Finding and counting vertex-colored subtrees

  • Authors:
  • Sylvain Guillemot;Florian Sikora

  • Affiliations:
  • Lehrstuhl für Bioinformatik, Friedrich-Schiller Universität Jena, Jena, Germany;Université Paris-Est, LIGM, UMR, CNRS, France

  • Venue:
  • MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
  • Year:
  • 2010

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Abstract

The problems studied in this article originate from the GRAPH MOTIF problem introduced by Lacroix et al. [17] in the context of biological networks. The problem is to decide if a vertex-colored graph has a connected subgraph whose colors equal a given multiset of colors M. Using an algebraic framework recently introduced by Koutis et al. [15,16], we obtain new FPT algorithms for GRAPH MOTIF and variants, with improved running times. We also obtain results on the counting versions of this problem, showing that the counting problem is FPT if M is a set, but becomes #W[1]-hard if M is a multiset with two colors.