Finding approximate and constrained motifs in 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;Laboratoire d'Informatique de Nantes-Atlantique, UMR, CNRS, Université de Nantes, Nantes Cedex 3, France;IGM-LabInfo, CNRS, UMR, Université Paris-Est, Marne-la-Vallée, France

  • Venue:
  • CPM'11 Proceedings of the 22nd annual conference on Combinatorial pattern matching
  • Year:
  • 2011

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Abstract

One of the emerging topics in the analysis of biological networks is the inference of motifs inside a network. In the context of metabolic network analysis, a recent approach introduced in [14], represents the network as a vertex-colored graph, while a motif M is represented as a multiset of colors. An occurrence of a motif M in a vertex-colored graph G is a connected induced subgraph of G whose vertex set is colored exactly as M. We investigate three different variants of the initial problem. The first two variants, MIN-ADD and MIN-SUBSTITUTE, deal with approximate occurrences of a motif in the graph, while the third variant, CONSTRAINED GRAPH MOTIF (or CGM for short), constrains the motif to contain a given set of vertices. We investigate the classical and parameterized complexity of the three problems. We show that MIN-ADD and MIN-SUBSTITUTE are NP-hard, even when M is a set, and the graph is a tree of degree bounded by 4 in which each color appears at most twice. Moreover, we show that MIN-SUBSTITUTE is in FPT when parameterized by the size of M. Finally, we consider the parameterized complexity of the CGM problem, and we give a fixed-parameter algorithm for graphs of bounded treewidth, while we show that the problem is W[2]-hard, even if the input graph has diameter 2.