The parameterized complexity of Graph Motif relatively to the structure of the input graph.
Édouard Bonnet, Florian Sikora · arXiv (Cornell University) · 2015
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 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. Though, in the many applications of Graph Motif, the input graph originates from real-life 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 an FPT algorithm close to the best possible running time under standard complexity assumptions, or show that the problem remains intractable when the parameter is bounded by a constant. We notice that the problem seems slightly easier on very dense graphs than on very sparse ones, the connectivity constraint being tamed on the former family.