# Эффективные алгоритмы, осень 2007: Приближённые алгоритмы

• View
82

• Category

## Documents

Embed Size (px)

### Text of Эффективные алгоритмы, осень 2007: Приближённые...

• / 2:

.

Computer Science http://logic.pdmi.ras.ru/infclub/

. (CS ) 2. 1 / 15

http://logic.pdmi.ras.ru/~infclub/

• 1

. (CS ) 2. 2 / 15

• A (relative performance guarantee) , I

I A(I )/OPT(I ) ;I A(I )/OPT(I ) .

-.

1, 1. , 1.

. (CS ) 2. 3 / 15

• A (relative performance guarantee) , I

I A(I )/OPT(I ) ;I A(I )/OPT(I ) .

-.

1, 1. , 1.

. (CS ) 2. 3 / 15

• A (relative performance guarantee) , I

I A(I )/OPT(I ) ;

I A(I )/OPT(I ) . -.

1, 1. , 1.

. (CS ) 2. 3 / 15

• A (relative performance guarantee) , I

I A(I )/OPT(I ) ;I A(I )/OPT(I ) .

-.

1, 1. , 1.

. (CS ) 2. 3 / 15

• A (relative performance guarantee) , I

I A(I )/OPT(I ) ;I A(I )/OPT(I ) .

-.

1, 1. , 1.

. (CS ) 2. 3 / 15

• A (relative performance guarantee) , I

I A(I )/OPT(I ) ;I A(I )/OPT(I ) .

-.

1, 1. , 1.

. (CS ) 2. 3 / 15

• 1

. (CS ) 2. 4 / 15

• {s1, . . . , sn}. (shortestcommon superstring) u, si .

NP-.

. (CS ) 2. 5 / 15

• {s1, . . . , sn}.

(shortestcommon superstring) u, si .

NP-.

. (CS ) 2. 5 / 15

• {s1, . . . , sn}. (shortestcommon superstring) u, si .

NP-.

. (CS ) 2. 5 / 15

• {s1, . . . , sn}. (shortestcommon superstring) u, si .

NP-.

. (CS ) 2. 5 / 15

• U = {u1, . . . , un} = {S1, . . . , Sk}, Si U. U: U =

S S .

Si pi 0. (set cover problem) , U .

Hn- .

. (CS ) 2. 6 / 15

• U = {u1, . . . , un} = {S1, . . . , Sk}, Si U.

U: U =

S S . Si pi 0. (set cover problem) , U .

Hn- .

. (CS ) 2. 6 / 15

• U = {u1, . . . , un} = {S1, . . . , Sk}, Si U. U: U =

S S .

Si pi 0. (set cover problem) , U .

Hn- .

. (CS ) 2. 6 / 15

• U = {u1, . . . , un} = {S1, . . . , Sk}, Si U. U: U =

S S .

Si pi 0.

(set cover problem) , U .

Hn- .

. (CS ) 2. 6 / 15

• U = {u1, . . . , un} = {S1, . . . , Sk}, Si U. U: U =

S S .

Si pi 0. (set cover problem) , U .

Hn- .

. (CS ) 2. 6 / 15

• U = {u1, . . . , un} = {S1, . . . , Sk}, Si U. U: U =

S S .

Si pi 0. (set cover problem) , U .

Hn- .

. (CS ) 2. 6 / 15

• , i , j , k , si k sj k , wijk = si sj [k + 1..|sj |]:

s6 = abcab X

bbca Y

, s2 = bbca Y

aaccbcac Z

w6,2,4 = abcab X

bbca Y

aaccbcac Z

s set(s) = {si |si s} set(s) s : U = {s1, . . . , sn}, = {set(si )} {set(wijk)}

. (CS ) 2. 7 / 15

• ,

i , j , k , si k sj k , wijk = si sj [k + 1..|sj |]:

s6 = abcab X

bbca Y

, s2 = bbca Y

aaccbcac Z

w6,2,4 = abcab X

bbca Y

aaccbcac Z

s set(s) = {si |si s} set(s) s : U = {s1, . . . , sn}, = {set(si )} {set(wijk)}

. (CS ) 2. 7 / 15

• , i , j , k , si k sj k , wijk = si sj [k + 1..|sj |]:

s6 = abcab X

bbca Y

, s2 = bbca Y

aaccbcac Z

w6,2,4 = abcab X

bbca Y

aaccbcac Z

s set(s) = {si |si s} set(s) s : U = {s1, . . . , sn}, = {set(si )} {set(wijk)}

. (CS ) 2. 7 / 15

• , i , j , k , si k sj k , wijk = si sj [k + 1..|sj |]:

s6 = abcab X

bbca Y

, s2 = bbca Y

aaccbcac Z

w6,2,4 = abcab X

bbca Y

aaccbcac Z

s set(s) = {si |si s} set(s) s : U = {s1, . . . , sn}, = {set(si )} {set(wijk)}

. (CS ) 2. 7 / 15

• , i , j , k , si k sj k , wijk = si sj [k + 1..|sj |]:

s6 = abcab X

bbca Y

, s2 = bbca Y

aaccbcac Z

w6,2,4 = abcab X

bbca Y

aaccbcac Z

s set(s) = {si |si s} set(s) s : U = {s1, . . . , sn}, = {set(si )} {set(wijk)}

. (CS ) 2. 7 / 15

• , i , j , k , si k sj k , wijk = si sj [k + 1..|sj |]:

s6 = abcab X

bbca Y

, s2 = bbca Y

aaccbcac Z

w6,2,4 = abcab X

bbca Y

aaccbcac Z

s set(s) = {si |si s}

set(s) s : U = {s1, . . . , sn}, = {set(si )} {set(wijk)}

. (CS ) 2. 7 / 15

• , i , j , k , si k sj k , wijk = si sj [k + 1..|sj |]:

s6 = abcab X

bbca Y

, s2 = bbca Y

aaccbcac Z

w6,2,4 = abcab X

bbca Y

aaccbcac Z

s set(s) = {si |si s} set(s) s

: U = {s1, . . . , sn}, = {set(si )} {set(wijk)}

. (CS ) 2. 7 / 15

• , i , j , k , si k sj k , wijk = si sj [k + 1..|sj |]:

s6 = abcab X

bbca Y

, s2 = bbca Y

aaccbcac Z

w6,2,4 = abcab X

bbca Y

aaccbcac Z

s set(s) = {si |si s} set(s) s : U = {s1, . . . , sn}, = {set(si )} {set(wijk)}

. (CS ) 2. 7 / 15

• ()

, , si , 2Hn-

.

. (CS ) 2. 8 / 15

• ()

,

, si , 2Hn-

.

. (CS ) 2. 8 / 15

• ()

, , si

, 2Hn-

.

. (CS ) 2. 8 / 15

• ()

, , si , 2Hn-

.

. (CS ) 2. 8 / 15

• ()

, , si , 2Hn-

.

. (CS ) 2. 8 / 15

• ()

, , si , 2Hn-

.

. (CS ) 2. 8 / 15

• si (-) s, : s1 si , s1 w1,j ,k , , , .. ,

. (CS ) 2. 9 / 15

• si (-) s

, : s1 si , s1 w1,j ,k , , , .. ,

. (CS ) 2. 9 / 15

• si (-) s,

: s1 si , s1 w1,j ,k , , , .. ,

. (CS ) 2. 9 / 15

• si (-) s, : s1 si , s1

w1,j ,k , , , .. ,

. (CS ) 2. 9 / 15

• si (-) s, : s1 si , s1 w1,j ,k

, , , .. ,

. (CS ) 2. 9 / 15

• si (-) s, : s1 si , s1 w1,j ,k , , , ..

,

. (CS ) 2. 9 / 15

• si (-) s, : s1 si , s1 w1,j ,k , , , .. ,

. (CS ) 2. 9 / 15

• ()

, s , s

.

. (CS ) 2. 10 / 15

• ()

, s

, s

.

. (CS ) 2. 10 / 15

• ()

, s , s

.

. (CS ) 2. 10 / 15

• ()

, s , s

.

. (CS ) 2. 10 / 15

• 1

. (CS ) 2. 11 / 15

• , :s1 = abc , s2 = bac , s3 = bcd , s4 = cde wijk :w132 = abcd , w141 = abcde, w241 = bacde, w342 = bcde set(si ) set(wijk), :S1 = set(s1) = {s1}, p1 = 3,S2 = set(s2) = {s2}, p2 = 3,S3 = set(s3) = {s3}, p3 = 3,S4 = set(s4) = {s4}, p4 = 3,S5 = set(w132) = {s1, s3}, p5 = 4S6 = set(w141) = {s1, s3, s4}, p6 = 5,S7 = set(w241) = {s2, s4}, p7 = 5,S8 = set(w342) = {s3, s4}, p8 = 4

. (CS ) 2. 12 / 15

• , :s1 = abc , s2 = bac , s3 = bcd , s4 = cde

wijk :w132 = abcd , w141 = abcde, w241 = bacde, w342 = bcde set(si ) set(wijk), :S1 = set(s1) = {s1}, p1 = 3,S2 = set(s2) = {s2}, p2 = 3,S3 = set(s3) = {s3}, p3 = 3,S4 = set(s4) = {s4}, p4 = 3,S5 = set(w132) = {s1, s3}, p5 = 4S6 = set(w141) = {s1, s3, s4}, p6 = 5,S7 = set(w241) = {s2, s4}, p7 = 5,S8 = set(w342) = {s3, s4}, p8 = 4

. (CS ) 2. 12 / 15

• , :s1 = abc , s2 = bac , s3 = bcd , s4 = cde wijk :w132 = abcd , w141 = abcde, w241 = bacde, w342 = bcde

set(si ) set(wijk), :S1 = set(s1) = {s1}, p1 = 3,S2 = set(s2) = {s2}, p2 = 3,S3 = set(s3) = {s3}, p3 = 3,S4 = set(s4) = {s4}, p4 = 3,S5 = set(w132) = {s1, s3}, p5 = 4S6 = set(w141) = {s1, s3, s4}, p6 = 5,S7 = set(w241) = {s2, s4}, p7 = 5,S8 = set(w342) = {s3, s4}, p8 = 4

. (CS ) 2. 12 / 15

• , :s1 = abc , s2 = bac , s3 = bcd , s4 = cde wijk :w132 = abcd , w141 = abcde, w241 = bacde, w342 = bcde set(si ) set(wijk), :S1 = set(s1) = {s1}, p1 = 3,S2 = set(s2) = {s2}, p2 = 3,S3 = set(s3) = {s3}, p3 = 3,S4 = set(s4) = {s4}, p4 = 3,S5 = set(w132) = {s1, s3}, p5 = 4S6 = set(w141) = {s1, s3, s4}, p6 = 5,S7 = set(w241) = {s2, s4}, p7 = 5,S8 = set(w342) = {s3, s4}, p8 = 4

. (CS ) 2. 12 / 15

• , U = {si}i[1..4], = {Si}i[1..8], Si pi

Recommended

Documents
Documents
Documents
Documents
Education
Documents
Documents
Documents
Education
Documents
Education
Documents