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Euler Polytopes and Convex Matroid Optimization

Antoine Deza (deza***at***mcmaster.ca)
George Manoussakis (george***at***lri.fr)
Shmuel Onn (onn***at***ie.technion.ac.il)

Abstract: Del Pia and Michini recently improved the upper bound of kd due to Kleinschmidt and Onn for the largest possible diameter of the convex hull of a set of points in dimension d whose coordinates are integers between 0 and k. We introduce Euler polytopes which include a family of lattice polytopes with diameter (k+1)d/2, and thus reduce the gap between the lower and upper bounds. In addition, we highlight connections between Euler polytopes and a parameter studied in convex matroid optimization and strengthen the lower and upper bounds for this parameter.

Keywords: Euler polytopes, convex matroid optimization, zonotopes, diameter of lattice polytopes

Category 1: Combinatorial Optimization

Category 2: Combinatorial Optimization (Polyhedra )

Citation: AdvOL report 2015/05 McMaster University, Hamilton, Ontario, Canada

Download: [PDF]

Entry Submitted: 12/25/2015
Entry Accepted: 12/25/2015
Entry Last Modified: 12/25/2015

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