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Experiments

Algorithms

Top down / Search: AnalyserAsSearch

Bottom up / CSP: AnalyserGrounder

Files

Each file tests a single BGP

File names are informative:

  • S: the bgp is satisfiable
  • N: the bgp is not satisfiable
  • [number]: the number of triples in the bgp
  • T: the bgp contains only variables without joins
  • J: the bgp contains one or more joins
  • P: the bgp contains a join on an object and must satisfy the single-path-to-root condition
  • R: the bgp contains a join on an object that is fx:root
  • C: the bgp contains a join on an object that is a container

Examples:

  • S_5T: a satisfiable bgp of 5 triples with only variables without joins
  • E.g. N_3P_C: a not satisfiable bgp of 3 triples that has multiple paths to an object container

N_1T

The bgp is not satisfiable.

The bgp has 1 triples

?s <iri> <http://sparql.xyz/facade-x/ns/root>

N_2J

The bgp is not satisfiable.

The bgp has 2 triples

?q ?r ?o
?s ?p ?r

N_2P_R

The bgp is not satisfiable.

The bgp has 2 triples

The bgp has multiple paths to an object

The bgp has multiple paths to fx:root

<iri1> ?p <http://sparql.xyz/facade-x/ns/root>
<iri2> ?p1 <http://sparql.xyz/facade-x/ns/root>

N_2T

The bgp is not satisfiable.

The bgp has 2 triples

?x ?y ?z
?s <iri> <http://sparql.xyz/facade-x/ns/root>

N_3J

The bgp is not satisfiable.

The bgp has 3 triples

?q ?r ?o
?a ?b ?c
?s ?p ?r

N_3P_C

The bgp is not satisfiable.

The bgp has 3 triples

The bgp has multiple paths to an object

The bgp has multiple paths to a container

<iri1> ?p ?o
<iri2> ?p1 ?o
?o a <Person>

N_3P_R

The bgp is not satisfiable.

The bgp has 3 triples

The bgp has multiple paths to an object

The bgp has multiple paths to fx:root

<iri1> ?p ?o
?o ?p <http://sparql.xyz/facade-x/ns/root>
?s ?p1 <http://sparql.xyz/facade-x/ns/root>

N_3T

The bgp is not satisfiable.

The bgp has 3 triples

?x ?y ?z
?a ?b ?c
?s <iri> <http://sparql.xyz/facade-x/ns/root>

N_4J

The bgp is not satisfiable.

The bgp has 4 triples

?q ?r ?o
?x ?y ?z
?a ?b ?c
?s ?p ?r

N_4P_C

The bgp is not satisfiable.

The bgp has 4 triples

The bgp has multiple paths to an object

The bgp has multiple paths to a container

?a ?b <iri2>
<iri1> ?p ?o
<iri2> ?p1 ?o
?o a <Person>

N_4T

The bgp is not satisfiable.

The bgp has 4 triples

?q ?r ?o
?x ?y ?z
?a ?b ?c
?s <iri> <http://sparql.xyz/facade-x/ns/root>

N_5J

The bgp is not satisfiable.

The bgp has 5 triples

?q1 ?r1 ?o1
?q ?r ?o
?x ?y ?z
?a ?b ?c
?s ?p ?r

N_5P_C

The bgp is not satisfiable.

The bgp has 5 triples

The bgp has multiple paths to an object

The bgp has multiple paths to a container

<iri1> ?b ?s
?s ?p ?o
<iri2> ?b1 ?s1
?s1 ?p1 ?o
?o a <Person>

N_5T

The bgp is not satisfiable.

The bgp has 5 triples

?q1 ?r1 ?o1
?q ?r ?o
?x ?y ?z
?a ?b ?c
?s <iri> <http://sparql.xyz/facade-x/ns/root>

S_1T

The bgp is satisfiable.

The bgp has 1 triples

?s ?p ?o

S_2J

The bgp is satisfiable.

The bgp has 2 triples

?s ?p ?o
?s ?p1 ?o1

S_2P_R

The bgp is satisfiable.

The bgp has 2 triples

The bgp has multiple paths to an object

The bgp has multiple paths to fx:root

?s ?p <http://sparql.xyz/facade-x/ns/root>
?s1 ?p1 <http://sparql.xyz/facade-x/ns/root>

S_2T

The bgp is satisfiable.

The bgp has 2 triples

?s ?p ?o
?x ?y ?z

S_3J

The bgp is satisfiable.

The bgp has 3 triples

?s ?p ?o
?s ?p1 ?o1
?o ?p2 ?o2

S_3P_C

The bgp is satisfiable.

The bgp has 3 triples

The bgp has multiple paths to an object

The bgp has multiple paths to a container

?s ?p ?o
?s1 ?p1 ?o
?o a <Person>

S_3T

The bgp is satisfiable.

The bgp has 3 triples

?s ?p ?o
?x ?y ?z
?q ?r ?t

S_4J

The bgp is satisfiable.

The bgp has 4 triples

?s ?p ?o
?s ?p1 ?o1
?o ?p2 ?o2
?o ?p3 ?o3

S_4P_C

The bgp is satisfiable.

The bgp has 4 triples

The bgp has multiple paths to an object

The bgp has multiple paths to a container

?a ?b ?s1
?s ?p ?o
?s1 ?p1 ?o
?o a <Person>

S_4T

The bgp is satisfiable.

The bgp has 4 triples

?s ?p ?o
?x ?y ?z
?q ?r ?t
?u ?i ?m

S_5P_C

The bgp is satisfiable.

The bgp has 5 triples

The bgp has multiple paths to an object

The bgp has multiple paths to a container

?a ?b ?s
?s ?p ?o
?a1 ?b1 ?s1
?s1 ?p1 ?o
?o a <Person>

S_5T

The bgp is satisfiable.

The bgp has 5 triples

?s ?p ?o
?x ?y ?z
?q ?r ?t
?u ?i ?m
?a ?b ?c

Bottom up / CSP

Bottom up, only satisfiability

The algorithm stops when 1 satisfiable annotation is found

name satisfiable? found type size ms tested
N_1T false 0 T 1 19 2
N_2J false 0 J 2 0 2
N_2P_R false 0 P 2 7 36
N_2T false 0 T 2 5 24
N_3J false 0 J 3 0 24
N_3P_C false 0 P 3 4 18
N_3P_R false 0 P 3 6 36
N_3T false 0 T 3 21 288
N_4J false 0 J 4 0 288
N_4P_C false 0 P 4 3 54
N_4T false 0 T 4 116 3456
N_5J false 0 J 5 1 3456
N_5P_C false 0 P 5 7 162
N_5T false 0 T 5 646 41472
S_1T true 1 T 1 0 12
S_2J true 1 J 2 0 144
S_2P_R true 1 P 2 1 36
S_2T true 1 T 2 1 144
S_3J true 1 J 3 1 432
S_3P_C true 1 P 3 1 18
S_3T true 1 T 3 1 1728
S_4J true 1 J 4 12 5184
S_4P_C true 1 P 4 0 54
S_4T true 1 T 4 6 20736
S_5P_C true 1 P 5 0 162
S_5T true 1 T 5 419 248832

Bottom up, all annotations (only satisfiable bgps)

The algorithm proceeds to find all possible satisfiable annotations

name satisfiable? found type size ms tested
S_1T true 6 T 1 1 12
S_2J true 36 J 2 1 144
S_2P_R true 1 P 2 0 36
S_2T true 36 T 2 1 144
S_3J true 60 J 3 3 432
S_3P_C true 4 P 3 0 18
S_3T true 216 T 3 15 1728
S_4J true 300 J 4 42 5184
S_4P_C true 8 P 4 1 54
S_4T true 1296 T 4 202 20736
S_5P_C true 16 P 5 3 162
S_5T true 7776 T 5 2096 248832

Top down / Search

Top down, only satisfiability

The algorithm stops when 1 satisfiable annotation is found

name satisfiable? found type size ms tested
N_1T false 0 T 1 1 12
N_2J false 0 J 2 0 0
N_2P_R false 0 P 2 69 1957
N_2T false 0 T 2 598 16364
N_3J false 0 J 3 0 0
N_3P_C false 0 P 3 2776 109601
N_3P_R false 0 P 3 304 12330
N_3T false -1 T 3 -1 -1
N_4J false 0 J 4 0 1
N_4P_C false -1 P 4 -1 -1
N_4T false -1 T 4 -1 -1
N_5J false 0 J 5 0 6
N_5P_C false -1 P 5 -1 -1
N_5T false -1 T 5 -1 -1
S_1T true 1 T 1 1 29
S_2J true 1 J 2 1 15
S_2P_R true 1 P 2 19 628
S_2T true 1 T 2 0 18
S_3J true 1 J 3 1250 193205
S_3P_C true 1 P 3 79 13678
S_3T true 1 T 3 1 66
S_4J true 1 J 4 2841 438338
S_4P_C true -1 P 4 -1 -1
S_4T true 1 T 4 0 94
S_5P_C true -1 P 5 -1 -1
S_5T true 1 T 5 1 174

Top down, all satisfiable annotations

The algorithm proceeds to find all possible satisfiable annotations

name satisfiable? found type size ms tested
S_1T true 6 T 1 7 203
S_2J true 36 J 2 570 72564
S_2P_R true 1 P 2 37 6218
S_2T true 36 T 2 3720 662653
S_3J true -1 J 3 -1 -1
S_3P_C true -1 P 3 -1 -1
S_3T true -1 T 3 -1 -1
S_4J true -1 J 4 -1 -1
S_4P_C true -1 P 4 -1 -1
S_4T true -1 T 4 -1 -1
S_5P_C true -1 P 5 -1 -1
S_5T true -1 T 5 -1 -1