Polytopes — Combinatorics and Computation

Volume 29 of the series DMV Seminar pp 131-154

Exact Volume Computation for Polytopes: A Practical Study

  • Benno BüelerAffiliated withInstitute for Operations Research Swiss Federal Institute of Technology
  • , Andreas EngeAffiliated withLehrstuhl für Diskrete Mathematik Optimierung und Operations Research Institut für Mathematik, Universität Augsburg
  • , Komei FukudaAffiliated withDepartment of Mathematics, Swiss Federal Institute of Technology

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We study several known volume computation algorithms for convex d-polytopes by classifying them into two classes, triangulation methods and signed-decomposition methods. By incorporating the detection of simplicial faces and a storing/reusing scheme for face volumes we propose practical and theoretical improvements for two of the algorithms. Finally we present a hybrid method combining advantages from the two algorithmic classes. The behaviour of the algorithms is theoretically analysed for hypercubes and practically tested on a wide range of polytopes, where the new hybrid method proves to be superior.