Simulated annealing in convex bodies and an O*(n4) volume algorithm

László Lovász, Santosh Vempala

Research output: Contribution to journalArticle

96 Citations (Scopus)


We present a new algorithm for computing the volume of a convex body in Rn. The main ingredients of the algorithm are (i) a "morphing" technique that can be viewed as a variant of simulated annealing and (ii) a new rounding algorithm to put a convex body in near-isotropic position. The complexity is O*(n4), improving on the previous best algorithm by a factor of n.

Original languageEnglish
Pages (from-to)392-417
Number of pages26
JournalJournal of Computer and System Sciences
Issue number2
Publication statusPublished - Mar 1 2006


  • Convex bodies
  • Logconcave functions
  • Random walks
  • Simulated annealing
  • Volume computation

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Networks and Communications
  • Computational Theory and Mathematics
  • Applied Mathematics

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