1. Local-as-View Data Integration Zachary G. Ives University of Pennsylvania CIS 650 – Database & Information Systems October 16, 2008

2. 2 Administrivia Next week: Please read Section 3, 6, 7 in the Deshpande et al. survey Midterm assignment will be handed out Thursday, with a one week clock

3. Recall: Kinds of Schema Mappings Global As View (GAV):  x M(x)   y 1 y 2 R1(x 1 y 1 )  R 2 (x 2 y 2 )  c(x 1 y 1 x 2 y 2 ) where x  x 1 x 2 …x n Local As View (LAV):  x,y,z M R (x,y)  M S (y,z)  c(xyz)   w R 1 (x 1 y 1 z 1 w) where x 1 y 1 z 1  xyz Global-Local As View (GLAV), aka Tuple-Generating Dependencies (TGDs):   xyz M R (x,y)  M S (y,z)  c 1 (xyz)   y 1 y 2 R1(w 1 y 1 )  R 2 (w 2 y 2 )  c 2 (xyzy 1 y 2 )  …where w 1 w 2  xyz Query is of the form Q(x) :- M R (x 1,y 1 ), M S (x 2,y 2 ), … 3

4. Global-As-View Mappings  Very easy to implement – doesn’t require any new logic on the part of a regular DBMS engine  For instance, Starburst QGM rewrites would work  But some drawbacks – primarily that:  We don’t have a mechanism to describe when a source contains only a subset of the data in the mediated schema  e.g., “All books from this source are of type textbook”  The mediated schema often needs to change as we add sources – it is somewhat “brittle” because it’s defined in terms of sources 4

5. 5 An Alternate Approach: Local-As-View When you integrate something, you have some conceptual model of the integrated domain  Define that as a basic frame of reference, everything else as a view over it  “Local as View” using mappings that are conjunctive queries May have overlapping/incomplete sources  Define each source as the subset of a query over the mediated schema – the “open world assumption”  We can use selection or join predicates to specify that a source contains a range of values: ComputerBooks(…)  Books(Title, …, Subj), Subj = “Computers”

6. 6 The Local-as-View Model The basic model is the following:  “Local” sources are views over the mediated schema  Sources have the data – mediated schema is virtual  Sources may not have all the data from the domain – “open-world assumption” The system must use the sources (views) to answer queries over the mediated schema

7. 7 Answering Queries Using Views Assumption: conjunctive queries, set semantics  Suppose we have a mediated schema: show(ID, title, year, genre), rating(ID, stars, source)  A conjunctive query might be: q(t) :- show(i, t, y, g), rating(i, 5, s) Recall intuitions about this class of queries:  Adding a conjunct to a query (e.g., t = 1997) removes answers from the result but never adds any  Any conjunctive query with at least the same constraints & conjuncts will give valid answers

8. 8 Why This Class of Mappings & Queries?  Abiteboul & Duschka showed the data complexity of answering queries using views with OWA: viewsqueries CQCQ != PQdatalogFO CQPTIMEco-NPPTIME undec CQ != PTIMEco-NPPTIME undec PQco-NP undec datalogco-NPundecco-NPundec FOundec  Note that the common “inflationary semantics” version of Datalog must terminate in PTIME, even with recursion

9. 9 Query Answering Suppose we have the query: q(t) :- show(i, t, y, g), rating(i, 5, s) and sources: 5star(i) :- show(i, t, y, g), rating(i, 5, s) TVguide(t,y,g,r) :- show(i, t, y, g), rating(i, r, “TVGuide”) movieInfo(i,t,y,g) :- show(i, t, y, g) critics(i,r, s) :- rating(i, r, s) goodMovies(t,y) :- show(i, t, y, “drama”), rating(i, 5, s), y = 1997 We want to compose the query with the source mappings – but they’re in the wrong direction!

10. 10 Query Answering Suppose we have the query: q(t) :- show(i, t, y, g), rating(i, 5, s) and sources: 5star(i)  show(i, t, y, g), rating(i, 5, s) TVguide(t,y,g,r)  show(i, t, y, g), rating(i, r, “TVGuide”) movieInfo(i,t,y,g)  show(i, t, y, g) critics(i,r, s)  rating(i, r, s) goodMovies(t,y)  show(i, t, y, “drama”), rating(i, 5, s), y = 1997 We want to compose the query with the source mappings – but they’re in the wrong direction!

11. 11 Inverse Rules We can take every mapping definition and “invert” it, though sometimes we may have insufficient information: If 5star(i)  show(i, t, y, g), rating(i, 5, s) then it is also the case that: show(i,???,???,???,???)  5star(i) and we can write this as a datalog rule: show(i,-,-,-,-) :- 5star(i) But how to handle the absence of attributes?  We know that there must be AT LEAST one instance of ??? for each attribute for each show ID  So we might simply insert a NULL and define that NULL means “unknown” (as opposed to “missing”)…

12. 12 But NULLs Lose Information Suppose we take these rules and ask for: q(t) :- show(i, t, y, g), rating(i, 5, s) If we look at the rule: goodMovies(t,y)  show(i, t, y, “drama”), rating(i, 5, s), y = 1997 “By inspection,” q(t)  goodMovies(t,y) But if apply our inversion procedure, we get: show(i, t, y, g)  goodMovies(t,y), i = NULL, g = “drama”, y = 1997 rating(i, r, s)  goodMovies(t,y), i = NULL, r = 5, s = NULL We need “a special NULL” so we can figure out which IDs and ratings match up

13. 13 The Solution: “Skolem Functions” Skolem functions:  Conceptual “perfect” hash functions  Each function returns a unique, deterministic value for each combination of input values  Every function returns a non-overlapping set of values (Skolem function F will never return a value that matches any of Skolem function G’s values) Skolem functions won’t ever be part of the answer set or the computation – it doesn’t produce real values  They’re just a way of logically generating “special NULLs”

14. 14 Query Answering Using Inverse Rules Invert all rules using the procedures described Take the query and the possible rule expansions and execute them in a Datalog interpreter  Really the same process as GAV unfolding!  In the previous query, we expand with all combinations of expansions of show and of rating – every possible way of combining and cross-correlating info from different sources  Then discard unsatisfiable rewritings via unification, i.e., substituting in constants from the query for variables in the view  Finally, execute the union of all satisfiable rewritings

15. 15 Pros & Cons of Inverse Rules  Works even with recursive queries, binding patterns, FDs on schemas  Generally, they take view definitions, split them, and re-join them to produce answers  Not very efficient  No treatment of predicates  Can we do better? i.e., be more efficient?

16. 16 The Bucket Algorithm  Given a query Q with relations and predicates  Create a bucket for each subgoal in Q  Iterate over each view (source mapping)  If source includes bucket’s subgoal:  Create mapping between q’s vars and the view’s var at the same position  If satisfiable with substitutions, add to bucket  Do cross-product of buckets, see if result is contained (exptime, but queries are probably relatively small)  For each result, do a containment check to make sure the rewriting is contained within the query

17. 17 Let’s Try a Bucket Example Query q(t) :- show(i, t, y, g), rating(i, 5, s) Sources 5star(i)  show(i, t, y, g), rating(i, 5, s) TVguide(t,y,g,r)  show(i, t, y, g), rating(i, r, “TVGuide”) movieInfo(i,t,y,g)  show(i, t, y, g) critics(i,r,s)  rating(i, r, s) goodMovies(t,y)  show(i, t, y, “drama”), rating(i, 5, s), y = 1997 good98(t,y)  show(i, t, y, “drama”), rating(i, 5, s), y = 1998

18. 18 Populating the Buckets show(i,t,y,g)rating(i,5,s) 5star(i) TVguide(t,y,g,r) movieInfo(i,t,y,g) critics(i,r,s) goodMovies(t,y) good98(t,y)

19. 19 Evaluation  On the board…

20. 20 Example of Containment Testing Suppose we have two queries: q1(t) :- show(i, t, y, g), rating(i, 5, s), y = 1997 q2(t,y) :- show(i, t, y, “drama”), rating(i, 5, s) Intuitively, q1 must contain the same or fewer answers vs. q2:  It has all of the same conditions, except one extra conjunction (i.e., it’s more restricted)  There’s no union or any other way it can add more data We can say that q2 contains q1 because this holds for any instance of our mediated schema

21. 21 Checking Containment via Canonical Databases  To test for q1 µ q2:  Create a “canonical DB” that contains a tuple for each subgoal in q1  Execute q2 over it  If q2 returns a tuple that matches the head of q1, then q1 µ q2 (This is an NP-complete algorithm in the size of the query. Testing for full first-order logic queries is undecidable!!!)  Let’s see this for our example…

22. 22 Example Canonical DB q1(t) :- show(i, t, 1997, g), rating(i, 5, s) q2(t,y) :- show(i, t, y, “drama”), rating(i, 5, s) show rating it1997g i5s Need to get tuple in executing q2 over this database What if q2 didn’t ask for g = drama?

23. 23 Buckets, Rev. 2: The MiniCon Algorithm  A “much smarter” bucket algorithm:  In many cases, we don’t need to perform the cross- product of all items in all buckets  Eliminates the need for the containment check  This – and the Chase & Backchase strategy of Tannen et al – are the two methods most used in virtual data integration today  The chase procedure (though not the backchase) can be achieved using a Datalog program that looks much like the inverse rules!

24. 24 Minicon Descriptions (MCDs)  Basically, a modification to the bucket approach  “head homomorphism” – defines what variables must be equated by the query  Variable-substituted version of the subgoals  Mapping of variable names  Info about what’s covered  Property 1:  If a variable occurs in the head of a query, then there must be a corresponding variable in the head of the MCD view  If a variable participates in a join predicate in the query, then it must be in the head of the view

25. 25 MCD Construction For each subgoal of the query For each subgoal of each view Choose the least restrictive head homomorphism to match the subgoal of the query If we can find a way of mapping the variables, then add MCD for each possible “maximal” extension of the mapping that satisfies Property 1

26. 26 MCDs for Our Example 5star(i)  show(i, t, y, g), rating(i, 5, s) TVguide(t,y,g,r)  show(i, t, y, g), rating(i, r, “TVGuide”) movieInfo(i,t,y,g)  show(i, t, y, g) critics(i,r,s)  rating(i, r, s) goodMovies(t,y)  show(i, t, 1997, “drama”), rating(i, 5, s) good98(t,y)  show(i, t, 1998, “drama”), rating(i, 5, s) viewh.h.mappinggoals sat. 5star(i)iiiiiiii2 TVguide(t,y,g,r)t  t, y  y, g  gt  t, y  y, g  g, r  r1,2 movieInfo(i,t,y,g)i  i, t  t, y  y, g  g 1 critics(i,r,s)i  i, r  r, s  s 2 goodMovies(t,y)t  t,y  y 1,2 good98(t,y)t  t,y  y 1,2 q(t) :- show(i, t, y, g), rating(i, r, s), r = 5

27. 27 Combining MCDs  Now look for ways of combining pairwise disjoint subsets of the goals  Greatly reduces the number of candidates!  Also proven to be correct without the use of a containment check  Variations need to be made for:  Constants in general (I sneaked those in)  “Semi-interval” predicates (x <= c)  Note that full-blown inequality predicates are co-NP-hard in the size of the data, so they don’t work

28. 28 MiniCon and LAV Summary  The state-of-the-art for AQUV in the relational world of data integration  It’s been extended to support “conjunctive XQuery” as well  Scales to large numbers of views, which we need in LAV data integration  Chase & Backchase by Tannen et al.  A procedure that has very close connections to inverse rules  Slightly more general in some ways – but:  Typically produces equivalent rewritings, not maximally contained ones  Not always polynomial in the size of the data (though for some useful settings it is!!!)