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Computational results on an algorithm for finding all vertices of a polytope

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Abstract

This paper provides answers to several questions raised by V. Klee regarding the efficacy of Mattheiss' algorithm for finding all vertices of convex polytopes. Several results relating to the expected properties of polytopes are given which indicate thatn-polytopes defined by “large” numbers of constraints are difficult to obtain by random processes, the expected value of the number of vertices of polytope is considerably less than Klee's least upper bound the expected performance of Mattheiss' algorithm is far better than Klee's upper bound would suggest.

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Authors and Affiliations

  1. Department of Management Science and Statistics, The University of Alabama, Tuscaloosa, AL, USA

    T. H. Mattheiss

  2. Mitre Corporation, Bedford, MA, USA

    Brian K. Schmidt

Authors
  1. T. H. Mattheiss
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  2. Brian K. Schmidt
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Mattheiss, T.H., Schmidt, B.K. Computational results on an algorithm for finding all vertices of a polytope. Mathematical Programming 18, 308–329 (1980). https://doi.org/10.1007/BF01588326

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  • DOI: https://doi.org/10.1007/BF01588326

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