2 log1-εn hardness for the closest vector problem with preprocessing

Subhash A. Khot; Preyas Popat; Nisheeth K. Vishnoi

doi:10.1145/2213977.2214004

2 ^log1-εn hardness for the closest vector problem with preprocessing

Subhash A. Khot, Preyas Popat, Nisheeth K. Vishnoi

Computer Science

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

We prove that for an arbitrarily small constant ε > 0, assuming NP⊈DTIME (2 ^{log O(1-εn}), the preprocessing versions of the closest vector problem and the nearest codeword problem are hard to approximate within a factor better than 2 ^{log 1-ε n}. This improves upon the previous hardness factor of (log n) ^δ for some δ > 0 due to [AKKV05].

Original language	English (US)
Title of host publication	STOC '12 - Proceedings of the 2012 ACM Symposium on Theory of Computing
Pages	277-288
Number of pages	12
DOIs	https://doi.org/10.1145/2213977.2214004
State	Published - 2012
Event	44th Annual ACM Symposium on Theory of Computing, STOC '12 - New York, NY, United States Duration: May 19 2012 → May 22 2012

Publication series

Name	Proceedings of the Annual ACM Symposium on Theory of Computing
ISSN (Print)	0737-8017

Other

Other	44th Annual ACM Symposium on Theory of Computing, STOC '12
Country/Territory	United States
City	New York, NY
Period	5/19/12 → 5/22/12

Keywords

PCP
closest vector problem
hardness of approximation
lattices
nearest codeword problem

ASJC Scopus subject areas

Software

Access to Document

10.1145/2213977.2214004

Cite this

2 ^log1-εn hardness for the closest vector problem with preprocessing. / Khot, Subhash A.; Popat, Preyas; Vishnoi, Nisheeth K.
STOC '12 - Proceedings of the 2012 ACM Symposium on Theory of Computing. 2012. p. 277-288 (Proceedings of the Annual ACM Symposium on Theory of Computing).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Khot, SA, Popat, P & Vishnoi, NK 2012, 2 ^log1-εn hardness for the closest vector problem with preprocessing. in STOC '12 - Proceedings of the 2012 ACM Symposium on Theory of Computing. Proceedings of the Annual ACM Symposium on Theory of Computing, pp. 277-288, 44th Annual ACM Symposium on Theory of Computing, STOC '12, New York, NY, United States, 5/19/12. https://doi.org/10.1145/2213977.2214004

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