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Hardness of Approximating the Closest Vector Problem with Pre-Processing [Extended Abstract]
 

Summary: Hardness of Approximating the Closest Vector Problem with Pre-Processing
[Extended Abstract]
Mikhail Alekhnovich
Subhash A. Khot
Guy Kindler
Nisheeth K. Vishnoi
Abstract
We show that, unless NPDTIME(2poly log(n)
), the clos-
est vector problem with pre-processing, for p norm for
any p 1, is hard to approximate within a factor of
(log n)1/p-
for any > 0. This improves the previous best
factor of 31/p
- due to Regev [19]. Our results also im-
ply that under the same complexity assumption, the nearest
codeword problem with pre-processing is hard to approxi-
mate within a factor of (log n)1-
for any > 0.
1. Introduction

  

Source: Alekhnovich, Michael - Institute for Advanced Study, Princeton University
Khot, Subhash - Computer Science Department, Courant Institute of Mathematical Sciences, New York University

 

Collections: Computer Technologies and Information Sciences; Mathematics