CPM 2011: Combinatorial Pattern Matching pp 388-401

# Finding Approximate and Constrained Motifs in Graphs

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

## 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 $$\mathcal{M}$$ 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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## 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