Lattice problems in NP ∩ coNP

Dorit Aharonov, Oded Regev

Research output: Contribution to journalArticle

Abstract

We show that the problems of approximating the shortest and closest vector in a lattice to within a factor of √n lie in NP intersect CoNP. The result (almost) subsumes the three mutually-incomparable previous results regarding these lattice problems: Banaszczyk [1993], Goldreich and Goldwasser [2000], and Aharonov and Regev [2003]. Our technique is based on a simple fact regarding succinct approximation of functions using their Fourier series over the lattice. This technique might be useful elsewhere - we demonstrate this by giving a simple and efficient algorithm for one other lattice problem (CVPP) improving on a previous result of Regev [2003]. An interesting fact is that our result emerged from a "dequantization" of our previous quantum result in Aharonov and Regev [2003]. This route to proving purely classical results might be beneficial elsewhere.

Original languageEnglish (US)
Pages (from-to)749-765
Number of pages17
JournalJournal of the ACM
Volume52
Issue number5
DOIs
StatePublished - Sep 2005

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Fourier series
Approximation of Functions
Intersect
Efficient Algorithms
Demonstrate

Keywords

  • Algorithms
  • Approximation
  • Fourier series
  • Lattices

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Computer Graphics and Computer-Aided Design
  • Hardware and Architecture
  • Information Systems
  • Software
  • Theoretical Computer Science

Cite this

Lattice problems in NP ∩ coNP. / Aharonov, Dorit; Regev, Oded.

In: Journal of the ACM, Vol. 52, No. 5, 09.2005, p. 749-765.

Research output: Contribution to journalArticle

Aharonov, Dorit ; Regev, Oded. / Lattice problems in NP ∩ coNP. In: Journal of the ACM. 2005 ; Vol. 52, No. 5. pp. 749-765.
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