k-sets and random hulls


We re-examine the probabilistic analysis of Clarkson and Shor [5] involvingk-sets of point sets and related structures. By studying more carefully the equations that they derive, we are able to obtain refined analysis of these quantities, which lead to a collection of interesting relationships involvingk-sets, convex hulls of random samples, and generalizations of these constructs.

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Work on this paper has been supported by Office of Naval Research Grant N00014-89-J-3042 and N00014-90-J-1284, by National Science Foundation Grant CCR-89-01484, and by grants from the U.S.-Israeli Binational Science Foundation, the Fund for Basic Research administered by the Israeli Academy of Sciences, and the G.I.F., the German-Israeli Foundation for Scientific Research and Development.

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Sharir, M. k-sets and random hulls. Combinatorica 13, 483–495 (1993). https://doi.org/10.1007/BF01303520

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AMS subject classification code (1991)

  • 52 A 22
  • 52 A 37
  • 05 C 99