English

A simple proof of tail--polynomial bounds on the diameter of polyhedra

Optimization and Control 2016-04-18 v1 Metric Geometry

Abstract

Let Δ(d,n)\Delta(d,n) denote the maximum diameter of a dd-dimensional polyhedron with nn facets. In this paper, we propose a unified analysis of a recursive inequality about Δ(d,n)\Delta(d,n) established by Kalai and Kleitman in 1992. This yields much simpler proofs of a tail--polynomial and tail--almost--linear bounds on Δ(d,n)\Delta(d,n) which are recently discussed by Gallagher and Kim.

Keywords

Cite

@article{arxiv.1604.04338,
  title  = {A simple proof of tail--polynomial bounds on the diameter of polyhedra},
  author = {Shinji Mizuno and Noriyoshi Sukegawa},
  journal= {arXiv preprint arXiv:1604.04338},
  year   = {2016}
}