Efficient computation of the Hausdorff distance between polytopes by exterior random covering. (English summary) Comput. Optim. Appl. 30 (2005), no. 2, 161–194. The paper introduces ERC (efficient random covering), a simple and efficient randomized algorithm for finding the maximum distance between a point set and an arbitrary compact set in R d. This algorithm is used to obtain an efficient algorithm for computing the Hausdorff distance between two convex polytopes. Degenerate cases and the influence of rounding errors in floatingpoint are also discussed. The authors show that finding the directed Hausdorff distance between a point set and a union of convex polytopes is well conditioned. The authors give an exact expression for the expected running time of ERC. The paper also includes experimental evidence on the efficiency of the algorithms discussed
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