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Time-Approximation Trade-offs for Inapproximable Problems

hal.structure.identifierInstitute for Computer Science and Control [Budapest] [SZTAKI]
dc.contributor.authorBonnet, Édouard
HAL ID: 171728
ORCID: 0000-0002-1653-5822		*
hal.structure.identifierLaboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
dc.contributor.authorLampis, Michael
HAL ID: 182546
ORCID: 0000-0002-5791-0887		*
hal.structure.identifierLaboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
dc.contributor.authorPaschos, Vangelis*
dc.date.accessioned2017-03-14T13:17:54Z
dc.date.available2017-03-14T13:17:54Z
dc.date.issued2016
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/16336
dc.language.isoenen
dc.subjectApproximationen
dc.subjectComplexityen
dc.subjectPolynomial and Subexponential Approximationen
dc.subjectReductionen
dc.subjectInapproximabilityen
dc.subject.ddc003en
dc.titleTime-Approximation Trade-offs for Inapproximable Problemsen
dc.typeCommunication / Conférence
dc.description.abstractenIn this paper we focus on problems which do not admit a constant-factor approximation in polynomial time and explore how quickly their approximability improves as the allowed running time is gradually increased from polynomial to (sub-)exponential. We tackle a number of problems: For MIN INDEPENDENT DOMINATING SET, MAX INDUCED PATH, FOREST and TREE, for any r(n), a simple, known scheme gives an approximation ratio of r in time roughly r^{n/r}. We show that, for most values of r, if this running time could be significantly improved the ETH would fail. For MAX MINIMAL VERTEX COVER we give a non-trivial sqrt{r}-approximation in time 2^{n/{r}}. We match this with a similarly tight result. We also give a log(r)-approximation for MIN ATSP in time 2^{n/r} and an r-approximation for MAX GRUNDY COLORING in time r^{n/r}. Furthermore, we show that MIN SET COVER exhibits a curious behavior in this super-polynomial setting: for any delta>0 it admits an m^delta-approximation, where m is the number of sets, in just quasi-polynomial time. We observe that if such ratios could be achieved in polynomial time, the ETH or the Projection Games Conjecture would fail.en
dc.identifier.citationpages22:1-22:14en
dc.relation.ispartoftitle33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016)en
dc.relation.ispartofeditorOllinger, Nicolas
dc.relation.ispartofeditorVollmer, Heribert
dc.relation.ispartofpublnameSchloss Dagstuhl--Leibniz-Zentrum fuer Informatiken
dc.relation.ispartofpublcityWadernen
dc.relation.ispartofdate2016-02
dc.relation.ispartofpages798en
dc.relation.ispartofurl10.4230/LIPIcs.STACS.2016.0en
dc.subject.ddclabelRecherche opérationnelleen
dc.relation.ispartofisbn978-3-95977-001-9en
dc.relation.conftitle33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016)en
dc.relation.confdate2016-02
dc.relation.confcityOrléansen
dc.relation.confcountryFranceen
dc.relation.forthcomingnonen
dc.identifier.doi10.4230/LIPIcs.STACS.2016.22en
dc.description.ssrncandidatenonen
dc.description.halcandidateouien
dc.description.readershiprechercheen
dc.description.audienceInternationalen
dc.relation.Isversionofjnlpeerreviewednonen
dc.relation.Isversionofjnlpeerreviewednonen
dc.date.updated2017-03-14T12:56:03Z
hal.identifierhal-01489450*
hal.version1*
hal.faultCodeThe supplied format packaging is not supported by the server
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