, Volume 2, Issue 1, pp 319-326

Computing the volume is difficult

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Abstract

For every polynomial time algorithm which gives an upper bound \(\overline {vol}\) (K) and a lower boundvol(K) for the volume of a convex setKR d , the ratio \(\overline {vol}\) (K)/vol(K) is at least (cd/logd) d for some convex setKR d .

This paper was partly written when both authors were on leave from the Mathematical Institute of the Hungarian Academy of Sciences, 1364 Budapest, P.O. Box 127, Hungary.