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dc.contributor.authorDondi, Riccardo
dc.contributor.authorSikora, Florian
dc.date.accessioned2019-04-30T10:46:10Z
dc.date.available2019-04-30T10:46:10Z
dc.date.issued2018
dc.identifier.issn0304-3975
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/18868
dc.language.isoenen
dc.subjectColorful componentsen
dc.subjectParameterized complexityen
dc.subjectAlgorithmsen
dc.subjectComputational biologyen
dc.subject.ddc005en
dc.titleParameterized complexity and approximation issues for the colorful components problemsen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenThe quest for colorful components (connected components where each color is associated with at most one vertex) inside a vertex-colored graph has been widely considered in the last ten years. Here we consider two variants, Minimum Colorful Components (MCC) and Maximum Edges in transitive Closure (MEC), introduced in 2011 in the context of orthology gene identification in bioinformatics. The input of both MCC and MEC is a vertex-colored graph. MCC asks for the removal of a subset of edges, so that the resulting graph is partitioned in the minimum number of colorful connected components; MEC asks for the removal of a subset of edges, so that the resulting graph is partitioned in colorful connected components and the number of edges in the transitive closure of such a graph is maximized. We study the parameterized and approximation complexity of MCC and MEC, for general and restricted instances.For MCC on trees we show that the problem is basically equivalent to Minimum Cut on Trees, thus MCC is not approximable within factor 1.36−ε, it is fixed-parameter tractable and it admits a poly-kernel (when the parameter is the number of colorful components). Moreover, we show that MCC, while it is polynomial time solvable on paths, it is NP-hard even for graphs with constant distance to disjoint paths number. Then we consider the parameterized complexity of MEC when parameterized by the number k of edges in the transitive closure of a solution (the graph obtained by removing edges so that it is partitioned in colorful connected components). We give a fixed-parameter algorithm for MEC parameterized by k and, when the input graph is a tree, we give a poly-kernel.en
dc.relation.isversionofjnlnameTheoretical Computer Science
dc.relation.isversionofjnlvol739en
dc.relation.isversionofjnldate2018-08
dc.relation.isversionofjnlpages1-12en
dc.relation.isversionofdoi10.1016/j.tcs.2018.04.044en
dc.relation.isversionofjnlpublisherElsevieren
dc.subject.ddclabelProgrammation, logiciels, organisation des donnéesen
dc.relation.forthcomingnonen
dc.relation.forthcomingprintnonen
dc.description.ssrncandidatenonen
dc.description.halcandidateouien
dc.description.readershiprechercheen
dc.description.audienceInternationalen
dc.relation.Isversionofjnlpeerreviewedouien
dc.relation.Isversionofjnlpeerreviewedouien
dc.date.updated2019-03-22T09:35:13Z
hal.person.labIds119452
hal.person.labIds989
hal.identifierhal-02115544*


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