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Generating Efficient Plans for Queries Using Views

This study focuses on generating efficient query plans using views under the Closed-World Assumption. It explores cost models, logical plan generation methods, and an algorithm called CoreCover to minimize subgoals. The approach aims to reduce joins and view accesses for improved query processing efficiency.

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Generating Efficient Plans for Queries Using Views

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  1. Generating Efficient Plans for Queries Using Views Chen Li Stanford University with Foto Afrati (National Technical University of Athens) and Jeff Ullman (Stanford University) SIGMOD, Santa Barbara, CA, May 23, 2001

  2. Q Query V1 V2 … Vn Views Base relations R1 Rm … Answering queries using views • How to answer a query using only the results of views? [LMSS95] • Many applications: • Data warehouses • Data integration • Query optimization • …

  3. car loc Make Dealer Dealer City BMW Alison Palo alto Anderson Honda Redwood City Anderson Varsity Ford Alison Mountain View Varsity … … … … An example View: V1(M, D, C) :- car(M, D), loc(D, C) Query Q:Q(M, C) :- car(M, anderson), loc(anderson, C) Rewriting P1: Q(M, C) :- V1(M, anderson, C)

  4. Existing algorithms • Bucket algorithm [LRO96], Inverse-rule algorithm [DG97], MiniCon algorithm [PL00], … • However, instead of generating P1: Q(M, C) :- V1(M, anderson, C) they generate rewriting P2: Q(M, C) :- V1(M, anderson, C1), V1(M1, anderson, C) • Why P2, not P1? • These algorithms take the Open-World Assumption (OWA): “P2  P1.” • However, under the Closed-World Assumption (CWA): “P1 = P2.”

  5. OWA CWA W1 W2 All car tuples W1 = W2 = Differences between OWA and CWA W1(Make, Dealer) :- car(Make, Dealer) W2(Make, Dealer) :- car(Make, Dealer) • W1 and W2 have some car tuples. • E.g.: W1 and W2 are from two different web sites. • W1 and W2 have allcar tuples. • E.g.: W1 and W2 are computed from the samecar table in a database.

  6. Our problem: generating efficient plans using views under CWA Efficient plans? Query Q Materialized views V1 V2 … Vn Base relations R1 R2 Rm • Existing algorithms work under both assumptions. • Our study • takes the CWA assumption. • considers efficiency of rewritings.

  7. Q(S, C) :- car(M, a), loc(a, C), part(S, M, C) V1(M, D, C) :- car(M, D), loc(D, C) V2(S, M, C) :- part(S, M, C) V3(S) :- car(M, a), loc(a, C), part(S, M, C) a = ‘anderson’ Challenge: in what space should we generate rewritings? car(Make, Dealer) loc(Dealer, City) part(Store, Make, City) Rewritings: P1: Q(S, C) :- V1(M, a, C), V2(S, M, C) P2: Q(S, C) :- V3(S), V1(M, a, C), V2(S, M, C) P2 could be more efficient than P1!

  8. Focus Views V1,V2,…,Vn Step 2: generate an efficient physical plan from P Step 1: generate a rewriting P (logical plan) Query Q Cost model CM • We focus on the logical level (step 1). • Prune rewriting space to generate “good” rewritings. • Different from the one-step approach: [CKPS95, ZCLPU00]. • Both steps are cost-based. • Consider select-project-join queries, i.e., conjunctive queries.

  9. Rest of the talk • Three cost models: • CM1: number of subgoals in a physical plan • CM2: sizes of views and intermediate relations • CM3: CM2 + dropping attributes in intermediate relations • Experimental results • Conclusion and future directions

  10. Cost model CM1 • CM1: number of subgoals in a physical plan • Goal: generate rewritings with minimum number of subgoals • Motivations: • Reduce the number of joins • Reduce the number of view accesses • Example: • P1: Q(S, C) :- V1(M, a, C), V2(S, M, C)  more efficient • P2: Q(S, C) :- V1(M1, a, C), V1(M, a, C1), V2(S, M, C) A view can appear more than once in different “forms.”

  11. Results under CM1 • Analyze the rewriting space: • Find an interesting structure of the space; • Show a procedure to reduce number of subgoals in a rewriting. • Develop an algorithm CoreCover: • Input: a query Q, views V1, …, Vn • Output: rewritings with minimum number of subgoals • Optimality: if there is a rewriting, then CoreCover guarantees to find a rewriting with minimum number of subgoals.

  12. Construct database D = { car(m0, a), loc(a, c0), part(s0, m0, c0) } D View tuples: V1(M, a, C), V2(S, M, C), V3(S) CoreCover: example Intuition: translate the problem to a set-covering problem. Query: Q(S, C) :- car(M, a), loc(a, C), part(S, M, C) Evaluate views on D: V1(M, D, C) :- car(M, D), loc(D, C)  V1(m0, a, c0) V2(S, M, C) :- part(S, M, C)  V2(s0, m0, c0) V3(S) :- car(M, a), loc(a, C), part(S, M, C)  V3(s0)

  13. View tuples: V1(M, a, C), V2(S, M, C), V3(S) Find query subgoals “covered” by each view tuple: V1(M, a, C) car(M, a) V2(S, M, C) loc(a, C) V3(S) part(S, M, C) V1(M, D, C):- car(M, D), loc(D, C) V2(S, M, C) :- part(S, M, C) V3(S) :- car(M, a), loc(a, C), part(S, M, C) Find minimal covers of query subgoals using view tuples Q(S, C) :- V1(M, a, C) , V2(S, M, C) CoreCover: example (cont.) Query: Q(S, C) :- car(M, a), loc(a, C), part(S, M, C)

  14. Query subgoals View tuples Q Construct database D from Q T1 T2 … Tk G1 G2 G3 … Gm Evaluate views on D D “View tuples” Find query subgoals “answered” by each view tuple. Find minimal covers of query subgoals using view tuples. rewritings Algorithm: CoreCover

  15. Physical plan: Q( ) :- V1, V2, V3, …, Vn “IR”: intermediate relation IRn IR1 IR2 • Cost = size(V1) + size(V2) + … + size(Vn) • + size(IR1) + size(IR2) + … + size(IRn) Cost model CM2: considering sizes of views and intermediate relations Motivation: cost of V1 V2 is related to size(V1) and size(V2).

  16. Results under CM2 • Observation: Adding more views may make a rewriting more efficient. P1: Q(S, C) :- V1(M, a, C), V2(S, M, C) P2: Q(S, C) :- V3(S), V1(M, a, C), V2(S, M, C) If V3(S) is very selective, P2 can be more efficient than P1. • Larger search space: rewritings using view tuples produce an optimal physical plan under CM2. • Modify CoreCover to find these rewritings. • We discuss how to condense rewritings.

  17. Cost model CM3: dropping nonrelevant attributes • CM2: assumes all attributes are kept in IRs. • CM3: assumes attributes can be dropped in IRs to reduce sizes. • Bad news: didn’t find a space that guarantees to produce an optimal physical plan. • Good news: found a heuristic for optimizer to drop more attributes. Q( ) :- … Vi Vi+1 … Y IRi

  18. Drop what attributes? • Drop Y if: (1) Y is not used in later joins, and (2) Y is not in the answers. Called the “supplementary-relation approach.” [BR87] Q( ) :- … Vi Vi+1 … Y IRi

  19. Rewriting using view tuples: P1: Q(A) :- V1(A, B), V2(A, B) A more efficient rewriting: P2: Q(A) :- V1(A, C), V2(A, B) Note: P1 and P2 both compute the answers to Q. Search space under CM3? Rewritings using view tuples may not produce optimal physical plans! r(A,B) s(C,D) t(E,F) Q(A) :- r(A, A), t(A, B), s(B, B) V1(A, B) :- r(A, A), s(B, B) V2(A, B) :- t(A, B), s(B, B)

  20. Q( ) :- … Vi Vi+1 … YY’ IRi P1: Q(A) :- V1(A, B), V2(A, B) P2: Q(A) :- V1(A, C), V2(A, B) Targeting rewritings to facilitate dropping of attributes • Goal: after the transformation, we may drop more attributes. • Main idea: given a sequence of subgoals, rename variables. • If YY’, the new rewriting is still equivalent to Q, then drop Y’ in IRi even if Y appears in later joins.

  21. Experimental study • Purpose: • Test how fast CoreCover generates rewritings (cost model CM1). • Analyze its efficiency and scalability. • Experiment setup: • A query generator (in Java). Input parameters: • Number of base relations • Number of attributes in a relation • Number of views (1-1000), queries (5) • Number of subgoals in a view and a query • Shape of queries and views (star, chain, …) • Implemented in Java on a dual-processor Sun Ultra 2 workstation, running SUNOS 5.6, 256MB memory

  22. Star queries and views • Each query has 8 subgoals, and each view has 1, 2, or 3 subgoals. • No attribute projection in the head of the queries/views.

  23. Chain queries and views • Each query has 8 subgoals, and each view has 1, 2, or 3 subgoals. • 1 variable is projected in the head of the queries/views.

  24. Conclusion Generating efficient plans using views under CWA: • Cost model CM1: number of subgoals in a plan • Analysis of the rewriting space • A search space for rewritings • CoreCover: finding rewritings with minimum number of subgoals • Cost model CM2: sizes of views and IRs • A search space for rewritings • Condense rewritings • Cost model CM3: dropping irrelevant attributes in IRs • A heuristic to help optimizer drop attributes

  25. Future work • More complicated queries and views: • Arithmetic comparisons ( <=, >=, …) • Aggregations • Different assumptions: • Open-world assumption • Maximally-contained rewritings • Constraints: • Functional dependencies • Foreign-key constraints

  26. Thank you! Questions?

  27. Differences between CoreCover and MiniCon • CoreCover takes CWA, and MiniCon takes the OWA. • MiniCon tries to minimize the number of query subgoals, but it has no guarantee. • Technical differences: • CoreCover is more “aggressive” than MiniCon about finding query subgoals answered by a view tuple. • Finding set covers of query subgoals: CoreCover allows overlapping, and MiniCon does not allow it.

  28. Difference from earlier studies Views V1,V2,…,Vn Step 2: generate an efficient physical plan from P Step 1: generate a rewriting P (logical plan) Query Q Cost model CM • One-step approach: [CKPS95, ZCLPU00]. • We focus on the logical level (step 1). • Prune rewriting space to generate “good” rewritings. • Cost-based.

  29. Rewriting space All rewritings Minimal rewritings Containment minimal rewritings Locally minimal rewritings P’ Globally minimal rewritings P Rewriting P P’: Remove its redundant subgoals [Chandra & Merlin 77]:

  30. Rewriting space (cont.) All rewritings Minimal rewritings Containment minimal rewritings Locally minimal rewritings P’’ P’ Globally minimal rewritings P P’ P’’: Remove its subgoals while retaining its equivalence to Q: P3: Q(S, C) :- V3(S), V1(M, a, C), V2(S, M, C) V3(S) can still be removed.

  31. Rewriting space (cont.) All rewritings Minimal rewritings Containment minimal rewritings Locally minimal rewritings P* P’’ P’ Globally minimal rewritings P P’’ P*: transform P’’ using the mapping from the expansion of P’’ to the query: P1: Q(S,C) :- v1(M1,a,C),v1(M,a,C1),v2(S,M,C)  P2: Q(S,C) :- v1(M,a,C), v2(S,M,C)

  32. Concise representation of rewritings • Problem: as the number of views increases, the number of rewritings could be large! • Solution: • Group views into equivalence classes • Group view tuples into equivalence classes based on their covered query subgoals.

  33. Advantages View tuples Equivalence classes Views Equivalence classes • Advantages: • Number of equivalence classes bounded by the number of query subgoals. • The optimizer finds efficient physical plans by considering the “representative rewritings,” then decides how to make them more efficient by adding more view tuples. • The optimizer can replace a view tuple in a rewriting by another view tuple in the same equivalence class to have another rewriting. T1 V1 {T2, T5} {V1, V3} T2 V2 {T1,T6,T9} {V4,V10,V15} … … … … {T3} {V2, V9} Tn Vn

  34. Main results of experiments • CoreCover has good efficiency and scalability. • By grouping views and view tuples into equivalence classes, we can reduce the number of views and view tuples used by CoreCover.

  35. Star queries and views:Number of equivalence classes

  36. Star queries and views: Number of view tuples

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