Abstract
We describe the computation of polytope volumes by descent in the face lattice, its implementation in Normaliz, and the connection to reverse-lexicographic triangulations. The efficiency of the algorithm is demonstrated by several high dimensional polytopes of different characteristics. Finally, we present an application to voting theory where polytope volumes appear as probabilities of certain paradoxa.
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Released July 7, 2018.
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The second author was partially supported by a grant of Romanian Ministry of Research and Innovation, CNCS - UEFISCDI, Project Number PN-III-P4-ID-PCE-2016-0157, within PNCDI III.
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Bruns, W., Ichim, B. Polytope volume by descent in the face lattice and applications in social choice. Math. Prog. Comp. 13, 415–442 (2021). https://doi.org/10.1007/s12532-020-00198-z
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DOI: https://doi.org/10.1007/s12532-020-00198-z