An improved Kalai-Kleitman bound for the diameter of a polyhedron

TL;DR

This paper improves the theoretical upper bound on the diameter of a polyhedron from Kalai and Kleitman's original bound to a tighter estimate, enhancing understanding of polyhedral geometry.

Contribution

The authors present a refined upper bound for polyhedron diameters, reducing the previous bound to a more precise estimate.

Findings

New bound: (n-d)^{log(d)} for polyhedron diameter

Improved theoretical understanding of polyhedral structure

Potential implications for optimization algorithms

Abstract

Kalai and Kleitman established the bound $n^{\log(d) + 2}$ for the diameter of a $d$-dimensional polyhedron with $n$ facets. Here we improve the bound slightly to $(n-d)^{\log(d)}$.