Computing the volume is difficult

Imre Bárány, Z. Füredi

Research output: Contribution to journalArticle

79 Citations (Scopus)

Abstract

For every polynomial time algorithm which gives an upper bound {Mathematical expression}(K) and a lower bound vol(K) for the volume of a convex set K⊂Rd, the ratio {Mathematical expression}(K)/vol(K) is at least (cd/log d)d for some convex set K⊂Rd.

Original languageEnglish
Pages (from-to)319-326
Number of pages8
JournalDiscrete & Computational Geometry
Volume2
Issue number1
DOIs
Publication statusPublished - Dec 1987

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Convex Sets
Polynomials
Computing
Polynomial-time Algorithm
Lower bound
Upper bound

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics

Cite this

Computing the volume is difficult. / Bárány, Imre; Füredi, Z.

In: Discrete & Computational Geometry, Vol. 2, No. 1, 12.1987, p. 319-326.

Research output: Contribution to journalArticle

Bárány, Imre ; Füredi, Z. / Computing the volume is difficult. In: Discrete & Computational Geometry. 1987 ; Vol. 2, No. 1. pp. 319-326.
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