Representing and Querying XML with Incomplete Information

Representing and QueryingXMLwith Incomplete Information

Serge AbiteboulINRIA

Luc SegoufinINRIA

Victor VianuUCSD

pods 2001 Abiteboul-Segoufin-Vianu 2

Organization

• Motivations• Simplifying assumptions• Model of incompleteness• Answering queries• Results• Discussion• Conclusion

Motivations


The Web is a world of incompleteness

• Information you get from the web is seldom complete:• Queries return you some - not all - data • Limited storage capability• Documents change on the Web:

expiration• Sites are unavailable…

• Context: A warehouse of XML documents from the Web, Xyleme


This work

• This work: simple, practically appealing approach to managing incomplete information

• Sequence of queries to the web • (q1,A1)+(q2,A2)+… • Answers are cached

• Process a new query without access to the web• Give an incomplete answer• Explain incompleteness to user • Seek additional information, i.e., find minimal set

of queries to fully answer


Related works

• Semantic caching• Answering queries using views

• keep (Qi,Ai)

• try to rewrite query Q into Q’(A1,...,An)

• reject if you cannot

• Incomplete database • (Qi,Ai) is some incomplete knowledge of DB

• Related to querying incomplete information – e.g. Lipski-Imielinski


Challenge: balance expressiveness and tractability

• Choice of data model• Choice of the query language• Choice of a representation of

incompleteness

• Results• Simple, practical solution• Extra features lead to serious problems

Simplifying Assumptions


Data is XML: trees

dealer

UsedCars NewCars

ad ad

model year model

<dealer> <UsedCars> <ad> <model>Honda</model> <year>96</year> </ad> </UsedCars> <NewCars> <ad> <model>Acura</model> </ad> </NewCars></dealer>

Honda 96 Acura


Simplified XML

=can =444 =electronique=can =444 =electronique=nik =234 =electronic=nik =234 =electronic

=camera=camera=camera=camera

=c.jpg=c.jpg

value functionvalue function

unordered treesunordered trees

name price cat picturename price cat picture

catalogcatalog

productproduct

subcategorysubcategory

productproduct

name price categoryname price category


labelling functionlabelling function


Simple XML types

catalogcatalog

productproduct



**

**

1 : 1 child (default)1 : 1 child (default)* : 0 or more* : 0 or more+ : 1 or more+ : 1 or more? : 0 or 1? : 0 or 1


Prefix Selection Queries (ps-queries)

catalogcatalog

productproduct

name price cat=elecname price cat=elec


<200<200

Query1Query1catalogcatalog

productproduct

name name

Query2Query2

picturepicture


Simplifications

Data

• No order• No distinction

attribute/element• No recursion• No links

Query

• No complex path expressions

• No join• No repeated child

productproduct

name cat=elec cat=toyname cat=elec cat=toy

NONO


Crucial assumption: XID

prodprod

canon 120 eleccanon 120 elec

cameracamera

&245&245 prodprod&245&245

c.jpgc.jpg

++c.jpgc.jpg

prodprod


&245&245

cameracamera

==

• URLsURLs• ID/IDrefsID/IDrefs

Representation of incomplete information:

Incomplete trees


Document Type Definition (DTD) are used to represent incompleteness

• Set of rules: e r• e element name• r regular expression• Set of trees satisfying a

DTD d: tree(d)• Shortcoming of DTDs

• An element has a single definition independently of the context

• Type of ad depends on the context

dealerdealer

newxarnewxarusedcarusedcar

adadadad

modelmodel yearyear modelmodel


Solution: specialization (decoupled tags)

• adused and adnew h(adused)=h(adnew )=ad

dealerdealer


adadnewadadused


dealerdealer


adadadad


hh


DTDs + Specialization

The sets of trees that can be specified: the regular unranked tree languages [Bruggeman—Klein+Murata+Wood]

• Same closure properties: intersection, union, complement

• Same complexity


Example

Q1: name, subcat, price of electronic products with price Q1: name, subcat, price of electronic products with price less than $200less than $200

Q2: name, pictures of cameras at least pictured onceQ2: name, pictures of cameras at least pictured once

--------------------------------------------------------

Q3: name, price, pictures of cameras costing less than Q3: name, price, pictures of cameras costing less than $100 and at least pictured once$100 and at least pictured once

can be can be completelycompletely answered using A1, A2 answered using A1, A2

Q4: list all camerasQ4: list all cameras

can be can be partiallypartially answered using A1, A2 answered using A1, A2


catalogcatalog

cdplayercdplayer

productproduct


cameracamera

productproduct

nikon 199 elecnikon 199 elec

cameracamera

productproduct

sony 175 elecsony 175 elec

product1product1 product2product2

****

Q1: name, subcat, price of electronic products with price less than 200Q1: name, subcat, price of electronic products with price less than 200

missingmissing


Missing data after Q1

product1product1



**

product2product2



**

!=elec!=elec =elec=elec>200>200


catalogcatalog

productproduct


cameracamera

productproduct

nikon 199 elecnikon 199 elec

cameracamera

productproduct

sony 175 elecsony 175 elec

cdplayercdplayer

product2aproduct2a

Q2: name, pictures of cameras at least pictured onceQ2: name, pictures of cameras at least pictured once

product1product1

missingmissingproduct2cproduct2c

product2product2**

** product2bproduct2b**

c.jpgc.jpg akai a.jpg elecakai a.jpg elec

cameracamera

3333


Incomplete information

• Known information• Prefix of the real data tree

• Missing information• Extended tree type• Conditions on data values• Specializations, disjunctions


product1product1

name price name price catcat picture picture


**

!=elec!=elec

product2product2aa

name name priceprice catcat picture picture


=elec=elec>200>200

name price name price catcat

product3product3

elecelecproduct2product2bb

namename priceprice catcat picturepicture

**

=elec=elec>200>200

product2product2cc

namename priceprice catcat


=elec=elec>200>200

subcategorysubcategory!=camera!=camera


no pictureno picture

no pictureno picture

product +product +

Known data

Missing data

Answering Queries


Complete answer to Q3

• Q3: name, price, Q3: name, price, pictures of cameras pictures of cameras costing less than $150 costing less than $150 and having at least one and having at least one picturepicture

• Can be fully answered Can be fully answered using available using available informationinformation

• Need to check whether Need to check whether answer is completeanswer is complete

catalogcatalog

prodprod

canon 120 canon 120 c.jpgc.jpg


Incomplete answer to Q4• Provide known cameras• Explain incompleteness

canoncanon nikonnikon sony sony akaiakai

more productsmore products

name name

price>200price>200andandno pictureno picture


Completing answer to Q4

• It suffices to ask:

productproduct

name price cat name price cat

sub=camerasub=camera

=elec=elec>200>200 picturepicture

00


Revisit the types• DTD • Conditions• Specialization: same

element name may have several types

• Not sufficient

• Need to extend again the types: disjunctions

productproduct2b2b

**

=elec=elec>200>200


namename priceprice catcat picturepicture


Disjunction

??

??

vehiclevehicle

datadata engineengine

descriptiondescription

sailsail

vehiclevehicle

datadata


vehiclevehicle

datadataengineengine

sailsail

Query1’Query1’ Query2’Query2’

vehiclevehicle

data=“….”data=“….”

description=“….”description=“….”

Empty!Empty!&322&322


Disjunction continued

• Type of &322vehicle1 + vehicle2

vehicle2vehicle2

datadata


sailsail

vehicle1vehicle1

datadata engineengine


The type of &322 can not be described independently of that of data below

Results


Representation System:Lipski’s+Imielinski’s

reprep rep(T)rep(T)Set of possible Set of possible worldsworlds

q(rep(T))q(rep(T))==

rep(q(T))rep(q(T))

qq

Set of possible Set of possible answersanswers

TT

Representation Representation of informationof information

q(T)q(T) reprep

qq

Representation Representation of resultof result


Representation System for PS-queries

• Incomplete tree T to representq1

-1(A1) … qk-1(Ak)

• PS-query q

• q(T) can be computed in ptime(representation of the answer can be

computed in ptime)


Querying Incomplete Trees

• Given T and a query q, one can • Give in ptime the sure answers up to

our current knowledge• Check in ptime whether query q can be

fully anwered• Generate in ptime queries to complete

answer


Comparison with IL

Relational model

• Relational calculus/algebra

• Conditional table

• Closed or open world

• Representation system

XML tree model

• Weaker language (no join)

• Weaker system (no variable)

+ Closed and open World

• Representation system


Drawback: exponential blowup

• Incomplete information may become exponential w.r.t the sequence of query/answer q1/A1;q2/A2…

11 11 qqii::

Answers are emptyAnswers are empty

databasedatabase

a=ia=i b=ib=i

databasedatabase

aa bb

Type:Type:


Dealing with exponential blowup

• Make the representation more complex using disjunctions of types• Size of representation stays polynomial• Manipulations much more complex

• Restrict tree types and PS-queries • Already very/too? simple

• Accept to loose some information • Ask extra queries to simplify

representation

Discussion


Discussion: extend language

• Some results in paper• Extensions often lead to intractability

• E.G. : K-pebble transducers [Milo,Suciu,Vianu] that somehow subsume XML-QL and XSL• No (known) representation system• Testing rep(T) is empty is non-

elementary


Discussion : node Ids

Without node Ids• much less information to integrate

results• more complex• tedious case analysis


Discussion: ordering

• Ordering in XML, DTD, queries • Problem is totally different and very complex

• Example: • Q1/A1: list of males; Q2/A2: list of females; Q3: list all

• Depending on the type of input• (Male)*(Female)* A3= A1 || A2• (Male Female)* A3= shuffle(A1,A2)• (Male + Female)* we cannot answer A3

• Regular expression processing


Conclusion

• Framework for acquiring, maintaining, querying incomplete XML data

• Limitations: • simple queries• no order and Id assumption • small extensions lead to problems

• Possible to represent the incompleteness• Possible to answer with incompleteness• Possible to obtain queries to provide full

answer