Abstract
We show that there is no algorithm which, provided a polynomial number of random points uniformly distributed over a convex body in ℝn, can approximate the volume of the body up to a constant factor with high probability.
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Communicated by L. Lovasz.
The author is partially supported by the Israel Science Foundation and by a Farajun Foundation Fellowship.
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Eldan, R. A Polynomial Number of Random Points Does Not Determine the Volume of a Convex Body. Discrete Comput Geom 46, 29–47 (2011). https://doi.org/10.1007/s00454-011-9328-x
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DOI: https://doi.org/10.1007/s00454-011-9328-x