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
Volume6198 LNCS
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)03029743
ISSN (Electronic)16113349

Other

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

Fingerprint

Inapproximability
Vertex Cover
Hypergraph
Scheduling Problem
Hardness
Scheduling
Game
Open Shop
Total Weighted Completion Time
Assembly Line
Uniform Hypergraph
Concurrent

ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

Cite this

Bansal, N., & Khot, S. (2010). Inapproximability of hypergraph vertex cover and applications to scheduling problems. In Automata, Languages and Programming - 37th International Colloquium, ICALP 2010, Proceedings (PART 1 ed., Vol. 6198 LNCS, pp. 250-261). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6198 LNCS, No. PART 1). https://doi.org/10.1007/978-3-642-14165-2_22

Inapproximability of hypergraph vertex cover and applications to scheduling problems. / Bansal, Nikhil; Khot, Subhash.

Automata, Languages and Programming - 37th International Colloquium, ICALP 2010, Proceedings. Vol. 6198 LNCS PART 1. ed. 2010. p. 250-261 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6198 LNCS, No. PART 1).

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

Bansal, N & Khot, S 2010, Inapproximability of hypergraph vertex cover and applications to scheduling problems. in Automata, Languages and Programming - 37th International Colloquium, ICALP 2010, Proceedings. PART 1 edn, vol. 6198 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), no. PART 1, vol. 6198 LNCS, pp. 250-261, 37th International Colloquium on Automata, Languages and Programming, ICALP 2010, Bordeaux, France, 7/6/10. https://doi.org/10.1007/978-3-642-14165-2_22
Bansal N, Khot S. Inapproximability of hypergraph vertex cover and applications to scheduling problems. In Automata, Languages and Programming - 37th International Colloquium, ICALP 2010, Proceedings. PART 1 ed. Vol. 6198 LNCS. 2010. p. 250-261. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); PART 1). https://doi.org/10.1007/978-3-642-14165-2_22
Bansal, Nikhil ; Khot, Subhash. / Inapproximability of hypergraph vertex cover and applications to scheduling problems. Automata, Languages and Programming - 37th International Colloquium, ICALP 2010, Proceedings. Vol. 6198 LNCS PART 1. ed. 2010. pp. 250-261 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); PART 1).
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