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.

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U2 - 10.1109/SFCS.2005.40

DO - 10.1109/SFCS.2005.40

M3 - Conference contribution

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 -