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A Statistics Propagation Approach to Enable Cost-Based Optimization of Statement Sequences

A Statistics Propagation Approach to Enable Cost-Based Optimization of Statement Sequences. Tobias Kraft , Holger Schwarz, Bernhard Mitschang Institute of Parallel and Distributed Systems University of Stuttgart. Overview. Motivation Cost Estimation Approach Histogram Propagation

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A Statistics Propagation Approach to Enable Cost-Based Optimization of Statement Sequences

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  1. A Statistics Propagation Approachto Enable Cost-Based Optimizationof Statement Sequences Tobias Kraft, Holger Schwarz, Bernhard Mitschang Institute of Parallel and Distributed Systems University of Stuttgart

  2. Overview • Motivation • Cost Estimation Approach • Histogram Propagation • Related Work • Experiments • Conclusion & Future Work

  3. MotivationThe Case for Optimization • Many of today’s applicationsembed query generators. • Some of these generators notonly produce a single query buta sequence of SQL statements(e.g. MicroStrategy DSS tools). • Rewriting these sequences maylead to significant performanceimprovements! • Development of an optimizer based on rewrite rules and a heuristic priority-based control strategy • Coarse-Grained Optimization (CGO) [VLDB03]

  4. MotivationStatement Sequences CREATE TABLE q1 (custkey INTEGER, turnover1990 FLOAT); CREATE TABLE q2 (custkey INTEGER, turnover1991 FLOAT); CREATE TABLE q3 (custkey INTEGER, name VARCHAR(25)); INSERT INTO q1 SELECT o.custkey, SUM(o.totalprice) FROM orders o WHERE o.orderyear = 1990 GROUP BY o.custkey; INSERT INTO q2 SELECT o.custkey, SUM(o.totalprice) FROM orders o WHERE o.orderyear = 1991 GROUP BY o.custkey; INSERT INTO q3 SELECT c.custkey, c.name FROM q1, q2, customer c WHERE q1.custkey = c.custkey AND q1.custkey = q2.custkey AND q2.turnover1991 > q1.turnover1990; DROP TABLE q1; DROP TABLE q2; We focus on statement sequences that: • compute the final result of a requestin a set of subsequent steps, • allow to share intermediate results bymultiple subsequent steps, • temporarily store intermediate resultsin tables that are being created anddropped within the sequence, • store the final result in a table that isnot being dropped within the sequence. q1 q2 q3

  5. MotivationProblems of the Heuristic Control Strategy • In some scenarios a rule application may lead to deteriorationof performance. • Different behavior on different platforms and database management systems. • Alternative sequences of rule applications lead to different results. • Need for a cost-based approach.

  6. Cost Estimation ApproachProblems & Solutions • Cost estimates depend on the physical layout of the database and the capabilities and strategies of the DBMS‘s query optimizer. • A cost model on top of the DBMS is no feasible solution. • Make use of the cost estimates provided by the DBMS‘s query optimizer. • DBMSs only provide cost estimates for statements on existing tables. • Execute CREATE TABLES statements before cost estimation. • Missing statistics for the created tables causes the DBMS‘s query optimizer to use default values for cardinality and selectivity. • Propagate statistics through the INSERT statements. • Make these propagated statistics available to the DBMS‘s optimizer.

  7. Cost Estimation Approach Algorithm of Cost Estimation Input: A statement sequence S. Output: A cost estimate for S. totalcosts = 0 foreach CREATE TABLE statement c in S Execute c on the underlying database system. foreach INSERT statement i in S (in the order given by S) Retrieve a cost estimate for i from the optimizer of the underlying database system. Add this cost estimate to totalcosts. Translate i into an algebraic tree. Retrieve histograms for the base tables from the underlying database system and propagate them through the algebraic tree to retrieve histograms for the target table of i. Store the resulting histograms in the catalog of the underlying database system. foreach CREATE TABLE statement c in S Drop the table that has been created by c. returntotalcosts.

  8. Cost Estimation Approach Architectural Overview

  9. T4    X   T1 T2 T3 Histogram PropagationOverview • We have adopted techniques from approximate query answering and added some extensions: • interval arithmetic for arithmetic terms, • heuristics for grouping and aggregation, • unification of comparison operators, • normalization of histograms, • common subexpressions • SQL statement sequence  algebraic operator trees. • Everything is a bucket / histogram: • NULL values are represented by a special bucket. • Constant values (used in arithmetic terms) arerepresented by a histogram with a single bucket. • Sets of constants (used in IN-predicates) arerepresented by a histogram.

  10. Histogram PropagationHistograms • Buckets are 4-tuples:(low, high, card, dv ) • The NULL value:(null, null, card, 1) • A constant value c :(c, c, card, 1)

  11. Histogram PropagationAlgebra and Propagation • Operators: projection, selection, cartesian product, union, difference and grouping (including aggregation). • A join can be represented by a cartesian product followed by a selection that contains the join condition. • Arithmetic terms (projection / selection) and predicates (selection) are also represented by operator trees. • Propagation is done by recursively traversing the algebraic operator tree and the arithmetic trees in a post order manner.

  12. A3 A1 A2 A1 A2 A1‘ A2‘ selectivity A1 A2 A1 A2 Histogram PropagationAlgebra and Propagation • Arithmetic Operators: • histograms as input • a result histogram as output • iterate over all bucket combinations • compute a result bucket for each bucket combination • Comparison Operators: • histograms as input • selectivity as output • some operators also provide modified histograms • iterate over all bucket combinations • compute a selectivity for each bucket combination(and adapt the buckets)

  13. + BI1 = 0 10 20 30 40 50 + BI2 = 0 10 20 30 40 50 0 0 10 20 30 40 50 0 10 20 30 40 50 BO 10 20 30 40 50 60 Serialization 0 10 20 30 40 50 10 20 30 40 50 60 Histogram PropagationInterval Arithmetic for Arithmetic Terms • Example of using interval arithmetic for adding two buckets: • BO.low = BI1.low + BI2.low • BO.high = BI1.high + BI2.high

  14. cardinality cardinality histogramof SUM(A) 30 100 50 tuple 50 tuple 20 10 histogram of attribute A value value 950 0 10 20 30 40 50 60 70 80 90 100 110 4875 lower bound of SUM(A) =450 + 500 = 950 upper bound of SUM(A) =2100 + 1900 + 875 = 4875 Histogram PropagationHeuristics for Grouping and Aggregation • Determine amount of groups and average group sizes. • Use these values together with the histogram of the attribute that should be aggregated to compute the aggregate buckets. SUM(A) ? 100 groupswithgroup size 50

  15. Histogram PropagationUnification of Comparison Operators • Comparison operators compare histograms. • A single operator implementation can be used for different purposes. • No separate join implementation is necessary. • E.g., the comparison operator ‘=‘ can be used in: • a predicate comparing two attributes, • a predicate comparing an attribute and a constant, • a join condition of an equi-join cartesian product followed by a selection thatcontains the join-condition as predicate, • an IN predicate comparing an attribute with a set of values join with a table (represented by a histogram) thatcontains the values of the value set.

  16. Related Workon Histogram Propagation • Papers on Approximate Query Answering: • Yannis E. Ioannidis, Viswanath Poosala:Histogram-Based Approximation of Set-Valued Query-Answers. VLDB 1999 • Viswanath Poosala, Venkatesh Ganti, Yannis E. Ioannidis:Approximate Query Answering using Histograms.IEEE Data Eng. Bull. 1999 • Transformation of SQL queries on tables into SQL queries on histograms. • Join is done by creating two tables under the uniform spread assumption such that each table represents a value distribution which fits to the respective input histogram. • Only equi-joins, no support for predicates that compare two attributes, no grouping and no support of arithmetic terms.

  17. ExperimentsExperimental Setup • Database: TPC-H benchmark database on IBM DB2 V9. • Sample sequences: • Sequence S1 generated by the MicroStrategy DSS tool suite. • A set of semantically equivalent sequences that result from the application of the CGO rewrite rules. • Variants of those sequences resulting from the use of different values in the filter predicates of the sequence.

  18. ExperimentsResults for Alternative Sequences

  19. ExperimentsResults for Different Selectivities

  20. Conclusion & Future Work • Cost estimates for statement sequences are necessary to avoid rule applications that lead to performance deterioration. • Making use of the cost estimates of the underlying DBMS is a feasible solution. • Histogram propagation is necessary to get useable cost estimates for statements that access intermediate-result tables and to avoid bad plans. • Future Work: • A cost-based control strategy. • Extensive measurements.

  21. Thank you foryour attention!

  22. Statistics API DB2 implementation Oracle implementation SQL Server implementation JDBC DB2database Oracledatabase SQL Serverdatabase Cost Estimation Approach Statistics API • is an interface that offers uniform DBMS-independent access to DBMS statistics, meta data and optimizer estimates • provides a flexible histogram format that abstracts from proprietary data structures used in different DBMSs • implementations exist for IBM DB2, Oracle and MS SQL Server

  23. INSERT INTO temptable SELECT year(o.o_orderdate), count(*) FROM orders o WHERE year(o.o_orderdate) > 1992 AND o.o_orderpriority = ‘1-URGENT‘ GROUP BY year(o.o_orderdate) Histogram PropagationCommon Subexpressions • Identify arithmetic terms that appear multiple times in the different clauses of an SQL query. • Otherwise, the arithmetic term will be recomputed for each appearance and modifications of histograms may get lost.

  24. 10 buckets  4 buckets Merge 0 10 20 30 40 50 0 10 20 30 40 50 Histogram PropagationNormalization of Histograms • Worst case: • The number of buckets in the output histogram is the product of the number of buckets in the input histograms. • Serializing a histogram may double the number of buckets. • Normalization: • prior to the enumeration phase and / or after an output histogram has been produced, • reduces the number of buckets by merging adjacent buckets, • trade-off between complexity / performance and quality.

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