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Computing convex hulls and counting integer points with polymake. (English) Zbl 1370.90009
This paper presents the state of the art of computing integer hulls and their facets as well as counting lattice points in convex polytopes, by making use of the polymake system that allows exploring and testing different algorithmical methods and implementations from the literature. These observations are summarized in ten “rules of thumb”. After the introduction, the reader is familiarized with the polymake system (which provides a common interface for employing and comparing various algorithms and is available from polymake.org). Then, in the third section, various convex hull algorithms and their implementations are implemented and investigated in the polymake system, while Section 4 is devoted to enumerating lattice points in polytopes. Two appendices on the experimental setup and on the computational details close the paper.

MSC:
90-08 Computational methods for problems pertaining to operations research and mathematical programming
52-04 Software, source code, etc. for problems pertaining to convex and discrete geometry
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