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Maximum Motif Problem in Vertex-Colored Graphs

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Combinatorial Pattern Matching (CPM 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5577))

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Abstract

Searching for motifs in graphs has become a crucial problem in the analysis of biological networks. In this context, different graph motif problems have been considered [13,7,5]. Pursuing a line of research pioneered by Lacroix et al. [13], we introduce in this paper a new graph motif problem: given a vertex colored graph G and a motif \(\mathcal{M}\), where a motif is a multiset of colors, find a maximum cardinality submotif \(\mathcal{M}' \subseteq \mathcal{M}\) that occurs as a connected motif in G. We prove that the problem is APX-hard even in the case where the target graph is a tree of maximum degree 3, the motif is actually a set and each color occurs at most twice in the tree. Next, we strengthen this result by proving that the problem is not approximable within factor \(2^{\rm {log^{\delta} n}}\), for any constant δ< 1, unless NPDTIMEclass(2POLY log n). We complement these results by presenting two fixed-parameter algorithms for the problem, where the parameter is the size of the solution. Finally, we give exact fast exponential-time algorithms for the problem.

Supported by the Italian-French PAI= Galileo Project 08484VH.

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Dondi, R., Fertin, G., Vialette, S. (2009). Maximum Motif Problem in Vertex-Colored Graphs. In: Kucherov, G., Ukkonen, E. (eds) Combinatorial Pattern Matching. CPM 2009. Lecture Notes in Computer Science, vol 5577. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02441-2_20

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  • DOI: https://doi.org/10.1007/978-3-642-02441-2_20

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02440-5

  • Online ISBN: 978-3-642-02441-2

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