Maximum Motif Problem in Vertex-Colored Graphs

  • Authors:

  • Riccardo Dondi;Guillaume Fertin;Stéphane Vialette

  • Affiliations:

  • Dipartimento di Scienze dei Linguaggi, della Comunicazione e degli Studi Culturali, Università degli Studi di Bergamo, Bergamo, Italy 24129;Laboratoire d'Informatique de Nantes-Atlantique (LINA), UMR CNRS 6241, Université de Nantes, Nantes Cedex 3, France 44322;IGM-LabInfo, CNRS UMR 8049, Université Paris-Est, Marne-la-Vallée, France 77454

  • Venue:
  • CPM '09 Proceedings of the 20th Annual Symposium on Combinatorial Pattern Matching
  • Year:
  • 2009

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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 *** 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.