Recently, Todd obtained a new bound on the diameter of a polyhedron using an analysis due to Kalai and Kleitman in 1992. In this short note, we prove that the bound by Todd can further be improved. Although our bound is not valid when the dimension is 1 or 2, it is tight when the dimension is 3, and fits better for a high-dimensional polyhedron with a large number of facets.
All Science Journal Classification (ASJC) codes
- Management Science and Operations Research
- Industrial and Manufacturing Engineering
- Applied Mathematics