Discrete & Computational Geometry

, Volume 1, Issue 4, pp 289–292

A geometric inequality and the complexity of computing volume


  • G. Elekes
    • Mathematical InstituteEötvös Loránd University

DOI: 10.1007/BF02187701

Cite this article as:
Elekes, G. Discrete Comput Geom (1986) 1: 289. doi:10.1007/BF02187701


The volume of the convex hull of anym points of ann-dimensional ball with volumeV is at mostV·m/2n. This implies that no polynomial time algorithm can compute the volume of a convex set (given by an oracle) with less than exponential relative error. A lower bound on the complexity of computing width can also be deduced.

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© Springer-Verlag New York Inc. 1986