE��[�S-`�c p � h [�akg'[�lwS-c�S-[�` [yn l�g'& h �X� u Sz\-��c u S_lbS_l+`$[�c>c u � h &�lT��nt[�#+c u � ��� cm#��"�X[�#+c u � � � �c�#��"��Y ��`�c��"#���l�cTSV`${y\V(�}no[�#>c u �Xl�g'&�c�S_&D\���[�S-`I}&9!$#�%$cm� � no[�# h ��&yg$g$#�[i& hmu c u &�c p [i��lb`$[�c@�"akg�\-[�( &9l�g'&yc�S_&D\p � h [�akg/[ilwS-c�S-[�`�g$#�[ r � p l�%$g'�"#TSV[�#�c�[+!/[�c u [�n�[�%$# ��� c�#m�"�>&�` p9� � � cm#��"��SVabg�\V�"ab�"`ice&yc�S-[�`'l"Y �u S4lqno%$#mc u �"#�"akg u &�l S �"��lbc u �+g/�"`'&D\-c (�S-` h %$#�#m� p !�(�%'lwS-`${9�]S-c u �"#>`$[�` ��p S4lo� [�S-`�c>[�#;S-#�#��"{�%�\_&�# p � h [�akg/[ilwS-c�S-[�`'lMSV` c u �p &�ce& � g'&�#e&D\z\-�]\ p [�a>&�SV`IY

�bFi:wF~0DF/OP��F$8

� � ` p ��� � � j;Y�|7Y � ` p �"#el�[�`IY � � hmu `�S � %$��l no[�#k#�� p % h S-`${�g'�"` g�\V[�c�c�S-`${�cTSVab��Y���� � � � ��� � � �� ������ � ���� � ��� � � � � } � � � ��� ����� � � ��� }���%�\-( ��� � � Y

� � #��]n ��� � � Y�W;Y � #��]nI&�` p Z�Y � &�ak�"c�Y/v`�S � %$�]\V(b#��"g'[�#mc�S-`${ l�g'&�cTS4&�\'[�!$��� h cel��R�"c�&y`$[�c u �"#R[�g/�"#e&�c�S-[�`;nt[�#h [�akg'&�#�S-`${kl�g'&�c�S_&D\ p &�c]&�l�c�#m% h c�%$#���l"Y<�w` ��� � �������.�������� � �� � �� ��� � ��� � �� ������ � ��� ���+�/������� ������ ���� �� � �� �� ���� ��� � �)�,� � }ig'&y{���l ��� � � � � � } � [�\-%$a;!�S_&$} �$� } � %${�%'l�c ������� Y

� ��&�%$a ��� � �CY'��&�%$ab{i&�#�c�Y � S-`${�� p�� � p {��;g'[y\V( u � p #�[�`X#��"g$#m��l��"`ic]&�c�S-[�`IY � [�akg$%$c��"# �ih S-�"` h �kjC�"g'&�#�c�ab�"`ic�i�J� * ����������� } � ce&y`�no[�# p v`�S r �"#el SVc�(�} � c]&�`�no[�# p } ��� } ������� Y

� ��� h U �� � *�YR��� h U�a>&�`$`I}�Z�Y � |NY�C#TSV�"{��]\ } � Y �ihmu `$�]S p �"#D}�&�` p �CY � �"�"{��"#�Y ��u � ����� c�#m�"��� � `��]� h S-�"`ic&y` p #�[�!$%'l�c;& h"h ��l�l;ak�"c u [ p no[�#�g'[ySV`�celk&y` p #�� h c]&�`${�\-��l"YX��` Z�Y�Wq&�# h S4& � x�[y\�S-`'&X&�` p Z�Y10;Y��&�{i& p S_l u }/� p S-c�[�#el"} ��� � �������.����� ��� � ��������� ��� ����� � �"!#�$� � � ��� �� ������ ��� � ���%��� � ��� � ���������� ������� ��� ����� �� �� }'g'&�{���l ����� � ���$� } � c�\_&�`�c�S h�� S-c (�} *&�$}/x &D( ������ Y

� ���"`�c � = � � Y � Y����"`�c�\-�"(�YIx�%�\-c�S p S-ak�"`'lwS-[�`'&�\P!�S-`'&�#m(MlT��&�# hmu cm#��"��lN%'l�� p nt[�#�&�l�lT[ h S_&�c�S r �Cl���&�# hmu S-`${'Y'� � � �� � � ����� �� ��� � ��� � � �(� � } � ��� � ��� = �� ��= ��� } � �"g$c��"a;!'�"# ����� = Y

��

Page 72: O'3 0D. - cs.umd.edu

� ����l�c ��� � � YI����lTc�%�\�Y ��� � � � ��� � ��� ��� � � � ��� � � ��� �� ����� � ���(����� ��#� � � �� �� Y>| u j c u ��lwS_l"}7v�`�S r �"#elwS-c�([ynqxX&�#�(�\4&y` p } � [�\z\-�"{�� |R&y#�U1}RxXj;} � g$#�Sz\ ������� � &D\_l�[9v�`�S r �"#elwS-c�(�[�n�x &y#�(�\_&�` p � [�abg$%$c��"#�ih S-�"` h � � � h�u `�S h &D\ � �"g'[�#�c ������������ � �~� �eY

� � u &�l �,� � � Y ;Y<� u &�l�U�&�#D} � Y � [il��"`�nt�]\ p }I&y` p+� Y ;Y��9%IYC|R&�#e&D\z\-�]\�g$#m[ h ��l�l SV`${+[yn�#��"{ySV[�`'l#��"g$#m��l��"`icm� p!�(@\zS-`$��&�# � %'& p c�#��"��l"Y�� � � � � ��� � ����� ����� � � ��� � ����� ��� ����� ����� ��� � � � ���,� � } �i� � � ��� ���i� � � � }�y%$`$� ��� �,�$Y

� � \-�]\���� � W;Y7Q�Y�� \-�]\z\-[ hmu &�` p �$Y �$Y � S-c�c�\-��Y9|R&�#]&D\z\V�]\ l�[y\V%$cTSV[�`'l�cm[ {��"[�ak�"c�#�S h g$#�[�!�\-�"a>l�[�`�c u �+l h &�`ab[ p �]\[�n h [�akg$%$ce&�cTSV[�`IY+��`�j;YIZ�YN��&DSz\V�"(�}�� p S-c�[�#�} ��� � �������.����� ��� � ��������� � � � ��� �� ������ ���� ���%��� � ��� � ����� ��� � � � ��� � ��������� �,� � } r [�\-%$ak� � }Rg'&�{���l �$� �� ����� } � c�Y ��u &�#�\-��l"}R� � } � %${�%'l�c�D� ���$Y

� � \-�]\�� � & � W;YRQY�� \-�]\z\V[ hmu Y �ih &�`'lk&�lMg$#�S-a;S-c�S r ��g'&�#]&D\z\V�]\C[�g'�"#e&yc�S-[�`'l"Y ����� � � ��� ������ ������ � ��� � � � �� � ��� � } � �~� ��� ��� � = ��� � � = � �$}�*�[ r �"a;!'�"# ��� � � � &�\4lT[�|R#�[ h �"� p S-`${il�[�n�c u � ��� � � ��`�c��"#�`'&�cTSV[�`'&D\� [�`�no�"#m�"` h ��[�`�|R&�#]&D\z\V�]\R|R#�[ h ��l�lwS-`${'} � c�Y ��u &�#�\-��l"}/� � }$g'&�{���l � =�=� ����� } � %${�%'l�c �D� � � �eY

� � \-�]\�� � ! � W;Y$QYi� \-�]\z\-[ hmu Y � ����� ��� � �� ��.- ��� ��� � ��� � � � � � � ���� ����+� ������� � YI| u j c u ��lwS_l"}$xX&�l�l�& hmu %'l��"c�cel�w`'l�c�S-c�%$c���[yn � � h�u `$[y\V[�{�(�} � &�a;!$#�S p {���}$x � }�& h cm[�!'�"# �D� � � ��&D\_l�[ � &�!'[�#e&�c�[�#m(�nt[�# � [�abg$%$c��"#�ih S-�"` h � � � h�u `�S h &D\ � �"g'[�#�cqx�� �C���N��$������t�i��� �eY

� ��[�#e& �� � Z�Y���[�#e&D\�} � Y � \-�]� &�` p �"#D} � Y � \_&D(�}CW Y � [�g'�]\_&�` p } � Y�j�&�`�nt[�#�c u }�x�Y�� #e&�`$U�\�S-`I}C� Y�ZC&�#�c�}x�Y � a;S-c u }&�` p |NY10�&D\ p %$#�S-���Y�|R#�[�cm[�c�(ig�S-`${9��%$!$!'&$}�& u SV{ u \V(�g'&y#e&D\z\-�]\ p &�ce&�!'&�l���l�($l�c��"a�Y����� � � ��� � ��� �� ��� � ��� � �0� � � ��� � � ��� ��� �� ����(� � �.� � �����,� � } � � � ��� � � �y� }�xX&�# hmu ������ Y

� ��#�S-` ��� � � Y���#�S-`$U u [ !�} Z�Y|7Y'C#�S-�"{��]\�}�&�` p �CY � �"�"{��"#DY Q�� h S-�"`ic+g$#m[ h ��l�l SV`${ [�n l�g'&�cTS4&�\���[�S-`'l@%'l �S-`${ �� c�#��"��l"Ys��` � ����� �����,� ���6��� � � ������� ��� � � � � � !#� � � ��� � �� ������ � � � ��� � ��� ��� ��� �������� ������� ��� ����� �� �� }'g'&�{���l ����� � ���i� },��&�l u S-`${�c�[�`I}'j � }$xX&�( ������� Y

� � [�ak� ��� � j;Y � [�ak�"#DY ��u ��%$!�S � %�S-c�[�%'l� � c�#m�"��Y ��� � � � �+� � ��.����� ����-�� � � } ��� � � ��� �D�$� � ����� } ��%$`$� �D����� Y

� � [�g'����� � W;Y � [�g'�]\_&�` p }6� Y � \-�]� &y` p �"#�}�QYN��[�%${ u c��"#�}R&�` p�� Y�C�]\z\-�"#�Y9j�&�ce&@g�\_& h �"ab�"`ic�S-` ��%$!$!'&$Y�w` � ����� �����,� ��� ��� � � ������� ��� � ��� � �"!#� � � ��� � �� �� ��� � � � ���%��� � ��� � �5��� � ��� � � ��� ��� ���� �� �� }/g'&�{���l ��� � �� �$} ��u S h &�{�['}$� � } ��%$`$� ��� ��� Y

� jC� u ` �$� � ��YjC� u `$��} � YCW;Y�$�"#�#��]S-#e& }q&y` p�� Y � &�% ����u &�g�\zS-`IY QN� h S-�"`�c�g'&�#e&�\�\-�]\ h [�`'l�c�#�% h cTSV[�` &�` pa@&�`�S-g$%�\4&yc�S-[�` [yn � %'& p c�#��"��l"Y �w` ;Y � ['}C� p S-c�[�#�} ��� � �������.����� ��� � � ������� � � � ��� �� ������ ���

�i�

Page 73: O'3 0D. - cs.umd.edu

� ���%��� � ��� � ����� ��� � � � ��� � ��������� �,� � } r [�\-%$ak� � }Rg'&�{���l � =�=� ����� } � c�Y ��u &�#�\-��l"}R� � } � %${�%'l�c�D���$� Y

� jC�� S�� � � j;Y �$YNjC�� SVcmc�} � Y�W �"#m!'�"#�}�W Y W #e&y�]no��}Rx�YRZ�"(�c��"`'l"}6;Y6C%$a>&�#�}�&�` p x�YNx�%$#]&D\zSVU�#�S_l u `'&$YW � xXx � � � u S-{ u g'�"#Tno[�#ma>&�` h � p &yce&�J'[�� p &�ce&y!'&�l���a@& h�u S-`$��Y���`B� Y ��u %I}IW;YIW�&�# p &�#�S-`I}� Y &`'lT%${i&$}<&�` p Y �&�a;!'&D(i&�l u S�}<� p S-c�[�#el } ��� � �������.��������� � � ���� ����� � ��� � �� ��� � � � ���%��� � ���� ��� ��� � � ����� ������� � � ���� � � � � }�g'&�{���l ��� �� ����� } � [�U�(�['} ��&�g'&y`I} � %${�%'l�c ��� � � Y

� jC�� S �� � j;Y�� YijC�� S-c�c�&�` p �$Y W #e&D(�Y$|R&�#e&�\�\-�]\ p &�ce&�!'&�lT�lT(~l�cm�"a>l�� �u ��no%$cm%$#��[�n p &�ce&�!'&�lT��g$#m[ h ��l�l SV`${[�# &;g'&�l�l SV`${Mn & p�� ��� � �"!#� ��� � ��� } �D� � � ��� �� �� � ����� }�jC� h �"a;!'�"# �D���� Y

� jC�� S ��� � j;Y �$Y/jC�� S-c�cC&�` p � Y<W #e&D(�Y ��u �Cnt%$c�%$#��C[�n u SV{ u g'�"#�nt[�#�a>&y` h � p &�ce&�!'&�lT��l�(~lTc��"a>l"Y � � �6� ���� � ���� ������ ����� � � ��� � } � =~� � ��� �,=� � �$}���%$`$� ������� Y

� Q p �]\<�,= � � YRQ p �]\Va@&�` &�` p QY ��u &yg�SV#m['Y�%'& p c�#��"��l�S-` h [�` h %$#�#��"`�ck|R#�[�\-[�{/Y+��` j;YNjC�"{�#�[�[�c�}I� p S-c�[�#�} � ����� �����,� ��� ��� �� ������ � � ��� � �� �� ��� � � � ���%��� � ��� � � ��� � ������� ���+ � � � � � ���.��� � � � ��� ���� }g'&y{���l = ��� � =�= � } � c�Y ��u &y#�\-��l"}$� � } � %${�%'l�c �D� ��=$Y

� Q�\Va@&�� � � � Y Q�\Va@&�l�#�S &y` p � Y�� Y * & r &yc u ��Y � � ��� � ��� �� � � ��� � �� �� � ����� � � �� ��� � Y ���"` ���&�a;S-` ��� %$aka;S-`${il"} � � p ��[i[ p�� S-c�(�} ��� } ��� � � Y

� �/&D\-[%� ��� � Y'�'&D\-[�%$c]l�[il"} � Y � �]\z\zS_l"}I&�` p *�Y � [�%'l�l�[�g/[�%�\-[il"Y � `'&D\-($lwS_lC[�n�[�!$� � h c�[�#TSV�"`�c�� p l�g'&�c�S_&D\�& h"h ��l�lab�"c u [ p l Y���`9v�YIj�&�(�&D\7&�` p �eY � #e&DS-{��"#�}<� p S-c�[�#]l"} � �����������,� � � ��� �� ������� ��� � � � � � !#�

��� � ��� � �� ��� � � � ���%��� � ��� � �6��������� ������� ��� ����� � �� }<g'&�{���l �i��� � �i��� } � &y`�� #e&�` h S_l h ['} ��� }xX&D( ��� � � Y

� � [�\-� �� � � Y~j;Y�� [�\-�"(�} � Y r &�`+j�&�a�} � Y%;Yi� �]S-`$�"#�}'&�` p � Yi��YiZ�%${ u ��l"Y#� � �+� � ����� � ��� � ����� ���,� ��� � � � ���� � � ��� �� ��� Y ��p$p S_l�[�` �%�9��l \V�"(�} � ��& p S-`${'}<x � }/l�� h [�` p � p S-c�S-[�`I} ������ Y

�zW�&�!'[ ��� � Z�Y�*�Y/W�&�!'[���YNv lwS-`${>Q %�\-�"#g'&�#�c�S-c�S-[�`'lc�[�� p {�� h [y\V[�#�!�S-g'&�#mc�S-c���a;%�\VcTSV{�#e&�g u l"Y � � � ��� �� ������ ���� ����� � � ����� � � �+� � � ���$� � � ����� �� ������ � � ����� � � � }/= � ��� =� � =�= } ������� Y

�zW�&�#�� ��� � x�Y � Y<Wq&�#m�"( &�` p j;Y � Y ��[ u `'l�[�`IY � � � � � ��� � ��� ��� � �� ��� �� ��� �)� ���� � � � � ��� �� ���� � � � �������� � � � �+� � �� ��� ����� Y � Y~Z�Y'� #��"�"a>&�`�&�` p�� [�akg'&y`i(�}�*��"��R[�#�U<} ������� Y

�zW u &�` ��� � � YNW u &�` p � u &�#�S���& p � u }Rj;Y<jC�� SVcmc�}I&�` p � Y��%$#���l u S Y � g'�"#�nt[�#�a@&�` h �k&�`'&D\-(~l S4lL[�n&�\Vcm�"#�`'& �cTS r ��a;%�\-c�S � &�c�c�#�S-!$%$c�� p � h \-%'l�c��"#TSV`${�lTc�#e&�c��"{ySV��l Y��w` � ����� �����,� ���5��� � ��������� ��� � � � � � !#�

���

Page 74: O'3 0D. - cs.umd.edu

��� � ��� � �� ��� � � � ���%��� � ��� ��� ��� ����� � � ��� ��� ����� �� �� }Ig'&y{���l ��� � � �$} � &y`�j�S-�"{�[/} ��� } �y%$`$��D����� Y

�zW��%$`ic ��� � &�Y W��%$`�c u �"#�Y�Q�� h S-�"`ic h [�akg$%$ce&yc�S-[�`X[�nl�g'&yc�S_&D\I� [ySV`'l Y;��` ��� � �������.��������� � � � �.� �������

��� � ��� � �� ��� � � � ���%��� � ��� � � �,� � �� �� �������,� ��� ���.��� }]g'&�{���l�= � = � }�0�S-�"`$`'&$} � %'lTc�#�S_&$} � g$#�Sz\ �D����� Y

�zWC%$c�c9� ��� � YJW %$c�c�a@&�`IY �� c�#��"��l�� � p (i`'&ya;S h S-` p �]�9l�c�#�% h c�%$#m��nt[�# l�g'&�cTS4&�\ l���&y# h�u S-`${'Y��w` ��� � �������.�������� � ��� ��� � ��� � ��� � �"!#� � � � ��� �� ������ ��� � ���%��� � ��� ������� � ��� � � ��� ��� ����� �� �� }7g'&y{���l� � � = � }$��[il�cm[�`I}$x � } ��%$`$� ��� � � Y

� ZSz\�\�� � � � Y�j;YRZSz\�\zS_l�&y` p W Y � Y � c��"�]\-� ��#�Y j�&�c]&�g'&y#e&D\z\-�]\L&D\-{�[�#�S-c u a>l"Y$� � �6� � � ������ ������ � ��� ��

�(� � } ��� � ��� ��� ������ � ��� � � }�jC� h �"a;!/�"# ��� � � Y

� Z�[i�]\ ��� � Q�Y�W;Y�Z�[i�]\'&�` p Z�Y � &�ab�"c�Y � � %'&D\zS-ce&�c�S r � h [�akg'&y#�S_l�[�` lTc�% p (�[�n p &�ce&l�cm#�% h c�%$#���lPno[�#<\_&�#�{�� \�S-`$�lT�"{�ak�"`�c p &�ce&�!'&�lT��l"Y���` ��� � �������.����� ��� � � � ����� ��� � ��� � �"!#� � � � ��� �� ������ � � � ���%��� � ��� � ���������� ������� ��� ����� �� �� }'g'&�{���l �� =� �$�"� } � &�`�j�S-�"{�['} ��� } ��%$`$� ������� Y

� Z�[i�]\ ��� � Q�Y�W;Y�Z�[i�]\'&�` p Z�Y � &�ak�"c�Y�j�&�ce& � g'&�#]&D\z\V�]\ ��� c�#m�"�&�\V{�[�#�S-c u a>l"Y���` � � � ����� �.����� ��� � ������� � ��� � ��� � �� ������ � � � ���%��� � ��� � �5��� ��� � � � ��� � ��������� �,� � }�g'&�{���l������ � �i� � = � } � c�Y ��u &�#�\-��l"}$� � } � %${�%'l�c�D����� Y

� Z�[i�]\ ��� & � Q�YNW Y<Z[��]\�&�` p Z�Y � &�ab�"c�Y�j�&�ce& � g'&�#]&D\z\V�]\�lTg'&�c�S_&D\<� [�S-`9&D\-{�[�#TSVc u a>l"Y��w` � ����� �����,� ��� ��� ��

� ��� � � � � ��� �� ������ � � � ���%��� � ��� � �(��� ��� � � � � � � �����������.��� }/g'&�{���lC����� � ���~� � ����� } � c�Y ��u &y#�\-��l"}� � } � %${�%'lTc ������� Y

� Z�[i�]\ ��� ! � Q�Y�W;Y�Z�[i�]\'&�` p Z�Y � &�ak�"c�Y�|N�"#�nt[�#�a@&�` h ��[�n p &�ce& � g'&�#e&D\z\-�]\ lTg'&�c�S_&D\$[�g'�"#e&yc�S-[�`'l"Y��w` ��� � �������.�������� � � � � ��� ����� ����� � ��� � �� ��� � � � ��� � ��� ��� ���6��� � ������� ����� ��� �� �� � ��� � � }Jg'&�{���l � = � � ����� }� &y`ic�S_&�{�['} ��u Sz\-��} � �"g$cm�"a !/�"# �D����� Y

� Z�%$`${%� � � ;Y$Z%$`${k&�` p@� Y � [il��"`�nt�]\ p Y�|R&�#e&D\z\-�]\Ig$#�[ h ��lmlwS-`${k[�nI\zS-`$��&�# � %'& p c�#��"��l�[�`+&�ak��l u$��h [�`$`$� h cm� ph [�akg$%$c��"#�Y � ����� � � � ��� ��� � � � ��� ��� ��� � � ���� ��� ��� � � �+� � ��.��� } � � � � ��� } ��� � � Y

���w!'&�# ��� � &�YRZ�YI�w!'&�#�#e&�&�` p x�YIZ�Y6�SVa�Y �%'& p c�#��"�@!$%�Sz\ p SV`${�&D\-{�[�#TSVc u a>l�[�`�&�` � ��xXj u (ig/�"# h %$!'��Y� ����� � � ����� ��� � � � ��� ��� � � � � ���� ��� ��� � � �+� � ��.��� } � ��� � ��� �i� � ��� }�x &D( �D����� Y

� �&�ab� ��� � �]Y��&�ak�]\7&�` p � Y$�'&D\-[�%$celT[il"YI|R&�#e&�\�\-�]\ ��� c�#m�"��l"YI�w` � ����� �����,� � � ��� � ����� ��� �(� � � � � � !#�

��� � ��� � �� ��� � � � ���%��� � ��� ��� ��� � ��� � ��� � ��� ����� �� �� � � � � � !#� � ��� � }'g'&y{���l ��� =� �� �� } � &�`j�S-�"{�[/} ��� } ��%$`$� �D����� Y

���

Page 75: O'3 0D. - cs.umd.edu

� �&�l S<�,� � � Y �&�lwSzn�Y &g$c�S-a>&D\'g'&�#e&�\�\-�]\1&D\-{�[�#�S-c u a>lPno[�# � %'& p c�#��"��g$#�[�!�\-�"a>l"Y � � �+� � � � � ����������� � � ��� � �������� � � � � ��� � � � � � ���.��� }�= � � � ��� � � � � � ��= }~xX&D( �D����� � &�\4lT[�|R#�[ h �"� p S-`${il�[�n�c u �k�JSzntc u � lT#e&��]\zS� (�akg/[ilwS-%$a [�` � #�cTS�� h S_&D\R��`�c��]\z\zS-{��"` h ��} 0S_lwS-[�`I}<&�` p |R&�cmc��"#�` � � h [�{�`�S-c�S-[�`I} � �]\ � r S r }$g'&y{���l� = � � ����� }ijC� h �"a;!'�"# ��� �,���eY

� �S-a �� � � Y/�SVa�Y � ��l���&y# h�u�p S-#�� h cTSV[�`'l�S-`>[�! � � h c � [�#�S-�"`ic�� p@p &�ce&y!'&�l�� l�($l�c��"a@l"Y<��` � �����������,� � ���� ��

� �,� � �(� � � � � ��� ����� � � �"!#�$� ���+�/����� � � ��� ���.� � � � � ��� ����� �� �� � ������� ���� ��� � }'g'&y{���l� � � =$}�*C&�l u�r Sz\z\-��} � *�} � g$#�Sz\ �D���� Y

� C#�%'l.��= � � Y'|NY�C#�%'l�U�&D\�} � Y � &�` p [�\-g u }<&�` p x�Y � `�S-#�Y ��u ��g'[����"#�[yn�g'&�#]&D\z\V�]\Rg$#��]�$�IY ����� � � ��� � � ��� ������ � ��� � � �+� � � � � } �y� � �� ��� ��� =� ��� �$}�*[ r �"a;!/�"# ��� ��= Y

� C% h U ����� j;Y�C% h U<Y � l�%$# r �"(�[�n'g'&y#e&D\z\-�]\1a>& hmu S-`$�[�#�{�&�`�S���&�c�S-[�`k&�` p g$#�[�{�#]&�aka;S-`${'Y ��� � � � �+� � ��.���� � ��-���� � } � � � ��� ��� � = � }�xX&�# hmu9������� Y

� � �]S-{ ��� � ��Y � Y � �]S-{ u cm[�`IY � � �� ����� � �� ��� �� � ������� ��� � � � � ���� � � � ��� � � � � ��� ���� ��� ��� Y�x�[�#�{i&�`)�&�%�n �a@&�`$`I} � &�`Xx &yc��"['} ��� } �D����� Y

� xX&�#�c(� � � x�YNx &y#�c�S-`I}Rj;Y7x�Y ��u S_&�#m%�\�\zS�}�&�` p�� Y � YI�w(��"`${i&�#�Y�|R&�#e&D\z\-�]\g$#�[ h ��lmlwS-`${ [yn � %'& p c�#m�"��l�[�`�&u [�#�S��"[�`ic]&D\z\V(X#�� h [�`��'{�%$#e&�!�\-�>&�# h�u S-c�� h c�%$#m� h [�akg$%$c�S-`${ l�($l�c��"a�Y���` � � � ����� �.����� ��� � � ����� �

��� � ��� � �� ��� � � � ��� � ��� ��� ������ � ������� ���� � ��������� �,� � }�g'&�{���l6� � =� �� �� } � c�Y ��u &�#�\-��l"}�� � } � %${�%'l�c�D� � � Y

� x��]S�� � � W;Y � W Y�x��]SP&�` p � Y � SV%IYR|R&�#]&D\z\V�]\Ig$#�[ h ��l�lwS-`${�nt[�# � %'& p cm#��"� g$#m[�!�\-�"a>l"YI�w` � �����������,� � � ��� ��

� ��� � � � � ��� �� ������ � � � ���%��� � ��� � �6��� ��� � � � � � � ��������� �,� � }'g'&�{���l � = � � � = � } � c�Y ��u &�#�\-��l"}N� � }� %${�%'l�c ��� � � Y

� *C&�` p ��� � � Y�;Y�*C&�` p (�} � Y$x�[�[�`'&$}�&�` p�� Y � &���&�{�[�g'&D\_&�`IY � S-`$��&�# � %'& p c�#��"��&D\-{�[�#TSVc u a>lR[�`@c u � u (�g'�"# �h %$!/��YI�w` ��� � �������.����� ��� �� �������(� � ��� � �� ������ � � � ���%��� � ��� � � ��� ��� � ��� � �� � ��������� �,� � }�g'&y{���l����� � ����� } � c�Y ��u &�#�\-��l"}$� � } � %${�%'lTc ��� ��� Y

� *��]\_l � � � � Y � Y�*�]\_l�[�`�&�` p Z�Y � &�ak�"c�Y � h [�`'lwS_l�cm�"`ic u SV�"#]&�# hmu S h &�\#m�"g$#���l��"`�ce&�c�S-[�`sno[�# r � h c�[�# p &�ce&$Y� � �+� � ��� � ��� � � ����� } �� � � ��� �D��� � �� �� } � %${�%'l�c ��� � � � &�\4lT[ � �����������,� � � ��� � �#� � ��� � � � � �� ���%��� � ��� � � }ij�&D\z\_&�l"} � %${�%'lTc ��� � � �eY

� *��]\_l � ��� � Y � Y *��]\4lT[�`9&�` p Z�Y � &yak�"c�Y � g'[�g$%�\4&yc�S-[�`9&�`'&D\-(~l S4l�nt[�# u S-�"#e&y# h�u S h &D\ p &yce&kl�c�#m% h c�%$#���l"Y��w`v�Y<j�&�(�&D\P&�` p �eY � #]&DS-{��"#�}$� p S-c�[�#]l"} � � � ����� �.��������� � ��������� ��� ��� � � �"!#� � � � ��� �� ������ ���� ���%��� � ��� � � ��� � ��� � ��� � ��� ��� � �� �� }$g'&�{���l ���� � ����� } � &�`��$#e&y` h S4l h ['} ��� }$xX&D( ��� � � Y

���

Page 76: O'3 0D. - cs.umd.edu

�"&#��"`�� � � � Y � Y &#m�"`'l�c��]S-`IY x�%�\-c�S p S-ak�"`'lwS-[�`'&D\;c�#�S-��lk%'lT� p nt[�#>&�l�l�[ h S4&yc�S r �9l���&�# hmu S-`${'Y � �%�#����� �� �� ��� � ��������� �,� ��� �� ��� � } �"� � � ��� � = � � = � }���%$`$� ��� � � Y

�"&#��"`�� � � � Y � Y &#��"`'lTc��]S-`IY � g'&�c�S_&D\ � %$�"#�(�g$#�[ h ��lmlwS-`${XS-` &�`�[�!$� � h c � [�#�S-�"`icm� p�p &�ce&�!'&�lT� l�($l�c��"a�Y��w` � ����� �����,� ������� � � ����� � ��� � ��� � �"!#� � � ��� � �� ������ � � � ��� � ��� ��� ��� ��� � ��� � ��� � ��� ����� �� �� }/g'&�{���l ����� � ����� }���&�l u S-`${�c�[�`I}/j � }$x &D( �D� � � Y

� |N��&�` �� � W;Y1|N��&y`$['Y � %$#�%$`$� h [�%$#�!'� � %�SR#��"akg�\zS-c�c�[�%$cm��%$`$�k&DS-#��;g�\_&DS-`$��Y ���� � ��� �� �� ��� � � � ��� � � ��� }��� � � = � � ���� } � � �� Y

� � [�!�S<� �� � Y � Y � [�!�S-`'l�[�`IY ��u �+U�� p �~� �ic�#��"��� � l���&�# hmu lTc�#�% h c�%$#��@nt[�#�\_&�#�{��+a;%�\-c�S p S-ak�"`'lwS-[�`'&D\ p ( �`'&ya;S h SV` p �]�$��l"YR�w` ��� � �������.�������� � ��������� �(� ����� � �"!#����� � ��� � �� ��� � � � ��� � ��� ��� ��� �������� ������� ��� ����� �� �� }'g'&�{���l �� � � �$} � `$` � #�!'[�#�}'x��e} � g$#�Sz\ ��� � � Y

� � [�l���� � � � Y � [il��"`�nt�]\ p }'Z�Y � &yak�"c�} � Y ��u & !P�"#D}i&�` p@� Y$QY/�9�"!$!/�"#�Y � g$g�\zS h &yc�S-[�`�[�n u SV�"#]&�# hmu S h &�\ p &�ce&lTc�#�% h c�%$#���lc�[k{��"[�{�#e&�g u S h &D\<S-`�no[�#ma>&�c�S-[�`Xl�(~lTc��"a>l��R| u &�l������eY � [�akg$%$c��"# �ih S-�"` h � �� � �D����� }v�`�S r �"#elwS-c�(+[�n�xX&�#�(�\4&y` p } � [�\z\-�"{�� |R&y#�U1}$xXj;} � �"g$c��"a;!'�"# ��� � � Y

� � [�c�� �$�� j;Y � [�c��"a�Y � g'&�cTS4&�\'� [ySV` S-` p S h ��l Y���` � � � ����� �.����� ��� ���� ��-���� ��� � � ��� �� ������ ��� � ���%��� � ��� � ������ �� ����(� ���,� ��� ���,� � }�g'&�{���l = � � = �� }%C[�!/��} ��&�g'&�`I} � g$#�Sz\ ����� � Y

� � &�ab����=�! � Z�Y � &�ak�"c�&�` p9� Y7QY �s�"!$!'�"#�Y � c�[�#�S-`${ & h [y\�\-� h c�S-[�`�[�ng'[y\V(�{�[�`'lL%'lwS-`${ � %'& p c�#��"��l Y���� �� � ��� � � �� ������ ����� � � ��� ��� � � } � � � ��� � � � � ����� } ��%�\-( ��� ��= � &D\_l�[+|R#�[ h �"� p S-`${ilC[�n � [�akg$%$c��"# 0�S �l SV[�` &�` p |R&�c�c��"#�` � � h [�{�`�S-c�S-[�`)� � }/��&�l u SV`${�c�[�` j � } ��%$`$� �D� � � } ����� � ����� �$&�` p v�`�S r �"#elwS-c�([yn xX&�#�(�\_&�` p�� [�abg$%$c��"# �ih S-�"` h � � � hmu `�S h &D\ � �"g'[�#�c ���������������� �]Y

� � &�ab� �� & � Z�Y � &�ak�"c�Y � � ��� ����� ��� ��� � � � � �)� �������� ��� �� ��#��� � �� ���� �� ��� ��� ��� Y �qp$p S_l�[�` �%�9��lw\-�"(�} � ��& p��S-`${'}<x � } ������ Y

� � &�ab� �� ! � Z�Y � &�ak�"cDY � ��� �)������ ������ � ���&� ���� �� � � � �� ���� �� ��� ��� ��� � � � �+� � ��� � � ��� � � � � � � � � ��� ��� � � � ����,� � � ��� � �#� � Y ��p$p S_l�[�` �%�s��lw\-�"(�} � ��& p S-`${'}<x � } ������ Y

� �ihmu � � � � Y � Y �ihmu �&�#mc ��Ykv�\-c�#]& h [�akg$%$c��"#]l"Y���� � � � ��� ������ ������ � ��� � ��� � � �6� �,� � � ��� � � ������� ��� �� � � � � � } � � � ��� � � � ��= �$� },& h c�[�!/�"# ��� � Y

�@�9�"!$!�� ��� � YIQY �9�"!$!/�"#�Y � � � �)����� � ����� � ��� �� ��� � � � ����� � � � Y�| u j c u ��lwS_l"}Iv�`�S r �"#elwS-c�(X[�n�xX&�#�(�\_&�` p }� [�\z\V�"{���|R&�#�U<}�xXj;}�xX&�# hmu;��� � � � &D\_l�[ v�`�S r �"#elwS-c�(�[�n'xX&�#�(�\4&y` p�� [�akg$%$c��"# �ih SV�"` h � � � h�u `�S h &D\� �"g'[�#�c ���������������� �]Y

� =