Hardness of approximating the Shortest Vector Problem in high ℓp norms

Research output: Contribution to journalArticle

Abstract

We present a new hardness of approximation result for the Shortest Vector Problem in ℓp norm (denoted by SVPp). Assuming NP ⊈ ZPP, we show that for every ε>0, there is a constant p(ε) such that for all integers p≥p(ε), the problem SVPp has no polynomial time approximation algorithm with approximation ratio p1-ε.

Original languageEnglish (US)
Pages (from-to)206-219
Number of pages14
JournalJournal of Computer and System Sciences
Volume72
Issue number2
DOIs
StatePublished - Mar 2006

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Approximation algorithms
Hardness
Polynomials
Hardness of Approximation
Norm
Polynomial-time Algorithm
Approximation Algorithms
Integer
Approximation

Keywords

  • Approximation algorithms
  • Computational complexity
  • Hardness of approximation
  • Lattices
  • Shortest vector problem

ASJC Scopus subject areas

  • Computational Theory and Mathematics

Cite this

Hardness of approximating the Shortest Vector Problem in high ℓp norms. / Khot, Subhash.

In: Journal of Computer and System Sciences, Vol. 72, No. 2, 03.2006, p. 206-219.

Research output: Contribution to journalArticle

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