Séminaire d'équipe(s) Graphs, ALgorithms and Combinatorics

Euler Polytopes and Convex Matroid Optimization
George Manoussakis

25 March 2016, 14:30 - 25 March 2016, 16:10 Salle/Bat : 435/PCRI-N
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Activités de recherche : Combinatorics

Résumé :

We introduce a novel family of polytopes strengthening bounds relevant to combinatorial optimization and convex matroid optimization. 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. The introduced Euler polytopes 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.