Maximum Motif Problem in Vertex-Colored Graphs

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 [12, 6, 4]. Pursuing a line of research pioneered by Lacroix et al. [12], we introduce in this paper a new graph motif problem: given a vertex colored graph G and a motif M, where a motif is a multiset of colors, find a maximum cardinality submotif M' included in 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. 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 efficient exponential-time algorithms for the problem.
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Riccardo Dondi, Guillaume Fertin, Stéphane Vialette. Maximum Motif Problem in Vertex-Colored Graphs. 20th Annual Symposium on Combinatorial Pattern Matching (CPM 2009), 2009, Lille, France. pp.221-235, ⟨10.1007/978-3-642-02441-2_20⟩. ⟨hal-00416463⟩

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