An improved Kalai-Kleitman bound for the diameter of a polyhedron
  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 $(n-d)^{\log(d)}$. 
Michael J. Todd
math.OC math.MG