, Volume 1, Issue 1, pp 289-292

A geometric inequality and the complexity of computing volume

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Abstract

The volume of the convex hull of anym points of ann-dimensional ball with volumeV is at mostV·m/2 n . 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.

Dedicated to my teacher Kõváry Károly