a statistics propagation approach to enable cost-based optimization of statement sequences

University of Stuttgart

aaAnwendungssoftware

ssA Statistics Propagation

Approachto Enable Cost-Based

Optimizationof Statement SequencesTobias Kraft, Holger Schwarz, Bernhard

Mitschang

Institute of Parallel and Distributed SystemsUniversity of Stuttgart

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Overview

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

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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]

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MotivationStatement Sequences

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.

CREATE TABLE q1(custkey INTEGER, turnover1990 FLOAT);

CREATE TABLE q2(custkey INTEGER, turnover1991 FLOAT);

CREATE TABLE q3(custkey INTEGER, name VARCHAR(25));

INSERT INTO q1SELECT o.custkey, SUM(o.totalprice)FROM orders oWHERE o.orderyear = 1990GROUP BY o.custkey;

INSERT INTO q2SELECT o.custkey, SUM(o.totalprice)FROM orders oWHERE o.orderyear = 1991GROUP BY o.custkey;

INSERT INTO q3SELECT c.custkey, c.nameFROM q1, q2, customer cWHERE q1.custkey = c.custkey AND q1.custkey = q2.custkey AND q2.turnover1991 >

q1.turnover1990;

DROP TABLE q1;

DROP TABLE q2;q1 q2

q3

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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.

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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.

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Cost Estimation Approach Algorithm of Cost Estimation

Input: A statement sequence S.Output: A cost estimate for S.

totalcosts = 0foreach 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 andpropagate them through the algebraic tree to retrieve histograms for the targettable of i.Store the resulting histograms in the catalog of the underlying database system.

foreach CREATE TABLE statement c in SDrop the table that has been created by c.

return totalcosts.

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Cost Estimation Approach Architectural Overview

cost-basedC

GO

optimizer

DBMS execution engineand data management

DBMS query optimizer

CGO ruleset

cost-estimation componentfor statement sequences

histogrampropagation

statement costaggregation

cost-basedcontrol strategy

Statistics API

DDL statementshistograms cost estimatesfor statements

JDBC

sequence optimizedsequence

cost-basedC

GO

optimizer

DBMS execution engineand data management

DBMS query optimizer

CGO ruleset

cost-estimation componentfor statement sequences

histogrampropagation

statement costaggregation

cost-basedcontrol strategy

Statistics API

DDL statementshistograms cost estimatesfor statements

JDBC

sequence optimizedsequence

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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) are

represented by a histogram with a single bucket. Sets of constants (used in IN-predicates) are

represented by a histogram.

X

T1 T2

T3

T4

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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)

1

* #buckets

1

1 #high

1

1 #low

Histogram#properties: Properties#dataType: int

Bucket#properties: Properties#dataType: int#cardinality: double#distinctValues: double

Value#dataType: int

CharValue-value: String

DateValue-value: Date

DecimalValue-value: double

IntegerValue-value: long

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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.

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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)

A1 A2

A1 A2

A3

A1 A2

A1 A2

A1‘ A2‘selectivi

ty

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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

+ =10 20 30 40 500 10 20 30 40 500 0 10 20 30 40 50 60

10 20 30 40 50 60Serializati

on

BI1

10 20 30 40 500

BI2

10 20 30 40 500

BO

10 20 30 40 500+ =

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10 20 30 400 50 60 70 80

102030

90 100110histogram of attribute Ahistogram of attribute A

cardinality

value

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.

lower bound of SUM(A) =450 + 500 = 950

upper bound of SUM(A) =2100 + 1900 + 875 = 4875

100 groupswith

group size 50

50 tuple

50 tuple

SUM(A) ?

950 4875

histograhistogramm

of SUM(A)of SUM(A)100

cardinality

value

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• 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.

Histogram PropagationUnification of Comparison Operators

CCC1

…Cn

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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.

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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.S1

S2 S3 S4 S5

S6 S7 S8 S9

S10

S1

S2 S3 S4 S5

S6 S7 S8 S9

S10

S1

Q1 Q2 Q3

Q4

Q5S1

Q1 Q2 Q3

Q4

Q5

S10

Q6

Q7S10

Q6

Q7

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ExperimentsResults for Alternative Sequences

6,859

6,858

9,375

3,791

6,805

6,803

6,802

3,735

9,455

6,862

S1

S2

S3

S4

S5

S6

S7

S8

S9

S10

cost estimate (timerons / 1000)

1,810

1,791

2,356

1,103

2,345

1,803

1,777

1,765

2,344

1,059

1,777

1,763

1,766

1,083

2,379

1,826

S1

S2

S3

S4

S5

S6

S7

S8

S9

S10

execution time (s)

without histogram propagation

with histogram propagation

55,170

16,815

16,887

16,887

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ExperimentsResults for Different Selectivities

cost estimate (timerons / 1000) for sequence S1

9,4009,425

9,4509,475

9,500

100,000 300,000 500,000parameter value

execution time (s) for sequence S1

2,2752,325

2,3752,425

2,475

100,000 300,000 500,000parameter value

without histogram propagation with histogram propagation

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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.

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Thank you foryour attention!

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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

DB2database

Statistics APIDB2

implementationOracle

implementationSQL Server

implementation

Oracledatabase

SQL Serverdatabase

JDBC

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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.

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)

orders o_orderdate, o_orderpriority

$1 = year(o_orderdate)

$1 > 1992

$1, $2 = count(*)

$1, $2

o_orderpriority = ‘1-URGENT‘

orders o_orderdate, o_orderpriority

$1 = year(o_orderdate)

$1 > 1992

$1, $2 = count(*)

$1, $2

o_orderpriority = ‘1-URGENT‘

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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.

10 20 30 40 500 0 10 20 30 40 50

10 buckets 4 buckets

Merge

a statistics propagation approach to enable cost-based optimization of statement sequences

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