Download presentation

Presentation is loading. Please wait.

Published byLauryn Welles Modified over 2 years ago

1
ICDT'2001, London, UK1 Minimizing View Sets without Losing Query-Answering Power Chen Li Stanford University joint work with Mayank Bawa and Jeff Ullman

2
2 source query answer Client cache user query A web-caching scenario Server

3
3 Client Source relation: Book(Title, Author, Pub, Price) Cached query results: Q1(T,A,Pr) :- book(T,A,Pub,Pr) Q2(T,A,Pr) :- book(T,A,prenhall,Pr) Q3(A1,A2) :- book(T,A1,prenhall,Pr1), book(T,A2,prenhall,Pr2)

4
4 Book(Title, Author, Pub, Price) Q2 Q1 Remove Q2? Cannot answer query: Q(T,Pr) :- book(T,smith,prenhall,Pr) What query results to remove? Cached query results: Q1(T,A,Pr) :- book(T,A,Pub,Pr) Q2(T,A,Pr) :- book(T,A,prenhall,Pr) Q3(A1,A2) :- book(T,A1,prenhall,Pr1), book(T,A2,prenhall,Pr2)

5
5 Compute Q3 using Q2: Q3(A1,A2) :- Q2(T,A1,Pr1),Q2(T,A2,Pr2) We are not losing any query-answering power! How about removing Q3? Book(Title, Author, Pub, Price) Cached query results: Q1(T,A,Pr) :- book(T,A,Pub,Pr) Q2(T,A,Pr) :- book(T,A,prenhall,Pr) Q3(A1,A2) :- book(T,A1,prenhall,Pr1), book(T,A2,prenhall,Pr2)

6
6 Observations: –Traditional query-containment does not help [Chandra and Merlin, 1977]. –We should consider query-answering power. General questions: –How to describe “query-answering power”? –How to minimize a view set without losing its query-answering power?

7
7 Rest of the talk Answering queries using views Query-answering power –p-containment –Relationship with traditional query containment –Minimizing a view set p-containment relative to a set of queries Conclusion and open problems

8
8 Answering queries using views Conjunctive queries and views: h(X) :- g 1 (X 1 ),…,g n (X n ) Example: V1(T,A,Pr) :- book(T,A,Pub,Pr) V2(T,A,Pr) :- book(T,A,prenhall,Pr) V3(A1,A2) :- book(T,A1,prenhall,Pr1), book(T,A2,prenhall,Pr2)

9
9 Query answerability A query Q is answerable by a view set V if we can rewrite Q using views in V [LMSS95]. Example: V2(T,A,Pr) :- book(T,A,prenhall,Pr) V3(A1,A2) :- book(T,A1,prenhall,Pr1), book(T,A2,prenhall,Pr2) V3 is answerable by V2: V3(A1,A2) :- V2(T,A1,Pr1),V2(T,A2,Pr2)

10
10 Algorithms Bucket algorithm [LRO96] Inverse-rule algorithm [DG97,Qia96] MiniCon algorithm [PL00] SVB algorithm [Mit99] CoreCover Algorithm [ALU00] Testing whether a query is answerable by a set of views is NP-complete.

11
11 Views are expensive to maintain Require storage space. Need to be kept up-to-date. We want to minimize a given view set while keeping its query-answering power.

12
12 p-containment A view set V is p-contained in another view set W if W can answer all the queries that are answerable by V. –“p” stands for “power.” –Denoted: V p W Two view sets are equipotent, if V p W and W p V. –They have the same power to answer queries.

13
13 Example: V1(T,A,Pr) :- book(T,A,Pub,Pr) V2(T,A,Pr) :- book(T,A,prenhall,Pr) V3(A1,A2) :- book(T,A1,prenhall,Pr1), book(T,A2,prenhall,Pr2) {v1,v2,v3} p {v1,v2} {v1,v2} p {v1,v2,v3} Therefore: {v1,v2,v3} and {v1,v2} are equipotent.

14
14 Lemma: V p W iff each view in V can be answered by W. –Implies an algorithm for testing p-containment. –Assuming view sets are finite. Theorem: Testing V p W is NP-complete.

15
15 p-containment and query containment V1(T,A,Pr) :- book(T,A,Pub,Pr) V2(T,A,Pr) :- book(T,A,prenhall,Pr) V3(A1,A2) :- book(T,A1,prenhall,Pr1), book(T,A2,prenhall,Pr2) Query containment does not imply p-containment {v1} and {v2} p-containment does not imply query containment {v2} and {v3}

16
16 Minimizing a view set Keep removing views from the view set while retaining the equipotence. Might have multiple equipotent minimals V1(A) :- r(A,B) V2(B) :- r(A,B) V3(A,B) :- r(A,X),r(Y,B) {V1,V2,V3} has two equipotent minimals: {V1,V2}, {V3}

17
17 p-containment relative to queries Queries: Q={Q1,Q2,…} V = {V1,V2,…,Vm}W = {W1,W2,…,Wn} V is p-contained in W w.r.t. Q if the queries in Q that are answerable by V are also answerable by W.

18
18 Example of relative p-containment Relations: car(Make,Dealer) loc(Dealer,City) Queries: Q1(D,C) :- car(toyota,D),loc(D,C) Q2(D,C) :- car(honda,D), loc(D,C) Views: V = {V1,V2}, V1 = Q1, V2 = Q2 W = {W1} W1(M,D,C) :- car(M,D),loc(D,C)

19
19 Testing relative p-containment Q is finite: test by the definition. Q is infinite?

20
20 Parameterized queries Motivation: web search forms. A PQ is a conjunctive query with placeholders. Example: q(D) :- car($M,D),loc(D,$C) –Placeholders $M,$C, replaced by constants –Instances: q(D) :- car(toyota,D),loc(D,sf) q(D) :- car(honda,D),loc(D,pa) –The domain of each placeholder is infinite. –Thus, represent infinite number of queries.

21
21 Q: q(D) :- car($M,D),loc(D,$C) v1(M,D,C) :- car(M,D),loc(D,C) –Answer all instances of Q. v2(M,D) :- car(M,D),loc(D,sf) –Answer some instances of Q. –Answerable instances of Q are instances of: q(D) :- car($M,D),loc(D,sf) v3(M) :- car(M,D),loc(D,sf) –Answer no instances of Q.

22
22 Assume queries are generated by one PQ; Results easily extendable to the case with finite set of PQs. Complete answerability of a PQ using views –V can answer all instances of a PQ Q. –Example: q(D) :- car($M,D),loc(D,$C) v1(M,D,C) :- car(M,D),loc(D,C)

23
23 An algorithm for testing complete answerability Replace each placeholder with a new distinct constant, get a canonical instance I; Test if I is answerable by V. Example: PQ: q(D) :- car($M,D),loc(D,$C) View: v1(M,D,C) :- car(M,D),loc(D,C) Canonical instance: q(D) :- car(m0,D),loc(D,c0) Rewriting: q(D) :- v1(m0,D,c0)

24
24 Partial answerability Some instances of Q are answerable by V q(D) :- car($M,D),loc(D,$C) v2(M,D) :- car(M,D),loc(D,sf) Theorem: All the answerable instances of a PQ using V are instances of a finite set of PQs, s.t. each of them is completely answerable by V. q(D) :- car($M,D),loc(D,sf)

25
25 a parameterized query Q All instances of Q answerable instances PQ1 PQ2 PQk … V={V1,…,Vn} An algorithm for finding the finite set of PQs.

26
26 Testing p-containment w.r.t. PQ Find the PQs whose instances are all the instances of Q that are answerable by V. For each of the PQs, test if it is completely answerable by V. Details are in the paper.

27
27 Conclusion Introduced p-containment, which is different from query containment. Showed how to minimize a view set without losing query-answering power. Developed an algorithm for testing relative p-containment w.r.t. instances of PQs. Extended to MCR-containment.

28
28 Open problems Find a view subset with lowest “cost.” If views are not given, find the best views to materialize.

Similar presentations

OK

Some important properties Lectures of Prof. Doron Peled, Bar Ilan University.

Some important properties Lectures of Prof. Doron Peled, Bar Ilan University.

© 2018 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on church leadership Ppt on introduction to object-oriented programming tutorial Ppt on swami vivekananda speech Ppt on equality in indian democracy A ppt on robotics Ppt on barack obama leadership academy Ppt on dispersal of seeds by animals pictures Download ppt on fdi in retail in india Ppt on classical economics school Ppt on light dependent resistor