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The Volume of a Crosspolytope Truncated by a Halfspace

  • Ei AndoEmail author
  • Shoichi Tsuchiya
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11436)

Abstract

In this paper, we consider the computation of the volume of an n-dimensional crosspolytope truncated by a halfspace. Since a crosspolytope has exponentially many facets, we cannot efficiently compute the volume by dividing the truncated crosspolytope into simplices. We show an \(O(n^6)\) time algorithm for the computation of the volume. This makes a contrast to the 0−1 knapsack polytope, whose volume is \(\#P\)-hard to compute. The paper is interested in the computation of the volume of the truncated crosspolytope because we conjecture the following question may have an affirmative answer: Does the existence of a polynomial time algorithm for the computation of the volume of a polytope K imply the same for K’s geometric dual? We give one example where the answer is yes.

Keywords

Polynomial time algorithm Volume computation Geometric duality 

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Senshu UniversityKawasakiJapan

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