Describing and Utilizing Constraints to Answer Queries in Data-Integration Systems Chen Li Information and Computer Science University of California, Irvine

Constraints in Data Integration Sources of Orange County (OC) housing information house(street,zip,price,sqft,year) Mediator s1(street, zip, price, sqft) s2(street, price, year) Constraints: s1 price at least $250K s2 price at least $280K Query: “Find Orange County houses cheaper than $200K” Answer: empty, without checking the source table instances

Another Example Constraint: OC houses have a unique street Query: Mediator house(street,zip,price,sqft,year) s2(street, price, year) s1(street, zip, price, sqft) Constraint: OC houses have a unique street Query: “Find sqft and year of OC houses” Plan: join two source relations on the “street” attributes The plan is invalid if the constraint is not true.

Importance of Constraints They express a rich amount of information about sources They can be utilized to help query answering

Our contributions There has been a lot of work on how to use constraints in query optimization, e.g.: [Hsu, Knoblock, 2000] [Godfrey, Gryz, Zuzarte, 2001] … To make this optimization possible, we primarily study: how to describe constraints; and how to manipulate constraints between “local” and “global”

Outline Constraints motivation Local constraints Global constraints Conclusions and open problems

Describing various constraints house(street,zip,price,year,sqft) s1(street, zip, price, sqft) s2(street, price, year) Examples: C1: s1.price >= $250K C2: s1.street is unique C3: s2.year < 1995, s2.price >= $280K C4: street is unique for all OC houses C5: all houses in the system are at least $250K Where to put them? Some constraints can be described at sources “locally” (C1,C2,C3) Others are more suitable to be described “globally” (C4,C5)

Local constraints: described at sources Designed by individual sources Common local constraints: Range constraints “price >= $250K” Enumeration constraints “state in {CA, NV, AZ, OR}” Functional dependencies “(street, zip)  (price, year)” Key constraints “(street) is a primary key of house predicate” Foreign-key constraints among tables at a source Inclusions …

Other ways to describe local constraints Could be described using traditional source-view definitions E.g., in the LAV (local-as-view) approach to data integration: “C1: s1.price >= $250K” can be described as s1(street, zip, price, sqft) :- house(street, zip, price, sqft, year),price >= 250K

Then why not use view/query languages to describe local constraints? View/query languages might not be expressive enough E.g., functional-dependency constraints Query answering could become complicated “Conjunctive-query rewriting” is already NP Arithmetic comparisons even require recursive queries Describing constraints separately have advantages: More expressive: can capture common knowledge We care more about those simple, common constraints Easier to understand and do reasoning

Limitations of local constraints house(street,zip,price,year,sqft) s1(street, zip, price, sqft) s2(street, price, year) C4: street is unique for all OC houses Cannot describe C4 using two local constraints: “street is a key at s1” & “street is a key at s1” Wrong! Since they cannot restrict two relations together! In particular, the following is still allowed S1: (main, 92697, $300K, 2100) S2: (main, $380K, 1993)

Global constraints (GC) Some constraints are more suitable to be described “globally” Example: C4: street is unique for all OC houses C5: all houses in the system are at least $250K

Describing global constraints Might need more expressive languages: “street” is unique for houses at s1 and s2 Need to formally define such a “global key” Consider special cases: We have source schemas and mediator schema Mappings exist between them: e.g., LAV, GAV, GLAV, or more general mapping language In this case, global constraints could be easier to describe

Other advantages of GC They “summarize” source contents Mediators can check queries against these conditions, before checking individual sources (thus could avoid unnecessary source checking) Users get an overview of the data (easier to ask queries) Give “outside world” a view of the source contents Especially useful when the mediation system is used as a component of a larger system E.g., peer-based mediation systems (Raccoon, Piazza, Hyperion, PeerDB, …) or hierarchies of mediators

Two kinds of global constraints General global constraints Source-derived global constraints

General global constraints Conditions that should be satisfied by any database instance of a global predicate: e.g., C4: street is unique for all OC houses It can be represented as the general global constraint on the house predicate (street) forms a key of house predicate Introduced during the system design to capture the semantics of the application domain Future new sources expected to satisfy this constraint Thus: may need to check if it is satisfied by existing and new-coming sources

Source-derived global constraints (Example) Local constraints: C1: s1.price >= $250K C3: s2.year < 1995, s2.price >= $200K  Global constraint C5: house.price >= $200K C5 is true only when the system has the two sources In general, there could be a house (not at s1 and s2) that is less than $250K We don’t care about these houses, pretending they didn’t exist When future sources come in, we need to check and update this constraint

Source-derived global constraints It is a condition on global predicates It must be satisfied by any derived database D of any source view instances satisfying those local constraints. Derived database D: certain tuples that can be decided based on the view definitions Depends on the view definition (LAV, GAV, …) s1(street, zip, price, sqft) :- house(street, zip, price, sqft, year), price >= 250K

Computing Source-derived GC Input: Sources with their local constraints Mappings between source schema and the mediator schema Output: source-derived GC on mediator schema We have preliminary results for the LAV approach

Comparisons General GC Source-derived GC When hold? Hold in general Hold for the system with current sources When new sources join.. Assume new sources satisfy the GC. Could be validated. New sources could violate the GC. Need to recalculate

Conclusions Describing constraints in data-integration system is important We classified different types of constraints: Local constraints Global constraints: General Source-derived We showed their advantages and limitations We studied how to manipulate these constraints (e.g., compute source-derived global constraints from local constraints)

Open problems Expressive languages to describe cross-source constraints “tuple-generating dependencies”? Other simpler but powerful languages Manipulating the constraints in general LAV, GAV more expressive mappings between sources and mediators Efficient techniques for testing and re-computing of global constraints as sources change

Work conducted in The RACCOON Project on Peer-based Data Integration and sharing, UC Irvine

Acknowledgements We thank Jia Li for her help on the preparation of these slides.