An Evolutionary Perspective on Approximate RDF Query Answering

An Evolutionary Perspective onApproximate RDF Query Answering

Christophe Guéret, Eyal Oren, Stefan Schlobach,Frank van Harmelen and Martijn Schut

Vrije Universiteit, Amsterdam

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Problem and context Method proposed Experimental results Conclusion

The next 30 minutes in 4 points...

I RDF

I Data on the WebI Inconsistent, uncertain, heterogeneous, Huge and growing!

I RDF Query answering

I Finding data matching criterionI ... many queries are actually not satisfiable

I Approximate RDF Query answering

I Finding some, almost valid, data

I The Evolutionary Perspective

I Test different solutionsI Progressive optimisation of the result

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I RDFI Data on the Web

I Inconsistent, uncertain, heterogeneous, Huge and growing!







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I RDFI Data on the WebI Inconsistent, uncertain, heterogeneous, Huge and growing!







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I RDF Query answeringI Finding data matching criterion

I ... many queries are actually not satisfiable





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I RDF Query answeringI Finding data matching criterionI ... many queries are actually not satisfiable





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I Approximate RDF Query answeringI Finding some, almost valid, data



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I The Evolutionary PerspectiveI Test different solutions

I Progressive optimisation of the result

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I The Evolutionary PerspectiveI Test different solutionsI Progressive optimisation of the result

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1 What’s the problem ?Querying RDF datastoresStandard techniques

2 And Now for Something Completely DifferentGuessing the solution insteadThe way we do it

3 Does it work ?Evolution of the qualitySome characteristics of this method

4 TODO list

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4 TODO list

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Example

I RDF dataset<Ullman88> type Book .<Ullman88> label "Principles of Database and

Knowledge-Base Systems" .<Ullman88> author b1 .b1 _1 ullman .ullman homepage <http://stanford.edu/~ullman/> .

I SPARQL querySELECT ?title WHERE {?publication type Book .?publication label ?title .}

I Expected answer?title = "Principles of Database and Knowledge-Base Systems"

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Problem description

I Triple =subject,predicate,object

I Dataset =graph oftriples

I Querying :find apattern inthe graph

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Standard techniques

I Standard approach :

1 Find all the possible results for ?publication typeBook

I?publication<Ullman88>

2 Find all the possible results for ?publication label?title

I?publication ?title<Ullman88> "Principles of ..."

3 Do a join on the two tables and return the result

I ?title = "Principles of ..."

I Fast thanks to the creation of indexes and queryoptimisation

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Standard techniques

I Standard approach :1 Find all the possible results for ?publication type

Book




3 Do a join on the two tables and return the result

I ?title = "Principles of ..."


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Standard techniques

I Standard approach :1 Find all the possible results for ?publication type

Book




3 Do a join on the two tables and return the resultI ?title = "Principles of ..."


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Motivation

I Designed to return results only when there are someI Not designed for incomplete and approximate

queries/answersI Hard to distribute

I Approximate answers to precise queries

I If the query is unsat, return the best almost sat solutionfound

I Precises answers to approximate queries

I Return a subset of existing solutions instead of showingthem all

I Interactive querying

I Use of intermediate results to help the user improving hisquery

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Motivation



I Approximate answers to precise queriesI If the query is unsat, return the best almost sat solution

found

I Precises answers to approximate queries

I Return a subset of existing solutions instead of showingthem all



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Motivation




found

I Precises answers to approximate queriesI Return a subset of existing solutions instead of showing

them all



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Motivation




found

I Precises answers to approximate queriesI Return a subset of existing solutions instead of showing

them all

I Interactive queryingI Use of intermediate results to help the user improving his

query

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4 TODO list

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Approach

I “I’m Feeling Lucky” approach :

1 Assign some random values to the variables

I?publication = <Ullman88>?title = Book

2 Verify if the solution is valid

I

Triple Is in the graph ?<Ullman88> type Book yes<Ullman88> label Book no

3 If the solution is OK, stop. Otherwise, try again withsomething else

I Rely on membership testing (instead of lookup)I The testing loop can be stopped at any timeI A result may satisfy part of the query

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Approach

I “I’m Feeling Lucky” approach :1 Assign some random values to the variables



I




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Approach




I



I Rely on membership testing (instead of lookup)

I The testing loop can be stopped at any timeI A result may satisfy part of the query

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Approach




I



I Rely on membership testing (instead of lookup)I The testing loop can be stopped at any time

I A result may satisfy part of the query

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Approach




I




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Our choices

I Need to pay attention to two aspects

1 Each try should be a step closer to the solution

I Random guessing may never endI Stopping the process at t + 1 should give better results than

at t

2 Testing a candidate solution must be fast

I Will try a lot of solutions

I We made the following choices

I Generation of solutions : Evolutionary algorithmI Verification of solutions : Bloom filter based testing

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Our choices

I Need to pay attention to two aspects1 Each try should be a step closer to the solution


at t

2 Testing a candidate solution must be fast




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Our choices



at t2 Testing a candidate solution must be fast




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Our choices



at t2 Testing a candidate solution must be fast


I We made the following choicesI Generation of solutions : Evolutionary algorithmI Verification of solutions : Bloom filter based testing

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Binary Bloom filters (1/2)

I Compact representation of information : a set of n = 8 bits

1 2 3 4 5 6 7 8

I Supports two operationsI INSERT(KEY) : Insert a key into the filterI CONTAINS(KEY) : Test for the presence of a key

I Use k = 3 hash functions to compute a set of bits from akey

HASH3(“HELLO WORLD”)=3HASH2(“HELLO WORLD”)=6HASH1(“HELLO WORLD”)=8

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Binary Bloom filters (2/2)

I INSERT(“HELLO WORLD”)Current

“Hello world”

New

OR

=

I Bit-wise or operation

I Always successful (i.e.unlimited capacity)

I Precision depends ofnumber of elements m.

I CONTAINS(“BONJOUR !”)Current

“Bonjour !”

Test result

AND

=

I Bit-wise and operation

I Positive result can be acollision

perror = (1− e−knm )k

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A first (naive) approach

I Insert all the triples into a unique Bloom filter.I INSERT(“<Ullman88>_type_Book”)I INSERT(“<Ullman88>_label_"Principles of ..."”)I . . .

I Use the CONTAINS operation to verify a solution

I CONTAINS(“<Ullman88>_type_Book”)⇒ trueI CONTAINS(“<Ullman88>_label_Book”)⇒ false

I Not the best approach ! Let’s see what happen in detail . . .

?publication label ?title

CONTAINS(“<Ullman88>_label_Book”)

modify ?publication and ?title

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A first (naive) approach

I Insert all the triples into a unique Bloom filter.I INSERT(“<Ullman88>_type_Book”)I INSERT(“<Ullman88>_label_"Principles of ..."”)I . . .

I Use the CONTAINS operation to verify a solutionI CONTAINS(“<Ullman88>_type_Book”)⇒ trueI CONTAINS(“<Ullman88>_label_Book”)⇒ false

I Not the best approach ! Let’s see what happen in detail . . .

?publication label ?title

CONTAINS(“<Ullman88>_label_Book”)

modify ?publication and ?title

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Graph parsing

I Every triple of the graph is inserted into 4 Bloom filters

type<Ullman88> Book

<Ullman88>_type_Book

SPO

<Ullman88>_type

SP

type_Book

PO

<Ullman88>_Book

SO

I Three domains are definedS = <Ullman88> b1 ullmanP = type label author _1 homepageO = Book "Principles of ..." b1 ullman <http://...>

I Each term is replaced by an integer (with a dictionary)I <Ullman88>→ 46

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Evolutionary algorithm flowchart [Eiben2003]

I Set of populations + Set of operators

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Query parsing

I Definition of the chromosome for the individuals?publication1 ?publication2 ?title

I Creation of constraints to verify

I Clause ?publication type Book .bloom(spo |?publication1 type Book)bloom(sp |?publication1 type)bloom(po |type Book)

I Clause ?publication label ?title .bloom(spo |?publication2 label ?title)bloom(sp |?publication2 label)bloom(po |label ?title)bloom(so |?publication2 ?title)

I Equality constraintequal(?publication1,?publication2)

Removedbecausealways true

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Query parsing

I Definition of the chromosome for the individuals?publication1 ?publication2 ?title

I Creation of constraints to verifyI Clause ?publication type Book .

bloom(spo |?publication1 type Book)bloom(sp |?publication1 type)bloom(po |type Book)

I Clause ?publication label ?title .bloom(spo |?publication2 label ?title)bloom(sp |?publication2 label)bloom(po |label ?title)bloom(so |?publication2 ?title)

I Equality constraintequal(?publication1,?publication2)

Removedbecausealways true

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Evaluation of a candidate solution

I Solution is checked against all the constraints. If one issatisfied,

I A global reward w is wonI Each variable used is equally rewarded

I Rewards for : bloom(spo|?publication2 label?title)

I reward(solution) += wI reward(?publication1) += w

2I reward(?title) += w

2

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Creation of new individuals

I Select two individuals and do a one point crossover

dblp:ullman <Ullman88> "Principles. . ."

<Ullman88> dblp:ullman _:b1

Randomly pick a pivot point

dblp:ullman <Ullman88> _:b1

<Ullman88> dblp:ullman "Principles. . ."

Swap the two parts

I Mutate the least efficient variable

dblp:ullman <Ullman88> "Principles. . ."

0 3× w 2× w

Select the variable with lowestreward

<Ullman88> <Ullman88> "Principles. . ."

Assign a random new value

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4 TODO list

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Results on some (small) datasets

I Database FOAF (15k triples) and DBLP (3M triples)I Query with, respectively, 4 and 11 different variablesI Average result for 200 individuals and 500 generations

0

10

20

30

40

50

60

0 100 200 300 400 500

fitne

ss v

alue

n-th generation

60

70

80

90

100

0 100 200 300 400 500

fitne

ss v

alue

n-th generation

I Solutions with maximum reward (52) are found for FOAFI Not enough time for DBLP (max 319)

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Scalibility & speed

I Low memory requirementsI Only depends on the number of individuals and the size of

the Bloom filters

(a) parsing

dataset memoryFOAF 65 MBDBLP 230 MB

(b) querying

dataset memoryFOAF 15 MBDBLP 140 MB

Table: Average memory usage (mostly due to dictionary)

I Computation can be distributedI Candidate solutions are independentI The dictionary can be based on a DHT

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4 TODO list

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Status and future work

I Current statusI The search process can be slow to convergeI Several parameters to tune (rewards, size of the population,

number of generations, . . . )

I Current work

1 Improve benchmarking

I Test with more queries and more datasetsI Better study of the influence of the parameters

2 Improve evolution

I Experiment different type of crossover and mutationI Implement dynamic valuations for the rewardsI Improve early results on tabbu search approach

3 Test other, easy to parallelize and anytime, optimizer

I Swarm based algorithm (PSO, ...) or an other EAI CSP solver

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I Current work1 Improve benchmarking


2 Improve evolution

I Experiment different type of crossover and mutationI Implement dynamic valuations for the rewardsI Improve early results on tabbu search approach



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2 Improve evolutionI Experiment different type of crossover and mutationI Implement dynamic valuations for the rewardsI Improve early results on tabbu search approach



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2 Improve evolutionI Experiment different type of crossover and mutationI Implement dynamic valuations for the rewardsI Improve early results on tabbu search approach

3 Test other, easy to parallelize and anytime, optimizerI Swarm based algorithm (PSO, ...) or an other EAI CSP solver

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An Evolutionary Perspective on Approximate RDF Query Answering

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