TY - GEN

T1 - 2 log1-εn hardness for the closest vector problem with preprocessing

AU - Khot, Subhash A.

AU - Popat, Preyas

AU - Vishnoi, Nisheeth K.

N1 - Copyright:
Copyright 2012 Elsevier B.V., All rights reserved.

PY - 2012

Y1 - 2012

N2 - 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].

AB - 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].

KW - PCP

KW - closest vector problem

KW - hardness of approximation

KW - lattices

KW - nearest codeword problem

UR - http://www.scopus.com/inward/record.url?scp=84862632621&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84862632621&partnerID=8YFLogxK

U2 - 10.1145/2213977.2214004

DO - 10.1145/2213977.2214004

M3 - Conference contribution

AN - SCOPUS:84862632621

SN - 9781450312455

T3 - Proceedings of the Annual ACM Symposium on Theory of Computing

SP - 277

EP - 288

BT - STOC '12 - Proceedings of the 2012 ACM Symposium on Theory of Computing

T2 - 44th Annual ACM Symposium on Theory of Computing, STOC '12

Y2 - 19 May 2012 through 22 May 2012

ER -