Inapproximability of hypergraph vertex cover and applications to scheduling problems

Nikhil Bansal, Subhash Khot

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Assuming the Unique Games Conjecture (UGC), we show optimal inapproximability results for two classic scheduling problems. We obtain a hardness of 2-ε for the problem of minimizing the total weighted completion time in concurrent open shops. We also obtain a hardness of 2-ε for minimizing the makespan in the assembly line problem. These results follow from a new inapproximability result for the Vertex Cover problem on k-uniform hypergraphs that is stronger and simpler than previous results. We show that assuming the UGC, for every k≥2, the problem is inapproximable within k-ε even when the hypergraph is almost k -partite.

Original languageEnglish (US)
Title of host publicationAutomata, Languages and Programming - 37th International Colloquium, ICALP 2010, Proceedings
Pages250-261
Number of pages12
EditionPART 1
DOIs
StatePublished - 2010
Event37th International Colloquium on Automata, Languages and Programming, ICALP 2010 - Bordeaux, France
Duration: Jul 6 2010Jul 10 2010

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
NumberPART 1
Volume6198 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other37th International Colloquium on Automata, Languages and Programming, ICALP 2010
CountryFrance
CityBordeaux
Period7/6/107/10/10

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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