1

Describing and Utilizing Constraints to Answer Queries in Data-Integration Systems

Chen Li

Information and Computer ScienceUniversity of California, Irvine

2

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

3

Another Example

house(street,zip,price,sqft,year)

Mediator

s1(street, zip, price, sqft) s2(street, price, year)

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.

4

Importance of Constraints They express a rich amount of

information about sources They can be utilized to help query

answering

5

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”

6

Outline Constraints motivation Local constraints Global constraints Conclusions and open problems

7

Describing various constraints

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)

house(street,zip,price,year,sqft)

s1(street, zip, price, sqft) s2(street, price, year)

8

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— …

9

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 ass1(street, zip, price, sqft) :- house(street, zip, price, sqft, year),price >=

250K

10

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

11

Limitations of local constraints

— 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)

house(street,zip,price,year,sqft)

s1(street, zip, price, sqft) s2(street, price, year)

12

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

13

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

14

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

15

Two kinds of global constraints

General global constraints Source-derived global constraints

16

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

17

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

18

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

19

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

20

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

21

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)

22

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

23

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

24

AcknowledgementsWe thank Jia Li for her help on the

preparation of these slides.