Upper and lower bounds for finding connected motifs in vertex-colored graphs

Michael R. Fellows; Guillaume Fertin; Danny Hermelin; Stéphane Vialette

doi:10.1016/j.jcss.2010.07.003

Upper and lower bounds for finding connected motifs in vertex-colored graphs

Michael R. Fellows, Guillaume Fertin, Danny Hermelin, Stéphane Vialette

Research output: Contribution to journal › Article › peer-review

Abstract

We study the problem of finding occurrences of motifs in vertex-colored graphs, where a motif is a multiset of colors, and an occurrence of a motif is a subset of connected vertices whose multiset of colors equals the motif. This problem is a natural graph-theoretic pattern matching variant where we are not interested in the actual structure of the occurrence of the pattern, we only require it to preserve the very basic topological requirement of connectedness. We give two positive results and three negative results that together give an extensive picture of tractable and intractable instances of the problem.

Original language	American English
Pages (from-to)	799-811
Number of pages	13
Journal	Journal of Computer and System Sciences
Volume	77
Issue number	4
DOIs	https://doi.org/10.1016/j.jcss.2010.07.003
State	Published - 1 Jan 2011
Externally published	Yes

Keywords

Graph motif
Graph pattern matching
Parameterized complexity
Treewidth
W hardness

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
General Computer Science
Applied Mathematics
Computer Networks and Communications
Computational Theory and Mathematics

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10.1016/j.jcss.2010.07.003

Cite this

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title = "Upper and lower bounds for finding connected motifs in vertex-colored graphs",

abstract = "We study the problem of finding occurrences of motifs in vertex-colored graphs, where a motif is a multiset of colors, and an occurrence of a motif is a subset of connected vertices whose multiset of colors equals the motif. This problem is a natural graph-theoretic pattern matching variant where we are not interested in the actual structure of the occurrence of the pattern, we only require it to preserve the very basic topological requirement of connectedness. We give two positive results and three negative results that together give an extensive picture of tractable and intractable instances of the problem.",

keywords = "Graph motif, Graph pattern matching, Parameterized complexity, Treewidth, W hardness",

author = "Fellows, {Michael R.} and Guillaume Fertin and Danny Hermelin and St{\'e}phane Vialette",

note = "Funding Information: ✩ An extended abstract of this paper appeared in Fellows et al. (2007) [23]. * Corresponding author. E-mail addresses: [email protected] (M.R. Fellows), [email protected] (G. Fertin), [email protected] (D. Hermelin), [email protected] (S. Vialette). 1 Supported by the Australian Research Council, by a Fellowship to the Durham University Institute for Advanced Studies, and by a William Best Fellowship at Grey College while the paper was in preparation. 2 Most of the work on this paper was done during the graduate studies of the author at the University of Haifa. At the time, the author was supported by the Adams Fellowship of the Israel Academy of Sciences and Humanities.",

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doi = "10.1016/j.jcss.2010.07.003",

language = "American English",

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AU - Fellows, Michael R.

AU - Fertin, Guillaume

AU - Hermelin, Danny

AU - Vialette, Stéphane

N1 - Funding Information: ✩ An extended abstract of this paper appeared in Fellows et al. (2007) [23]. * Corresponding author. E-mail addresses: [email protected] (M.R. Fellows), [email protected] (G. Fertin), [email protected] (D. Hermelin), [email protected] (S. Vialette). 1 Supported by the Australian Research Council, by a Fellowship to the Durham University Institute for Advanced Studies, and by a William Best Fellowship at Grey College while the paper was in preparation. 2 Most of the work on this paper was done during the graduate studies of the author at the University of Haifa. At the time, the author was supported by the Adams Fellowship of the Israel Academy of Sciences and Humanities.

PY - 2011/1/1

Y1 - 2011/1/1

N2 - We study the problem of finding occurrences of motifs in vertex-colored graphs, where a motif is a multiset of colors, and an occurrence of a motif is a subset of connected vertices whose multiset of colors equals the motif. This problem is a natural graph-theoretic pattern matching variant where we are not interested in the actual structure of the occurrence of the pattern, we only require it to preserve the very basic topological requirement of connectedness. We give two positive results and three negative results that together give an extensive picture of tractable and intractable instances of the problem.

AB - We study the problem of finding occurrences of motifs in vertex-colored graphs, where a motif is a multiset of colors, and an occurrence of a motif is a subset of connected vertices whose multiset of colors equals the motif. This problem is a natural graph-theoretic pattern matching variant where we are not interested in the actual structure of the occurrence of the pattern, we only require it to preserve the very basic topological requirement of connectedness. We give two positive results and three negative results that together give an extensive picture of tractable and intractable instances of the problem.

KW - Graph motif

KW - Graph pattern matching

KW - Parameterized complexity

KW - Treewidth

KW - W hardness

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DO - 10.1016/j.jcss.2010.07.003

M3 - Article

SN - 0022-0000

VL - 77

SP - 799

EP - 811

JO - Journal of Computer and System Sciences

JF - Journal of Computer and System Sciences

IS - 4

ER -

Upper and lower bounds for finding connected motifs in vertex-colored graphs

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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