Optimal long code test with one free bit

Nikhil Bansal, Subhash Khot

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

Abstract

For arbitrarily small constants ε, δ > 0, we present a long code test with one free bit, completeness 1 - ε and soundness δ. Using the test, we prove the following two inapproximability results: 1) Assuming the Unique Games Conjecture of Khot [15], given an n-vertex graph that has two disjoint independent sets of size (1/2 - ε)n each, it is NP-hard to find an independent set of size δn. 2) Assuming a (new) stronger version of the Unique Games Conjecture, the scheduling problem of minimizing weighted completion time with precedence constraints is inapprox-imable within factor 2 - ε.

Original languageEnglish (US)
Title of host publicationProceedings - 50th Annual Symposium on Foundations of Computer Science, FOCS 2009
Pages453-462
Number of pages10
DOIs
StatePublished - Dec 1 2009
Event50th Annual Symposium on Foundations of Computer Science, FOCS 2009 - Atlanta, GA, United States
Duration: Oct 25 2009Oct 27 2009

Publication series

NameProceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS
ISSN (Print)0272-5428

Other

Other50th Annual Symposium on Foundations of Computer Science, FOCS 2009
CountryUnited States
CityAtlanta, GA
Period10/25/0910/27/09

ASJC Scopus subject areas

  • Computer Science(all)

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  • Cite this

    Bansal, N., & Khot, S. (2009). Optimal long code test with one free bit. In Proceedings - 50th Annual Symposium on Foundations of Computer Science, FOCS 2009 (pp. 453-462). [5438609] (Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS). https://doi.org/10.1109/FOCS.2009.23