Computational results of an O(n4) volume algorithm

L. Lovász, I. Deák

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

Recently an O(n4) volume algorithm has been presented for convex bodies by Lovász and Vempala, where n is the number of dimensions of the convex body. Essentially the algorithm is a series of Monte Carlo integrations. In this paper we describe a computer implementation of the volume algorithm, where we improved the computational aspects of the original algorithm by adding variance decreasing modifications: a stratified sampling strategy, double point integration and orthonormalised estimators. Formulas and methodology were developed so that the errors in each phase of the algorithm can be controlled. Some computational results for convex bodies in dimensions ranging from 2 to 10 are presented as well.

Original languageEnglish
Pages (from-to)152-161
Number of pages10
JournalEuropean Journal of Operational Research
Volume216
Issue number1
DOIs
Publication statusPublished - Jan 1 2012

Keywords

  • Applied probability
  • Computational results
  • Markov processes
  • Monte Carlo computation
  • Simulation
  • Volume algorithm

ASJC Scopus subject areas

  • Computer Science(all)
  • Modelling and Simulation
  • Management Science and Operations Research
  • Information Systems and Management

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