Finding Approximate and Constrained Motifs in Graphs

  • Riccardo Dondi
  • Guillaume Fertin
  • Stéphane Vialette
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6661)


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 \(\mathcal{M}\) is represented as a multiset of colors. An occurrence of a motif \(\mathcal{M}\) in a vertex-colored graph G is a connected induced subgraph of G whose vertex set is colored exactly as \(\mathcal{M}\). 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 \(\mathcal{M}\) 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 \(\mathcal{M}\). 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.


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© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Riccardo Dondi
    • 1
  • Guillaume Fertin
    • 2
  • Stéphane Vialette
    • 3
  1. 1.Dipartimento di Scienze dei Linguaggi, della Comunicazione e degli Studi CulturaliUniversità degli Studi di BergamoBergamoItaly
  2. 2.Laboratoire d’Informatique de Nantes-Atlantique (LINA), UMR CNRS 6241Université de NantesNantes Cedex 3France
  3. 3.IGM-LabInfo, CNRS UMR 8049Université Paris-EstMarne-la-ValléeFrance

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