TL;DR
This paper reviews how Normaliz computes polytope volumes, highlighting the recent addition of the Lawrence algorithm which enabled volume calculations for high-dimensional social choice polytopes.
Contribution
It introduces the integration of the Lawrence algorithm into Normaliz, allowing for efficient volume computation in very high dimensions.
Findings
Successfully computed volumes of social choice polytopes in 119 dimensions
Implemented a sophisticated version of the Lawrence algorithm
Demonstrated the capability of Normaliz for high-dimensional volume calculations
Abstract
We survey the computation of polytope volumes by the algorithms of Normaliz to which the Lawrence algorithm has recently been added. It has enabled us to master volume computations for polytopes from social choice in dimension . This challenge required a sophisticated implementation of the Lawrence algorithm.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Game Theory and Voting Systems · Commutative Algebra and Its Applications