English

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

R2 v1 2026-06-22T13:09:47.224Z