How to Find the Convex Hull of All Integer Points in a Polyhedron?

We propose a cut-based algorithm for finding all vertices and all facets of the convex hull of all integer points of a polyhedron defined by a system of linear inequalities. Our algorithm DDM Cuts is based on the Gomory cuts and the dynamic version of the double description method. We describe the c...

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Bibliographic Details
Main Authors Semenov, S. O, Zolotykh, N. Yu
Format Journal Article
LanguageEnglish
Published 25.10.2020
Subjects
Computer Science - Computational Geometry
Mathematics - Combinatorics
Mathematics - Optimization and Control
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DOI10.48550/arxiv.2010.13147

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Summary:We propose a cut-based algorithm for finding all vertices and all facets of the convex hull of all integer points of a polyhedron defined by a system of linear inequalities. Our algorithm DDM Cuts is based on the Gomory cuts and the dynamic version of the double description method. We describe the computer implementation of the algorithm and present the results of computational experiments comparing our algorithm with a naive one.
DOI:10.48550/arxiv.2010.13147