Deterministic parameterized algorithms for the Graph Motif problem

We study the classic Graph Motif problem. Given a graph G=(V,E) with a set of colors for each node, and a multiset M of colors, we seek a subtree T⊆G, and a coloring assigning to each node in T a color from its set, such that T carries exactly (also with respect to multiplicity) the colors in M. Gra...

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Bibliographic Details
Published in:Discrete Applied Mathematics Vol. 213; pp. 162 - 178
Main Authors: Pinter, Ron Y., Shachnai, Hadas, Zehavi, Meirav
Format: Journal Article
Language:English
Published: Elsevier B.V 20.11.2016
Subjects:
Graph motif
Guiding tree
Parameterized algorithm
Representative family
RGM
Parameterized algorithm
Representative family
GM
Graph motif
Guiding tree
ISSN:0166-218X, 1872-6771
Online Access:Get full text
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Summary:We study the classic Graph Motif problem. Given a graph G=(V,E) with a set of colors for each node, and a multiset M of colors, we seek a subtree T⊆G, and a coloring assigning to each node in T a color from its set, such that T carries exactly (also with respect to multiplicity) the colors in M. Graph Motif plays a central role in the study of pattern matching problems, primarily motivated from the analysis of complex biological networks. Previous algorithms for Graph Motif and its variants either rely on techniques for developing randomized algorithms that − if derandomized − render them inefficient, or the algebraic narrow sieves technique for which there is no known derandomization. In this paper, we present fast deterministic parameterized algorithms for Graph Motif and its variants. Specifically, we give such an algorithm for the more general Graph Motif with Deletions problem, followed by faster algorithms for Graph Motif and other well-studied special cases. Our algorithms make non-trivial use of representative families, and a novel tool that we call guiding trees, together enabling the efficient construction of the output tree.
ISSN:0166-218X
1872-6771
DOI:10.1016/j.dam.2016.04.026