A note on the diameter of convex polytope

TL;DR

This paper extends an upper bound on the diameter of convex polytopes from integer to real matrices and demonstrates that the new bound can be tighter through an example.

Contribution

It generalizes a recent diameter bound for convex polytopes from integer to real matrices and shows potential improvements over previous bounds.

Findings

Extended the diameter bound to real matrices

Provided an example where the new bound is tighter

Connected the result to existing bounds in the literature

Abstract

This short note extends a recent result (Bonifas et al, On sub-determinants and the diameter of polyhedra, Discrete Computational Geometry, 52, 2014) of an upper bound of the diameter of a convex polytope defined by an integer matrix to a similar upper bound of the diameter of a convex polytope defined by a real matrix. It also shows, by an example, that the new bound may be better than the ones of Bonifas et al.