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Exact Volume Computation for Polytopes: A Practical Study

  • Benno Büeler
  • Andreas Enge
  • Komei Fukuda
Part of the DMV Seminar book series (OWS, volume 29)

Abstract

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.

Keywords

Delaunay Triangulation Volume Computation Signed Decomposition Triangulation Method Recursive Scheme 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Basel AG 2000

Authors and Affiliations

  • Benno Büeler
    • 1
  • Andreas Enge
    • 2
  • Komei Fukuda
    • 3
  1. 1.Institute for Operations Research Swiss Federal Institute of TechnologyZurichSwitzerland
  2. 2.Lehrstuhl für Diskrete Mathematik Optimierung und Operations Research Institut für MathematikUniversität AugsburgDeutschland
  3. 3.Department of MathematicsSwiss Federal Institute of TechnologyLausanneSwitzerland

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