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- W1573571013 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 NP ⊆ DTIMEclass(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." @default.
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- W1573571013 date "2009-01-01" @default.
- W1573571013 modified "2023-10-17" @default.
- W1573571013 title "Maximum Motif Problem in Vertex-Colored Graphs" @default.
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- W1573571013 doi "https://doi.org/10.1007/978-3-642-02441-2_20" @default.
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