On the Complexity of Various Parameterizations of Common Induced Subgraph Isomorphism - CNRS - Centre national de la recherche scientifique Accéder directement au contenu
Communication Dans Un Congrès Année : 2015

On the Complexity of Various Parameterizations of Common Induced Subgraph Isomorphism

Résumé

Maximum Common Induced Subgraph (henceforth MCIS) is among the most studied classical NP-hard problems. MCIS remains NP-hard on many graph classes including bipartite graphs, planar graphs and k-trees. Little is known, however, about the parameterized complexity of the problem. When parameterized by the vertex cover number of the input graphs, the problem was recently shown to be fixed-parameter tractable. Capitalizing on this result, we show that the problem does not have a polynomial kernel when parameterized by vertex cover unless NP⊆coNP/poly. We also show that Maximum Common Connected Induced Subgraph (MCCIS), which is a variant where the solution must be connected, is also fixed-parameter tractable when parameterized by the vertex cover number of input graphs. Both problems are shown to be W[1]-complete on bipartite graphs and graphs of girth five and, unless P=NP, they do not belong to the class XP when parameterized by a bound on the size of the minimum feedback vertex sets of the input graphs, that is solving them in polynomial time is very unlikely when this parameter is a constant.

Dates et versions

hal-01366670 , version 1 (15-09-2016)

Identifiants

Citer

Faisal N. Abu-Khzam, Edouard Bonnet, Florian Sikora. On the Complexity of Various Parameterizations of Common Induced Subgraph Isomorphism. 25th International Workshop on Combinatorial Algorithms, IWOCA 2014, Oct 2014, Duluth, United States. pp.1-12, ⟨10.1007/978-3-319-19315-1_1⟩. ⟨hal-01366670⟩
36 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More