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Author Aharonov, Dorit ♦ Regev, Oded
Source ACM Digital Library
Content type Text
Publisher Association for Computing Machinery (ACM)
File Format PDF
Copyright Year ©2005
Language English
Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Subject Keyword Algorithms ♦ Fourier series ♦ Approximation ♦ Lattices
Abstract We show that the problems of approximating the shortest and closest vector in a lattice to within a factor of &nradic; 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.
ISSN 00045411
Age Range 18 to 22 years ♦ above 22 year
Educational Use Research
Education Level UG and PG
Learning Resource Type Article
Publisher Date 2005-09-01
Publisher Place New York
e-ISSN 1557735X
Journal Journal of the ACM (JACM)
Volume Number 52
Issue Number 5
Page Count 17
Starting Page 749
Ending Page 765

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Source: ACM Digital Library