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The Graph Motif problem parameterized by the structure of the input graph

Bonnet, Édouard; Sikora, Florian (2017), The Graph Motif problem parameterized by the structure of the input graph, Discrete Applied Mathematics, 231, p. 78-94. 10.1016/j.dam.2016.11.016

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Type
Article accepté pour publication ou publié
Date
2017
Journal name
Discrete Applied Mathematics
Volume
231
Publisher
Elsevier
Pages
78-94
Publication identifier
10.1016/j.dam.2016.11.016
Metadata
Show full item record
Author(s)
Bonnet, Édouard cc
Institute for Computer Science and Control [Budapest] [SZTAKI]
Sikora, Florian cc
Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
Abstract (EN)
The Graph Motif problem was introduced in 2006 in the context of biological networks. It consists of deciding whether or not a multiset of colors occurs in a connected subgraph of a vertex-colored graph. Graph Motif has been mostly analyzed from the standpoint of parameterized complexity. The main parameters which came into consideration were the size of the multiset and the number of colors. In the many utilizations of Graph Motif, however, the input graph originates from real-life applications and has structure. Motivated by this prosaic observation, we systematically study its complexity relatively to graph structural parameters. For a wide range of parameters, we give new or improved FPT algorithms, or show that the problem remains intractable. For the FPT cases, we also give some kernelization lower bounds as well as some ETH-based lower bounds on the worst case running time. Interestingly, we establish that Graph Motif is W[1]-hard (while in W[P]) for parameter max leaf number, which is, to the best of our knowledge, the first problem to behave this way.
Subjects / Keywords
Parameterized complexity; Graph motif problem; Structural parameterization; Computational biology

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