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 setK⊂R d, the ratio\(\overline {vol}\)(K)/vol(K) is at least (cd/logd) d for some convex setK⊂R d.
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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.
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Bárány, I., Füredi, Z. Computing the volume is difficult. Discrete Comput Geom 2, 319–326 (1987). https://doi.org/10.1007/BF02187886
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DOI: https://doi.org/10.1007/BF02187886