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ETH hardness for densest-k-Subgraph with perfect completeness

Author(s): Braverman, Mark; Ko, YK; Rubinstein, A; Weinstein, O

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dc.contributor.authorBraverman, Mark-
dc.contributor.authorKo, YK-
dc.contributor.authorRubinstein, A-
dc.contributor.authorWeinstein, O-
dc.date.accessioned2018-07-20T15:09:26Z-
dc.date.available2018-07-20T15:09:26Z-
dc.date.issued2017-01-16en_US
dc.identifier.citationBraverman, M, Ko, YK, Rubinstein, A, Weinstein, O. (2017). ETH hardness for densest-k-Subgraph with perfect completeness. 1326 - 1341en_US
dc.identifier.urihttp://arks.princeton.edu/ark:/88435/pr1tw9k-
dc.description.abstractWe show that, assuming the (deterministic) Exponential Time Hypothesis, distinguishing between a graph with an induced k-clique and a graph in which all k-subgraphs have density at most 1- ϵ, requires n (log n) time. Our result essentially matches the quasi-polynomial algorithms of Feige and Seltser [FS97] and Barman [Bar15] for this problem, and is the first one to rule out an additive PTAS for Densest k-Subgraph. We further strengthen this result by showing that our lower bound continues to hold when, in the soundness case, even subgraphs smaller by a near-polynomial factor (ko = k 2 (log n)) are assumed to be at most (1 - ϵ)-dense. Our reduction is inspired by recent applications of the birthday repetition technique [AIM14, BKW15]. Our analysis relies on information theoretical machinery and is similar in spirit to analyzing a parallel repetition of two- prover games in which the provers may choose to answer some challenges multiple times, while completely ignoring other challenges.en_US
dc.format.extent1326 - 1341en_US
dc.language.isoen_USen_US
dc.relation.ispartofProceedings of the Annual ACM-SIAM Symposium on Discrete Algorithmsen_US
dc.rightsAuthor's manuscripten_US
dc.titleETH hardness for densest-k-Subgraph with perfect completenessen_US
dc.typeJournal Articleen_US
dc.date.eissued2017en_US
pu.type.symplectichttp://www.symplectic.co.uk/publications/atom-terms/1.0/conference-proceedingen_US

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