Zero-Knowledge Query Planning for an Iterator Implementation of Link Traversal Based Query Execution

Zero-Knowledge
Query Planning
for an Iterator Implementation of
Link Traversal Based Query Execution

Olaf Hartig
http://olafhartig.de/foaf.rdf#olaf
@olafhartig

Database and Information Systems Research Group
Humboldt-Universität zu Berlin

Iterator Based Execution Plan
tp1 = ( ?p , ex:affiliated_with , <http://.../orgaX> ) I1

tp2 = ( ?p , ex:interested_in , ?b ) I2

tp3 = ( ?b , rdf:type , <http://.../Book> ) I3
Query

?p ex:affiliated_with <http://.../orgaX>
?p ex:interested_in ?b
?b rdf:type <http://.../Book>
Olaf Hartig - Zero-Knowledge Query Planning for an Iterator Implementation of Link Traversal Based Query Execution 2


Next?
query-local tp2 = ( ?p , ex:interested_in , ?b ) I2
dataset

Next?

Next?



Next?
dataset

Next?
Descriptor object <http://.../Book> )
tp3 = ( ?b , rdf:type , I3

: Next?
<http://.../alice> ex:affiliated_with <http://.../orgaX>
:


Next?
dataset

Next?

: Next?
:


{ ?p = <http://.../alice> }

dataset

Next?

: Next?
:


{ ?p = <http://.../alice> }

dataset
tp2' = ( <http://.../alice> , ex:interested_in , ?b )

Next?

Next?



{ ?p = <http://.../alice> }

dataset

Next?

: Next?
<http://.../alice> ex:interested_in <http://.../b1>
:


{ ?p = <http://.../alice> }

dataset

{ ?p = <http://.../alice> , ?b = <http://.../b1> }


: Next?
<http://.../alice> ex:interested_in <http://.../b1>
:


{ ?p = <http://.../alice> }

dataset


tp3' = ( <http://.../b1> , rdf:type , <http://.../Book> )

Next?



{ ?p = <http://.../alice> }

dataset



: Next?
<http://.../Book> rdfs:subClassOf <http://.../CreativeWork>
:


{ ?p = <http://.../alice> }

dataset



: Next?
<http://.../b1> rdf:type <http://.../Book>
:


{ ?p = <http://.../alice> }

dataset





Example Query Execution Plan
tp1 = ( ?p , ex:affiliated_with , <http://.../orgaX>) I1


Query


An Alternative Execution Plan


Query



Next?
dataset

Next?

Next?



Next?
dataset

Next?

: Next?
:


END!

dataset

Next?

: Next?
:


END!

dataset

END!


END!



END!

dataset

END!


Number of results may depend END!
on the order of triple patterns
= logical query execution plan

Query Plan Selection
● Assessment criteria:
● Cost (query execution time)
● Benefit (number of results)
● Cost and benefit must be estimated without plan execution
● Estimation impossible due to “zero knowledge”
● Heuristic Based Plan Selection
● DEPENDENCY RESPECT RULE
● SEED TP RULE
● NO VOCAB SEED RULE
● FILTERING TP RULE


SEED TP RULE

Use a plan with a seed triple pattern

● Potential seed triple pattern
… is a triple pattern that contains at least one HTTP URI
● Seed triple pattern of a plan
… is the first triple pattern in the plan and
… is a potential seed triple pattern

Query ● Rationale: good
starting point
?p ex:affiliated_with <http://.../orgaX> √
?p ex:interested_in ?b √
?b rdf:type <http://.../Book> √

NO VOCAB SEED RULE

Avoid a seed triple pattern with vocabulary terms

● Not only vocabulary term URIs in the seed triple pattern
● Patterns to avoid: ?s ex:any_property ?o
?s rdf:type ex:any_class
● Rationale: URIs for vocabulary term usually resolve to
vocabulary definitions with little instance data
Query

?p ex:affiliated_with <http://.../orgaX> √

FILTERING TP RULE

Use a plan where all filtering triple patterns are
as close to the seed triple pattern as possible

● Filtering triple pattern: each variable already occurs in one
of the preceding triple patterns
● For each result tp1 = ( ?p , ex:affiliated_with , <http://.../orgaX>) I1
consumed as input
a filtering TP can { ?p = <http://.../alice> }
only report 1 or 0
results as output tp2 = ( ?p , ex:interested_in , ?b ) I2
● Rationale: Reduce { ?p = <http://.../alice> , ?b = <http://.../b1> }
cost

Evaluation Procedure
● Generate all possible plans
● Execute each plan:
● 5 runs (+ 1 initial warm-up run)
● Use an initially empty query-local dataset for each run
● Measure for each plan:
● Avg. execution time
● Avg. number of descriptor objects retrieved during execution
● Avg. number of query results


Evaluation Query (Example)

SELECT ?spec ?genus WHERE { Of what genus are
the species that are
geospecies:4qyn7 gs:inFamily ?fam . ● classified in the

?fam skos:narrowerTransitive ?spec . same family as the
?spec skos:closeMatch ?sp2 . American Badger,
● and expected in the
?sp2 rdfs:subClassOf ?genus .
same states as the
?spec gs:isExpectedIn ?loc . American Badger ?
geospecies:4qyn7 gs:isExpectedIn ?loc
?loc rdf:type gs:State . }

● 2 potential seed triple patterns that
satisfy our NO SEED VOCAB RULE
● 56 different plans, each contains
2 filtering triple patterns Picture source: Wikipedia

Measurements
30 400

retrieved descr. objects
300
20
query results

200
10
100

0 0
0 30 60 90 120 150 180 0 30 60 90 120 150 180
query exec. times (in seconds) query exec. times (in seconds)

Percentage of plans in each group with a filtering TP in specific positions
1st Filtering TP 2nd Filtering TP
100 100
50 50
0 0
1 2 3 4 5 6 7 1 2 3 4 5 6 7
Olaf Hartig position in the ordered an Iterator Implementation of Link Traversal Based Query Execution BGP 27
TP - Zero-Knowledge Query Planning for BGP TP position in the ordered

Conclusions
● Approach that uses iterators to implement
Link Traversal Based Query Execution
… is sound
… guarantees termination
… cannot guarantee (reachability-) completeness
● Degree of completeness depends on
the query plans (i.e. orders of the BGP)
● Heuristic based plan selection

● Next steps:
● Algorithm to generate most suitable plans only
● Integrate adaptive query processing techniques

Backup Slides


Outline

1. Link Traversal Based
Query Execution
2. Characteristics of the
Iterator Based
Implementation Approach
3. Query Plan Selection
4. Evaluation


Link Traversal Based Querying
● Semantics defined
in two phases:
1. Reachability Descriptor
2. Query Results object

Query


in two phases:
1. Reachability
2. Query Results

Query


● Semantics defined Reachable
in two phases: descriptor
1. Reachability object
2. Query Results

The mapping μ : V → U  B  L
is a result to BGP bgp iff:
Condition 1: dom(μ) = vars(bgp)
Condition 2: μ[bgp]  Dreachable

● 2 phases do not reflect idea of actual execution strategy
● Intertwine query evaluation with the traversal of data links

Characteristics

● No need to know all data sources in advance
● Never complete w.r.t. all data on the Web
● Reason: reachability based on links that match query patterns
● New concept: reachability-completeness
● No guarantee for termination
● Reason: Web of Data is infinite (at any point in time)

Outline

3. Evaluation


Characteristics
● Sound
● Number of results may depend on order of triple patterns
● Reachability-completeness not guaranteed
● Main reason: inflexibility due to fixed order
● Termination is guaranteed
● No such guarantee for link traversal based
query execution in general because the Web
of Data is infinite (at any point in time)
● Efficient
● Easy to apply in existing query engines


Plan Selection Problem

● Number of results may depend on order of triple patterns

= logical query execution plan

➔ Problem: select a suitable plan


Outline

1. Link Traversal Based
Query Execution
Iterator Based
4. Evaluation


DEPENDENCY RESPECT RULE

Use a dependency respecting query plan

● Dependency respect: a variable from each triple pattern
already occurs in one of the preceding triple patterns


Query
tp2 = ( ?p , ex:interested_in , ?b ) √ I2

?p ex:affiliated_with tp3 = ( ?b , rdf:type , <http://.../Book> )
<http://.../orgaX> I3





Query

?p ex:affiliated_with tp3 = ( ?b , rdf:type , <http://.../Book> )



● Rationale: tp1 = ( ?p , ex:affiliated_with , <http://.../orgaX>) I1
Avoid
cartesian
products
Query

?p ex:affiliated_with tp3 = ( ?p , ex:interested_in , ?b )

These slides have been created by
Olaf Hartig

http://olafhartig.de

This work is licensed under a
Creative Commons Attribution-Share Alike 3.0 License
(http://creativecommons.org/licenses/by-sa/3.0/)


Zero-Knowledge Query Planning for an Iterator Implementation of Link Traversal Based Query Execution

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Zero-Knowledge Query Planning for an Iterator Implementation of Link Traversal Based Query Execution