Elsevier

Discrete Applied Mathematics

Volume 213, 20 November 2016, Pages 162-178
Discrete Applied Mathematics

Deterministic parameterized algorithms for the Graph Motif problem

https://doi.org/10.1016/j.dam.2016.04.026Get rights and content
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Abstract

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 TG, 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.

Abbreviations

GM
Graph Motif
RGM
Restricted GM

Keywords

Parameterized algorithm
Graph motif
Representative family
Guiding tree

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A preliminary version of this paper appeared in the proceedings of the 39th International Symposium on Mathematical Foundations of Computer Science (MFCS’14).