多表连接查询优化的相关研究吕彬 2009.3.5. motivation 图中表示连接顺序对查询效率的影响：准确估计选择度要考虑属性间的相关性问题关键：

多表连接查询优化的相关研究吕彬

2009.3.5

motivation星型连接效果对比图

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图中表示连接顺序对查询效率的影响：准确估计选择度要考虑属性间的相关性

问题关键：高效地计算属性间的相关度

AgendaMulti-table join overview

•Heuristic and randomized optimization for the join ordering problemMichael Steinbrunn ， et al, The VLDB Journal (1997) 6: 191–208

Attribute correlation detection•BHUNT: Automatic Discovery of Fuzzy Algebraic Constraints in Relational Data

Paul G. Brown Peter J. Haas , Proceedings of the 29th VLDB Conference, 2003

•CORDS: Automatic Discovery of Correlations and Soft Functional DependenciesIhab F. Ilyas ， Volker Markl, et al, SIGMOD 2004, June 13–18, 2004,

•COCA: More Accurate Multidimensional Histograms out of More Accurate Correlations Detection

CAO Wei1, QIN Xiongpai, WANG Shan,WAIM2008

Star join•Star Gazing from atop your DB2 z/OS Database Server

Terry Purcell, et al, Intelligent Optimizer

•Star join revisited: Performance internals for cluster architecturesJosep Aguilar-Saborit, Data & Knowledge Engineering 63 (2007) 995–1013

Heuristic and randomized optimization for the join ordering problem

•Choosing join type based on cost

•Solution space for the join ordering problem

•Join ordering strategies

•Quantitative analysis

•Conclusion

Multi-table join overview

Choosing join type based on cost•Cost models

•Nested loop join

•Sort-merge join

•Hash join


IO Cost

Elapsed Time

Row Cost

CPU Cost

Base Cost

Scan CostPage Cost

Solution space for the join ordering problem•Left-deep trees

n! ways to allocate n base relations

to the tree’s leavesgood solutions because of

exploiting the cost-reducing

pipelining technique

•Bushy treesan adaptable plan

enumeration strategylinear graphs

(n3 − n)/6 star graphs

(n−1) 2n−2


Join ordering strategies•Deterministic algorithms

heuristic or exhaustive search

•Randomized algorithmsDefine a set of moves which constitute edges between the different solutions of the solution spaceperforms a random walk along the edges according to certain rules,terminating as soon as no more applicable moves exist or a time limit is exceeded

•Genetic algorithmsmake use of a randomized search strategy very similar to biological evolution

•Hybrid algorithmscombine the strategies of pure deterministic and pure randomized algorithms


Quantitative analysis•Class of the join graph

•Relation cardinalities and domain sizes


Quantitative analysis•Solution spaces


Quantitative analysis•deterministic algorithms


Quantitative analysis•deterministic algorithms


Quantitative analysis•Randomized and

genetic algorithms



genetic algorithms



genetic algorithms



genetic algorithms


Quantitative analysis•Total running time

•Find final solution time


Conclusion•Heuristic algorithms Vs Randomized and genetic algorithms

compute quickly, but far from the optimum. better suited for join optimizations; although require a longer running time

•Solution spaceExcept the star join graph, the bushy tree is preferable than left-deep

processing trees.

•The extensibility of randomized and genetic algorithms


Query-Driven approaches•Query workload

•Query feedback

•Multidimensional histogram

•SASH algorithm

•Advantage and disadvantage

Data-Driven approaches•Statistical

Chi-square test, Log-linear model

•ProbabilityBayesian network, Markov network

•Full scan vs. Sample

•hard FDs, soft FDs, Correlation

Attribute correlation detection

BHUNT: Automatic Discovery of Fuzzy Algebraic Constraints in Relational Data

•Example


Overview of BHUNT•Algebraic Constraints

•Example a1 : deliveries.deliveryDate, a2 : orders.shipDate, ⊕:as the subtraction operator, P : orders.orderID = deliveries.orderID,I = { 2, 3, 4, 5} {∪ 12, 13, . . . , 19 } {∪ 31, 32, 33, 34, 35 } .


Overview of BHUNT•Generating Candidates C = (a1, a2, P,⊕).

Generating Pairing RulesTurning Pairing Rules Into Candidates

•Identifying Fuzzy ConstraintsConstructing Bump Intervals, by applying statistical histogramming, segmentation, or clustering techniques to a sample of the column valuesChoosing the Sample Size, The sample size is selected to control the number of “exception” records that fail to satisfy the constraint.

•Exploiting the ConstraintsIdentify the most useful set of constraints, and create “exception tables” to hold all of the exception records.

•Modify the queries to incorporate the constraints the optimizer uses the constraints to identify new, more efficient access paths.


Experimental results of BHUNT


CORDS: Automatic Discovery of Correlations and Soft Functional Dependencies

•.


CORDS: Automatic Discovery of Correlations and Soft Functional Dependencies

•soft functional dependencies•C1 => C2, the value of C1 determines the value of C2 not with certainty, but merely with high probability.

•hard functional dependencies•the value of C1 completely determines the value of C2.


CORDS overview•First: Enumerating and Pruning•Pruning rule

Type constraintStatistical constraintParing constraintWorkload constraintIdentify trivial cases


CORDS overview


Analyze distinct value of sampled

column (to test for SOFT FD)

Soft FD?

Chi-squared analysis (to test

for statistical dependency)

Correlated?

Column Group

(Top-k pair)

YES

NO

YES

CORDS discovers three property and relationship•Trivial cases

“soft” keys“trivial” column

•Soft FDs C1 => C2 |C1|/|C1, C2| CORDS estimates the |C1| and |C1, C2| using sample

•CorrelationsDetect statistical dependence using the sample-based chi-squared analysis


CORDS and query optimization

a query having a selection predicate p1 p2, p1 = “Make = Honda” ∧and p2 = “Model = Accord”. true selectivity : σp1 p2 = 1/10. ∧naïve estimate : Sp1 p2 = 1/|Make|∧ ・ 1/|Model| = 1/7 ・ 1/8 = 1/56,adjusted estimate : naïve estimate *|Make| |Model|/|Make, Model| = 1/56 * 56/9 = 1/9,


CORDS experimental result•Synthetic Data:

The Accidents database

•Benchmarking Data:The TPC-H benchmark

•Real-world Data: include a subset of the Census database and the Auto database,


CORDS experimental result


CORDS experimental result


COCA: More Accurate Multidimensional Histograms out of More Accurate Correlations Detection

robust and informative metric

—— entropy correlation coefficients

a novel yet simple kind of multi-dimensional synopses

—— COCA-Hist to cope with different correlations


Entropy correlation coefficients


Merits of COCA•Simple and straightforward

•Accurate and robust

•Informative and unified


Different histograms for different degrees of correlations•Histograms for value sparsity

MHIST+squeezing

•Histograms for mutual independenceAVI assumption

•Histograms for other situationsMHist-MaxDiff histograms

•Other improvementsdiscarding empty buckets


Experiments

CORDS: #1(0.39, 0.29) ,#3 (0.45, 0.58)


Experiments


Star Gazing from atop your DB2 z/OS Database Server•Index key feedback

•The problems are:• The cartesian join

•difficult to create suitable multi-column indexes unless the combination of filtering dimensions that are included in the queries are known.

Star join

Star Gazing from atop your DB2 z/OS Database Server•PAIR-WISE JOIN

Star join

Star Gazing from atop your DB2 z/OS Database Server•Performance

Star join

Star join revisited: Performance internals for cluster architectures

Star join

Cluster architectures and horizontal partitioning•partitioning schemes:

round robin,range partitioninghash partitioning

•Collocated and non-collocated

•Repartitioning Operator

Star join

Star join processing techniques•Bitmap join (BJ)

size ||T|| · ||S|| bitslarge size of the indicesthe maintenance of these indices

•Multi hierarchical clustering (MHC)reducing the number of I/O accesses to the fact table. a chunk-based file system specific to OLAP cubes is proposed. star join queries are transformed into range queries

•Star hash join (SHJ)Push down bit filters technique

Star join

Analysis

Star join

Analysis

Star join

Analysis

Star join

Thanks!Q & A

卡方检验 (Chi - square test) 作为非参数检验的一种 ,是常用的检验方法 , 通过比较两项或多项频数 , 旨在检测在一定显著性水平上实际频数与以某种理论模型或分布特征假设为基础的期望频数的差异度 [3 ] 。卡方检验第一步 , 建立原假设 H0 和备择假设 H1 ; 第二步 , 根据理论经验或理论分布计算期望频数 ; 第三步 , 根据实际频数和期望频数计算样本卡方值。如果运算出的卡方值大于卡方临界值 , 接受原假设 , 反之 , 接受备择假设[4 ,5 ,6 ]

Agenda

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多表连接查询优化的相关研究 吕 彬 2009.3.5. motivation 图中表示连接顺序对查询效率的 影响： 准确估计选择度要考虑属性间的 相关性 问题关键：

多表连接查询优化的相关研究吕彬 2009.3.5. motivation 图中表示连接顺序对查询效率的影响：准确估计选择度要考虑属性间的相关性问题关键：