Finding and counting vertex-colored subtrees

Sylvain Guillemot (1) , Florian Sikora (2)

1 Lehrstuhl Bioinformatik Jena
2 LIGM - Laboratoire d'Informatique Gaspard-Monge

The problems studied in this article originate in the Graph Motif problem introduced by Lacroix et al. (TCBB 2006) in the context of biological networks. The problem is to decide if a vertex-colored graph has a connected subgraph whose colors equals a given multiset of colors M. Using an algebraic framework recently introduced in Koutis (ICALP 2008) and Koutis, Williams (ICALP 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, 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.

Domaines: Complexité [cs.CC]

Sylvain Guillemot, Florian Sikora. Finding and counting vertex-colored subtrees. International Symposium on Mathematical Foundations of Computer Science (MFCS), Jun 2010, Brno, Czech Republic. pp.405-416. ⟨hal-00455134v3⟩