Hardness of the covering radius problem on lattices

Ishay Haviv, Oded Regev

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

Abstract

We provide the first hardness result for the Covering Radius Problem on lattices (CRP). Namely, we show that for any large enough p ≤ ∞ there exists a constant cp > 1 such that CRP in the ℓp norm is ∏2-hard to approximate to within any constant less than c p. In particular, for the case p = ∞, we obtain the constant c = 1.5. This gets close to the constant 2 beyond which the problem is not believed to be ∏2-hard. As part of our proof, we establish a stronger hardness of approximation result for the ∀∃-3-SAT problem with bounded occurrences. This hardness result might be useful elsewhere.

Original languageEnglish (US)
Title of host publicationProceedings - Twenty-First Annual IEEE Conference on Computational Complexity, CCC 2006
Pages145-158
Number of pages14
Volume2006
DOIs
StatePublished - 2006
Event21st Annual IEEE Conference on Computational Complexity, CCC 2006 - Prague, Czech Republic
Duration: Jul 16 2006Jul 20 2006

Other

Other21st Annual IEEE Conference on Computational Complexity, CCC 2006
CountryCzech Republic
CityPrague
Period7/16/067/20/06

Fingerprint

Covering Radius
Hardness
Hardness of Approximation
Norm

ASJC Scopus subject areas

  • Computational Mathematics

Cite this

Haviv, I., & Regev, O. (2006). Hardness of the covering radius problem on lattices. In Proceedings - Twenty-First Annual IEEE Conference on Computational Complexity, CCC 2006 (Vol. 2006, pp. 145-158). [1663733] https://doi.org/10.1109/CCC.2006.23

Hardness of the covering radius problem on lattices. / Haviv, Ishay; Regev, Oded.

Proceedings - Twenty-First Annual IEEE Conference on Computational Complexity, CCC 2006. Vol. 2006 2006. p. 145-158 1663733.

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

Haviv, I & Regev, O 2006, Hardness of the covering radius problem on lattices. in Proceedings - Twenty-First Annual IEEE Conference on Computational Complexity, CCC 2006. vol. 2006, 1663733, pp. 145-158, 21st Annual IEEE Conference on Computational Complexity, CCC 2006, Prague, Czech Republic, 7/16/06. https://doi.org/10.1109/CCC.2006.23
Haviv I, Regev O. Hardness of the covering radius problem on lattices. In Proceedings - Twenty-First Annual IEEE Conference on Computational Complexity, CCC 2006. Vol. 2006. 2006. p. 145-158. 1663733 https://doi.org/10.1109/CCC.2006.23
Haviv, Ishay ; Regev, Oded. / Hardness of the covering radius problem on lattices. Proceedings - Twenty-First Annual IEEE Conference on Computational Complexity, CCC 2006. Vol. 2006 2006. pp. 145-158
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