Algorithmica

, Volume 65, Issue 4, pp 828–844 | Cite as

Finding and Counting Vertex-Colored Subtrees

Article

Abstract

The problems studied in this article originate from the Graph Motif problem introduced by Lacroix et al. (IEEE/ACM Trans. Comput. Biol. Bioinform. 3(4):360–368, 2006) 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. It is a graph pattern-matching problem variant, where the structure of the occurrence of the pattern is not of interest but the only requirement is the connectedness. Using an algebraic framework recently introduced by Koutis (Proceedings of the 35th International Colloquium on Automata, Languages and Programming (ICALP), Lecture Notes in Computer Science, vol. 5125, pp. 575–586, 2008) and Koutis and Williams (Proceedings of the 36th International Colloquium on Automata, Languages and Programming (ICALP), Lecture Notes in Computer Science, vol. 5555, pp. 653–664, 2009), 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, proving that the counting problem is FPT if M is a set, but becomes #W[1]-hard if M is a multiset with two colors. Finally, we present an experimental evaluation of this approach on real datasets, showing that its performance compares favorably with existing software.

Keywords

Parameterized complexity Pattern matching in graphs Biological networks Vertex-colored graphs 

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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Lehrstuhl für BioinformatikFriedrich-Schiller Universität JenaJenaGermany
  2. 2.Department of Computer ScienceIowa State UniversityAmesUSA
  3. 3.Université Paris-EstLIGM–UMR CNRS 8049Marne-la-Vallée Cedex 2France

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