On the Complexity of Various Parameterizations of Common Induced Subgraph Isomorphism

Faisal Abu Khzam, Edouard Bonnet, Florian Sikora

Research output: Chapter in Book/Report/Conference proceedingConference Paper published in Proceedings

Abstract

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 xed-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 xedparameter 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 ve and, unless P = NP, they do not to 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.
Original languageEnglish
Title of host publicationCombinatorial Algorithms
Place of PublicationDuluth, USA
PublisherSpringer
Pages1-12
Number of pages12
ISBN (Electronic)9783319193151
ISBN (Print)978-3-319-19314-4
DOIs
Publication statusPublished - 2014
Externally publishedYes
EventInternational Workshop on Combinatorial Algorithms (IWOCA) 2014 25th - Duluth, Minnesota, USA
Duration: 15 Oct 201417 Oct 2014

Publication series

Name Lecture Notes in Computer Science book series
Volume8986

Conference

ConferenceInternational Workshop on Combinatorial Algorithms (IWOCA) 2014 25th
Period15/10/1417/10/14

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