Hardness of approximating the closest vector problem with pre-processing

Mikhail Alekhnovich, Subhash Khot, Guy Kindler, Nisheeth K. Vishnoi

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

Abstract

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.

Original languageEnglish (US)
Title of host publicationProceedings - 46th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2005
Pages216-225
Number of pages10
Volume2005
DOIs
StatePublished - 2005
Event46th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2005 - Pittsburgh, PA, United States
Duration: Oct 23 2005Oct 25 2005

Other

Other46th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2005
CountryUnited States
CityPittsburgh, PA
Period10/23/0510/25/05

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Hardness
Processing

ASJC Scopus subject areas

  • Engineering(all)

Cite this

Alekhnovich, M., Khot, S., Kindler, G., & Vishnoi, N. K. (2005). Hardness of approximating the closest vector problem with pre-processing. In Proceedings - 46th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2005 (Vol. 2005, pp. 216-225). [1530716] https://doi.org/10.1109/SFCS.2005.40

Hardness of approximating the closest vector problem with pre-processing. / Alekhnovich, Mikhail; Khot, Subhash; Kindler, Guy; Vishnoi, Nisheeth K.

Proceedings - 46th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2005. Vol. 2005 2005. p. 216-225 1530716.

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

Alekhnovich, M, Khot, S, Kindler, G & Vishnoi, NK 2005, Hardness of approximating the closest vector problem with pre-processing. in Proceedings - 46th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2005. vol. 2005, 1530716, pp. 216-225, 46th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2005, Pittsburgh, PA, United States, 10/23/05. https://doi.org/10.1109/SFCS.2005.40
Alekhnovich M, Khot S, Kindler G, Vishnoi NK. Hardness of approximating the closest vector problem with pre-processing. In Proceedings - 46th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2005. Vol. 2005. 2005. p. 216-225. 1530716 https://doi.org/10.1109/SFCS.2005.40
Alekhnovich, Mikhail ; Khot, Subhash ; Kindler, Guy ; Vishnoi, Nisheeth K. / Hardness of approximating the closest vector problem with pre-processing. Proceedings - 46th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2005. Vol. 2005 2005. pp. 216-225
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