SusaninaJulia / SCFPQ

Stochastic Context-Free Path Querying

This is the implementation of several methods to solve the most probable paths problem of Stochastic context-free path querying (SCFPQ). SCFPQ --- a way to specify path constraints in terms of stochastic context-free grammars. Our main task here to solve most probable path problem. Most probable paths problem is for a given stochastic context-free grammars and a labeled directed graph, to find the maximum probabilities between all pairs of nodes.

Our solution is a reduction to systems of nonlinear matrix equation solving. Two methods to solve this systems is proposed:

• Naive Iterative Method
• Newton-Krylov Method

Requirements

SCFPQ requires the following to run:

• Python v3.7+
• CUDA Toolkit 10.2+
• cupy

Usage

from main_structures import Grammar, Graph, Equation

You can download grammar and graph from file:

grm = Grammar(grammars_path)
grh = Graph(graph_path)
grh.fill()

And then construct the equation with:

eq = Equation(grm, grh)

Now you can solve the obtained system with two different methods:

• Naive Iterative Method

  res = eq.naive_iteration()
  

• Newton-Krylov Method

  res = eq.newton_krylov(equation)
  

Or you can also choose parameters, such as initial guess for iterative process and tolerance:

res = eq.newton_krylov(equation=another_function, initial_guess=x0, tol=10e-6, info=True)

Dataset

The graph data is selected from CFPQ_Data dataset. Graphs related to RDF analysis problems was chosen.

Performance

The results of the most probable paths problem on graphs related to RDF analysis are listed below.

For query g₁:

S -> subClassOf_r S subClassOf (0.4)
S -> subClassOf_r subClassOf (0.25)
S -> type_r S type (0.2)
S -> type_r type (0.15)

Graph	V	E	nnz	naive-iteration		newton-krylov
				it	time(sec)	it	time(sec)
generations	129	273	2164	5	0.02	2	0.4
travel	131	277	2499	11	0.05	3	0.6
funding	778	1086	17634	9	0.04	3	0.7
wine	733	1839	66572	11	0.06	3	0.7
pizza	671	1980	15195	15	0.09	4	0.9
core	1323	2752	204	50	0.3	4	0.9
pathways	6238	12363	884	9	0.2	4	2.1
enzyme	48815	86543	396	9	0.2	4	5.2
eclass	239111	360248	90994	11	19.6	-	-
go-hierarchy	45007	490109	588976	17	8.3	10	144.2
geospecies	450609	2201532	91	3	0.2	3	9.6

For query g₂:

S -> subClassOf_r S subClassOf (0.45)
S -> subClassOf (0.55)

Graph	V	E	nnz	naive-iteration		newton-krylov
				it	time(sec)	it	time(sec)
generations	129	273	0	0	<0.01	0	<0.01
travel	131	277	63	7	0.02	2	0.3
funding	778	1086	1158	7	0.02	2	0.4
wine	733	1839	133	7	0.02	2	0.3
pizza	671	1980	1262	13	0.04	3	0.5
core	1323	2752	214	7	0.02	2	0.3
pathways	6238	12363	3117	9	0.02	4	0.8
enzyme	48815	86543	8163	9	0.05	6	1.5
eclass	239111	360248	96163	9	5.3	5	213
go-hierarchy	45007	490109	738937	17	3.6	9	77.0
geospecies	450609	2201532	0	0	<0.01	0	<0.01