Data Mining for Query Optimization

1. Data Mining for Query Optimization Jarek Gryz

2. Outline • Semantic Query Optimization • Soft Constraints • Query Optimization via Soft Constraints • Selectivity Estimation via Soft Constraints

3. Use integrity constraints associated with a database to rewrite a query into a form that may be evaluated more efficiently Semantic Query Optimization Some Techniques: Join Elimination Predicate Elimination Join Introduction Predicate Introduction Detecting an Empty Answer Set

4. Few (if any!) Commercial implementations of SQO Early Experiences: • Could not spend too much time on optimization • Few integrity constraints are ever defined • Association with deductive databases

5. Join elimination: example • select p_name, p_retailprice, s_name, s_address • from tpcd.lineitem, tpcd.partsupp, tpcd.part, tpcd.supplier • where p_partkey = ps_partkey and s_suppkey = ps_suppkey and • ps_partkey = l_partkey and ps_suppkey = l_suppkey; RI constraints: part-partsupp (on partkey) supplier-partsupp (on partkey) partsupp-lineitem (on partkey and suppkey) select p_name, p_retailprice, s_name, s_address from tpcd.lineitem, tpcd.partsupp, tpcd.part, tpcd.supplier where p_partkey = l_partkey and s_suppkey = l_suppkey;

6. Algorithm for join elimination • 1. Derive column transitivity classes from the join predicates in the query • 2. Divide the relations in the query that are related through RI constraints into removable and non-removable • 3. Eliminate all removable relations from the query • 4. Add is not null predicate to foreign key columns of all tables whose RI parents were removed

7. S.S PS.S PS.S O.C C.C O.C O.C Algorithm for join elimination: example S.S PS.S C.C

8. Performance results for join elimination

9. Predicate Introduction: Example • select sum(l_extendedprice * l_discount) as revenue • from tpcd.lineitem • where shipdate >date('1994-01-01'); Check constraint: receiptdate >= shipdate Clustered Index on receiptdate select sum(l_extendedprice * l_discount) as revenue from tpcd.lineitem where shipdate >date('1994-01-01') and receiptdate >= date('1994-01-01');

10. N - set of predicates derivable from the query and check constraints • If N is inconsistent, stop. • Else, for each predicate A op B in N, add it to the query if: • A or B is a join column • B is a major column of an index • no other index on B’s table can be used in the plan for the original query Algorithm for Predicate Introduction

11. Queries • select 100.00 * sum • (case • when p_type like 'PROMO%' • then l_extendedprice * (1 - l_discount) • else 0 • end) • / sum(l_extendedprice * (1 - l_discount)) as promo_revenue • from tpcd.lineitem, tpcd.part • where l_partkey = p_partkey and • l_shipdate >= date('1998-09-01') and • l_shipdate < date('1998-09-01') + 1 month; Given the check constraint l_receiptdate >= l_shipdate we may add a new predicate to the query: l_receiptdate >= date(‘1998-09-01’)

12. Performance Results for Index Introduction

13. The Culprit New query plan uses an index, but the original table scan is still better! Why did this happen: • incorrect estimate of the filter factor • underestimation of the CPU cost of locking index pages

14. Soft Constraints

15. Soft Constraints • Traditional (“hard”) integrity constraints are defined to prevent incorrect updates. A soft constraint is a statement that is true about the current state of the database, but does not verify updates. In fact, a soft constraint can be invalidated by an update.

16. Soft Constraints (cont.) • Absolute soft constraints – no violation in the current state of the database • Absolute soft constraints can be used for optimization in exactly the same way traditional constraints are. Statistical soft constraints – can have some (small) degree of violation • Statistical soft constraints can be used for improved selectivity estimation

17. Implementation of Soft Constraints • In Oracle the standard integrity constraints are marked with a rely option, so that they are not verified on updates. • In DB2 soft constraints are called informational constraints.

18. Informational Check Constraint • Example 1: Create an employee table where a minimum salary of $25,000 is guaranteed by the application • CREATE TABLE emp(empno INTEGER NOT NULL PRIMARY KEY, • name VARCHAR(20), • firstname VARCHAR(20), • salary INTEGER CONSTRAINT minsalary • CHECK (salary >= 25000) • NOT ENFORCED • ENABLE QUERY OPTIMIZATION);

19. Enforcing Validation • Example 2: Alter the employee table to start enforcing the minimum wage of $25,000 using DB2. DB2 will also verify existing data right away. • ALTER TABLE emp ALTER CONSTRAINT minsalary ENFORCED

20. Informational RI Constraint • Example 3: Create a department table where the application ensures the existence of departments to which the employees belong. • CREATE TABLE dept(deptno INTEGER NOT NULL PRIMARY KEY, • deptName VARCHAR(20), • budget INTEGER); • ALTER TABLE emp ADD COLUMN dept INTEGER NOT NULL • CONSTRAINT dept_exist • REFERENCES dept • NOT ENFORCED • ENABLE QUERY OPTIMIZATION);

21. Query Optimization via Empty Joins

22. select Model from Tickets T, Registration R where T.RegNum = R.RegNum and T.date > “1990-01-01” and R.Model LIKE “BMW Z3%” Example First BMW Z3 series cars were made in 1997. select Model from Tickets T, Registration R where T.RegNum = R.RegNum and T.date > “1997-01-01” and R.Model LIKE “BMW Z3%”

23. Matrix representation of empty joins A,B(R S)

24. Jarek Gryz: Staircase data structure

25. Properties of the algorithm • Time Complexity O(nm) • requires a single scan of the sorted data • Space Complexity O(min(n,m)) • only two rows of the matrix need be kept in memory • Scalable with respect to: • number of tuples in the join result • number of discovered empty rectangles • size of the domain of one of the attributes

26. How many empty rectangles are there? Tests done on 4 pairs of attributes with numerical domain present in typical joins in a real-world workload of a health insurance company.

27. How big are the rectangles?

28. Query rewrite: simple case select … from R, S,... where R.C=S.C and 60<R.A<80 and 20<S.B<80 and... select … from R, S,... where R.C=S.C and 60<R.A<80 and 20<S.B<60 and...

29. Query rewrite: complex case select … from R, S,... where R.C=S.C and 60<R.A<80 and 20<S.B<80 and... select … from R, S,... where R.C=S.C and (… and …) or (… and …) or (… and …) or ...

30. Experiment I: Size of the Overlap

31. Experiment 2: Type of Overlap

32. Experiment 3: Number of Empty Joins Used in Rewrite

33. How much do the rectangles overlap with queries?

34. Query optimization experiments real-world workload of 26 queries 5 of the queries “qualified” for the rewrite only simple rewrites were considered all rewrites led to improved performance

35. Query Cardinality Estimate via Empty Joins

36. Query Cardinality Estimate via Empty Joins (SIEQE) • Cardinality estimates crucial for designing good query evaluation plans • Uniform data distribution (UDA): standard assumption in database systems • Histograms effective in single dimensions: too expensive to build and maintain otherwise

37. The Strategy • With UDA, the “density”: 1 tuple/sq unit • Empty joins cover 20% of the area • Adjusted density: 1.25 tuples/sq unit Q1 Q2

38. ExperimentsNumber of queries for which the error is less than a given limit

39. Discovery of Check Constraints and Their Application in DB2 We discover two types of (rules) check constraints: • correlations between attributes over ordered domains • partitioning of attributes

40. Correlations between attributes over ordered domains Rules have the form: Y = bX + a + [emin, emax] Algorithm for all tables in the database for all comparable variable pairs (X and Y) in the table apply OLS estimation to get the function of the form: Y = a + bX calculate the max and min error (or residual) emax and emin endfor endfor

41. Partitioning • Rules have the form: If X = a, then Y  [emin, emax] • Algorithm • for all tables in the database • for any qualifying variable pair (X and Y) in the table • calculate partitions by using GROUP BY X statements • find the max and min value of Y for each partition • endfor • endfor

42. Experiments in TPC-H TPC-H contains the following check constraint: L_RECEIPTDATE > L_SHIPDATE Our algorithm discovered the following rule: L_RECEIPTDATE = L_SHIPDATE + (1, 30), m = 0.0114. • Rules discovered through partitioning: • If L_LINESTATUS=F, then L_SHIPDATE=(01/04/1992, 06/17/1995), m = 0.50 • If L_LINESTATUS=O, then L_SHIPDATE=(06/19/1995, 12/25/1998), m = 0.50

43. Applications • DBA Wizard • Semantic Query Optimization • Improved Filter Factor Estimates

44. Example Consider a query issued against a hotel database, that requests the number of guests staying in the hotel on a given date. • ARRIVAL DATE <= ‘1999-06-15’ AND DEPARTURE_DATE >= ‘1999-06-15’ • Thefilter factor estimate for the query would be: • ff = ff1 * ff2 If ‘1999-06-15’ was approximately midway in the date ranges, we would estimate a quarter of all the guests that came in over the number of years would be in the answer of the query!

45. Example (cont.) • Assume that the following check constraint was discovered: • DEPARTURE_DATE >= ARRIVAL_DATE + (1 DAY, 5 DAYS) • The original condition in the query predicate can then be changed to: • ARRIVAL_DATE <= ‘1999-06-15’ AND ARRIVAL_DATE >= ‘1999-06-18’ • or • ARRIVAL_DATE BETWEEN ‘1999-06-15’ AND ‘1999-06-18’ The filter factor is now estimated to: ff = (ff1 + ff2 –1)

46. Other Research on the Use of Soft Constraints in Query Optimization

47. Query-driven Approach • Built multidimensional histograms based on query results (Microsoft) • Improve cardinality estimates by looking at the intermediate query results (IBM) • Both techniques generate statistical soft constraints

48. Data-driven Approach • Lots of methods using Bayesian networks to infer statistical soft constraint • Lots of methods to discover functional dependencies in data (absolute soft constraints) • Most recently, BHUNT and CORDS use sampling to discover soft constraints (IBM)

49. References • Q. Cheng, J. Gryz, F. Koo, T. Y. Cliff Leung, L. Liu, X. Qian, B. Schiefer: Implementation of Two Semantic Query Optimization Techniques in DB2 Universal Database. VLDB 1999. • J. Edmonds, J. Gryz, D. Liang, R. Miller: Mining for Empty Rectangles in Large Data Sets. ICDT 2001. • J. Gryz, B. Schiefer, J. Zheng, C. Zuzarte: Discovery and Application of Check Constraints in DB2. ICDE 2001. • P. Godfrey, J. Gryz, C. Zuzarte: Exploiting Constraint-Like Data Characterizations in Query Optimization. SIGMOD 2001. • J. Gryz, D. Liang: Query Optimization via Empty Joins. DEXA 2002. • J. Gryz, D. Liang: Query Cardinality Estimation via Data Mining. IIS 2004.