Tail diameter upper bounds for polytopes and polyhedra
Combinatorics
2016-03-15 v1 Optimization and Control
Abstract
In 1992, Kalai and Kleitman proved a quasipolynomial upper bound on the diameters of convex polyhedra. Todd and Sukegawa-Kitahara proved tail-quasipolynomial bounds on the diameters of polyhedra. These tail bounds apply when the number of facets is greater than a certain function of the dimension. We prove tail-quasipolynomial bounds on the diameters of polytopes and normal simplicial complexes. We also prove tail-polynomial upper bounds on the diameters of polyhedra.
Keywords
Cite
@article{arxiv.1603.04052,
title = {Tail diameter upper bounds for polytopes and polyhedra},
author = {J. Mackenzie Gallagher and Edward D. Kim},
journal= {arXiv preprint arXiv:1603.04052},
year = {2016}
}
Comments
15 pages