Mathematical Programming Computation

, Volume 9, Issue 1, pp 1–38 | Cite as

Computing convex hulls and counting integer points with polymake

  • Benjamin Assarf
  • Ewgenij Gawrilow
  • Katrin Herr
  • Michael Joswig
  • Benjamin Lorenz
  • Andreas Paffenholz
  • Thomas Rehn
Full Length Paper

Abstract

The main purpose of this paper is to report on the state of the art of computing integer hulls and their facets as well as counting lattice points in convex polytopes. Using the polymake system we explore various algorithms and implementations. Our experience in this area is summarized in ten “rules of thumb”.

Keywords

Convex hull computation Lattice point enumeration Facets of integer hulls 

Mathematics Subject Classification

90-08 52-04 

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Copyright information

© Springer-Verlag Berlin Heidelberg and The Mathematical Programming Society 2016

Authors and Affiliations

  • Benjamin Assarf
    • 1
  • Ewgenij Gawrilow
    • 2
  • Katrin Herr
    • 3
  • Michael Joswig
    • 1
  • Benjamin Lorenz
    • 1
  • Andreas Paffenholz
    • 3
  • Thomas Rehn
    • 4
  1. 1.Institut für Mathematik, TU BerlinBerlinGermany
  2. 2.TomTom International BVAmsterdamThe Netherlands
  3. 3.Fachbereich Mathematik, TU DarmstadtDarmstadtGermany
  4. 4.initOS GmbH & Co. KGMagdeburgGermany

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