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1 results

  • On the convex hull of random points in a polytope

  • Rex A. Dwyer
  • Journal:
    Journal of Applied Probability / Volume 25 / Issue 4 / December 1988
    Published online by Cambridge University Press:
    14 July 2016, pp. 688-699
    Print publication:
    December 1988

  • The convex hull of n points drawn independently from a uniform distribution on the interior of a d-dimensional polytope is investigated. It is shown that the expected number of vertices is O(logd–1n) for any polytope, the expected number of vertices is Ω(logd–1n) for any simple polytope, and the expected number of facets is O(logd–1n) for any simple polytope. An algorithm is presented for constructing the convex hull of such sets of points in linear average time.