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hal.structure.identifierThe University of Electro-Communication [Chofu]
dc.contributor.authorBelmonte, Rémy
hal.structure.identifierInstitut de Recherche en Informatique Fondamentale [IRIF (UMR_8243)]
dc.contributor.authorMitsou, Valia
dc.date.accessioned2023-08-18T15:04:38Z
dc.date.available2023-08-18T15:04:38Z
dc.date.issued2018
dc.identifier.urihttps://basepub.dauphine.psl.eu/handle/123456789/24860
dc.language.isoenen
dc.subjectTreewidthen
dc.subjectParameterized Complexityen
dc.subjectApproximationen
dc.subjectColoringen
dc.subject.ddc003en
dc.titleParameterized (Approximate) Defective Coloringen
dc.typeCommunication / Conférence
dc.description.abstractenIn Defective Coloring we are given a graph G=(V,E) and two integers chi_d,Delta^* and are asked if we can partition V into chi_d color classes, so that each class induces a graph of maximum degree Delta^*. We investigate the complexity of this generalization of Coloring with respect to several well-studied graph parameters, and show that the problem is W-hard parameterized by treewidth, pathwidth, tree-depth, or feedback vertex set, if chi_d=2. As expected, this hardness can be extended to larger values of chi_d for most of these parameters, with one surprising exception: we show that the problem is FPT parameterized by feedback vertex set for any chi_d != 2, and hence 2-coloring is the only hard case for this parameter. In addition to the above, we give an ETH-based lower bound for treewidth and pathwidth, showing that no algorithm can solve theproblem in n^{o(pw)}, essentially matching the complexity of an algorithm obtained with standard techniques.We complement these results by considering the problem's approximability and show that, with respect to Delta^*, the problem admits an algorithm which for any epsilon>0 runs in time (tw/epsilon)^{O(tw)} and returns a solution with exactly the desired number of colors that approximates the optimal Delta^* within (1+epsilon). We also give a (tw)^{O(tw)} algorithm which achieves the desired Delta^* exactly while 2-approximating the minimum value of chi_d. We show that this is close to optimal, by establishing that no FPT algorithm can (under standard assumptions) achieve a better than 3/2-approximation to chi_d, even when an extra constant additive error is also allowed.en
dc.identifier.citationpages10:1--10:15en
dc.relation.ispartoftitle35th Symposium on Theoretical Aspects of Computer Science (STACS 2018)en
dc.relation.ispartofeditorRolf Niedermeier
dc.relation.ispartofeditorBrigitte Vallée
dc.relation.ispartofpublnameSchloss Dagstuhl--Leibniz-Zentrum fuer Informatiken
dc.relation.ispartofdate2018-02
dc.relation.ispartofpages840en
dc.relation.ispartofurlhttps://drops-beta.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2018en
dc.identifier.urlsitehttps://www.lamsade.dauphine.fr/~mlampis/papers/defective-stacs.pdfen
dc.subject.ddclabelRecherche opérationnelleen
dc.relation.ispartofisbn978-3-95977-062-0en
dc.relation.conftitle35th Symposium on Theoretical Aspects of Computer Science (STACS 2018)en
dc.relation.confdate2018-02
dc.relation.confcityCaenen
dc.relation.confcountryFranceen
dc.relation.forthcomingnonen
dc.identifier.doi10.4230/LIPIcs.STACS.2018.10en
dc.description.ssrncandidatenon
dc.description.halcandidatenonen
dc.description.readershiprechercheen
dc.description.audienceInternationalen
dc.relation.Isversionofjnlpeerreviewedouien
dc.date.updated2023-03-02T17:06:10Z
hal.export.arxivnonen
hal.export.pmcnonen
hal.hide.repecnonen
hal.hide.oainonen
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