TY - GEN
T1 - Hardness of approximating the closest vector problem with pre-processing
AU - Alekhnovich, Mikhail
AU - Khot, Subhash A.
AU - Kindler, Guy
AU - Vishnoi, Nisheeth K.
PY - 2005
Y1 - 2005
N2 - We show that, unless NP⊆DTIME(2 Poly log(n)), the closest vector problem with pre-processing, for ℓ p norm for any p ≥ 1, is hard to approximate within a factor of (log n) 1/p-ε for any ε > 0. This improves the previous best factor of 3 1/p - ε due to Regev [19]. Our results also imply that under the same complexity assumption, the nearest codeword problem with pre-processing is hard to approximate within a factor of (log n) 1-ε for any ε > 0.
AB - We show that, unless NP⊆DTIME(2 Poly log(n)), the closest vector problem with pre-processing, for ℓ p norm for any p ≥ 1, is hard to approximate within a factor of (log n) 1/p-ε for any ε > 0. This improves the previous best factor of 3 1/p - ε due to Regev [19]. Our results also imply that under the same complexity assumption, the nearest codeword problem with pre-processing is hard to approximate within a factor of (log n) 1-ε for any ε > 0.
UR - http://www.scopus.com/inward/record.url?scp=33748617126&partnerID=8YFLogxK
U2 - 10.1109/SFCS.2005.40
DO - 10.1109/SFCS.2005.40
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AN - SCOPUS:33748617126
SN - 0769524680
SN - 9780769524689
T3 - Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS
SP - 216
EP - 225
BT - Proceedings - 46th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2005
T2 - 46th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2005
Y2 - 23 October 2005 through 25 October 2005
ER -