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Small Primitive Zonotopes

  • Antoine Deza
  • George Manoussakis
  • Shmuel Onn
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 234)

Abstract

We study a family of lattice polytopes, called primitive zonotopes, describe instances with small parameters, and discuss connections to the largest diameter of lattice polytopes and to the computational complexity of multicriteria matroid optimization. Complexity results and open questions are also presented.

Keywords

Lattice polytopes Primitive integer vectors Matroid optimization Diameter 

Notes

Acknowledgements

The authors thank the anonymous referees, Johanne Cohen, Nathann Cohen, Komei Fukuda, and Aladin Virmaux for valuable comments and for informing us of reference [31], Emo Welzl and Günter Ziegler for helping us access Thorsten Thiele’s Diplomarbeit, Dmitrii Pasechnik for pointing out reference [29], and Vincent Pilaud for pointing out that \(Z_1(d,2)\) is the permutahedron of type \(B_d\). This work was partially supported by the Natural Sciences and Engineering Research Council of Canada Discovery Grant program (RGPIN-2015-06163), by the Digiteo Chair C&O program at Université de Paris Sud, and by the Dresner Chair at the Technion.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Advanced Optimization Laboratory, Faculty of EngineeringMcMaster UniversityHamiltonCanada
  2. 2.Laboratoire de Recherche en InformatiqueCNRS – Université de Paris SudOrsayFrance
  3. 3.Operations Research, Davidson faculty of IE & MTechnion - Israel Institute of TechnologyHaifaIsrael

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