On the exact maximum complexity of Minkowski sums of polytopes

Efi Fogel*, Dan Halperin, Christophe Weibel

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We present a tight bound On the exact maximum complexity of Minkowski sums of polytopes in ℝ3. In particular, we prove that the maximum number of facets of the Minkowski sum of k polytopes with m1,m2,...,mk facets, respectively, is bounded from above by. Given k positive integers m1,m2,...,mk, we describe how to construct k polytopes with corresponding number of facets, such that the number of facets of their Minkowski sum is exactly. When k=2, for example, the expression above reduces to 4m1m2-9m1-9m2+26.

Original languageEnglish
Pages (from-to)654-669
Number of pages16
JournalDiscrete and Computational Geometry
Volume42
Issue number4
DOIs
StatePublished - Oct 2009

Keywords

  • Complexity
  • Gaussian maps
  • Minkowski sum
  • Polyhedra

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