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dc.contributor.authorFotakis, Dimitris
dc.contributor.authorLampis, Michail
dc.contributor.authorPaschos, Vangelis
dc.date.accessioned2017-03-14T13:36:47Z
dc.date.available2017-03-14T13:36:47Z
dc.date.issued2016
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/16338
dc.language.isoenen
dc.subjectrandomized roundingen
dc.subjectpolynomial and subexponential approximationen
dc.subjectsamplingen
dc.subject.ddc003en
dc.titleSub-exponential Approximation Schemes for CSPs: From Dense to Almost Sparseen
dc.typeCommunication / Conférence
dc.description.abstractenIt has long been known, since the classical work of (Arora, Karger, Karpinski, JCSS'99), that MAX-CUT admits a PTAS on dense graphs, and more generally, MAX-k-CSP admits a PTAS on "dense" instances with Omega(n^k) constraints. In this paper we extend and generalize their exhaustive sampling approach, presenting a framework for (1-epsilon)-approximating any MAX-k-CSP problem in sub-exponential time while significantly relaxing the denseness requirement on the input instance. Specifically, we prove that for any constants delta in (0, 1] and epsilon > 0, we can approximate MAX-k-CSP problems with Omega(n^{k-1+delta}) constraints within a factor of (1-epsilon) in time 2^{O(n^{1-delta}*ln(n) / epsilon^3)}. The framework is quite general and includes classical optimization problems, such as MAX-CUT, MAX-DICUT, MAX-k-SAT, and (with a slight extension) k-DENSEST SUBGRAPH, as special cases. For MAX-CUT in particular (where k=2), it gives an approximation scheme that runs in time sub-exponential in n even for "almost-sparse" instances (graphs with n^{1+delta} edges). We prove that our results are essentially best possible, assuming the ETH. First, the density requirement cannot be relaxed further: there exists a constant r < 1 such that for all delta > 0, MAX-k-SAT instances with O(n^{k-1}) clauses cannot be approximated within a ratio better than r in time 2^{O(n^{1-delta})}. Second, the running time of our algorithm is almost tight for all densities. Even for MAX-CUT there exists r<1 such that for all delta' > delta >0, MAX-CUT instances with n^{1+delta} edges cannot be approximated within a ratio better than r in time 2^{n^{1-delta'}}.en
dc.identifier.citationpages37:1--37:14en
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.contributor.countryeditoruniversityotherGREECE
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.2016.37en
dc.description.ssrncandidatenonen
dc.description.halcandidateouien
dc.description.readershiprechercheen
dc.description.audienceInternationalen
dc.relation.Isversionofjnlpeerreviewednonen
dc.relation.Isversionofjnlpeerreviewednonen
dc.date.updated2017-03-14T13:28:28Z
hal.person.labIds245158
hal.person.labIds989
hal.person.labIds989
hal.identifierhal-01489486*


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