A geometric inequality and the complexity of computing volume
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- Elekes, G. Discrete Comput Geom (1986) 1: 289. doi:10.1007/BF02187701
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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.