Improvement of Kalai-Kleitman bound for the diameter of a polyhedron
نویسندگان
چکیده
Recently, Todd got 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 fits better for a high-dimensional polyhedron with a large number of facets. Keyword: Polytopes, Diameter, Kalai and Kleitman bound.
منابع مشابه
An Improved Kalai-Kleitman Bound for the Diameter of a Polyhedron
Kalai and Kleitman [6] established the bound nlog(d)+2 for the diameter of a d-dimensional polyhedron with n facets. Here we improve the bound slightly to (n− d)log(d).
متن کاملA Quasi-polynomial Bound for the Diameter of Graphs of Polyhedra
The diameter of the graph of a ¿-dimensional polyhedron with n facets is at most ni0^d+2 Let P be a convex polyhedron. The graph of P denoted by G(P) is an abstract graph whose vertices are the extreme points of P and two vertices u and v are adjacent if the interval [v, u] is an extreme edge (= 1-dimensional face) of P. The diameter of the graph of P is denoted by ô(P). Let A(d, n) be the maxi...
متن کاملPushing the boundaries of polytopal realizability
Let ∆(d, n) be the maximum possible diameter of the vertex-edge graph over all d-dimensional polytopes defined by n inequalities. The Hirsch bound holds for particular n and d if ∆(d, n) ≤ n − d. Francisco Santos recently resolved a question open for more than five decades by showing that ∆(d, 2d) = d + 1 for d = 43; the dimension was then lowered to 20 by Matchske, Santos and Weibel. This prog...
متن کاملUpper bound and numerical analysis of cyclic expansion extrusion (CEE) process
Deformation of the material during cyclic expansion extrusion (CEE) is investigated using upper-bound theorem. The analytical approximation of forming loads agrees very well with the FEM results for different amounts of chamber diameter, friction factor and also for lower die angles. However, the difference between analytical and numerical solution increases at higher die angles which are expla...
متن کاملConnected Layer Families and Diameter of Polyhedra Semester Project
Given a polyhedron, its diameter is defined as the maximum distance between two of its vertices, where the distance between two vertices u and v is the number of edges contained in the shortest u− v path in the skeleton of the polyhedron. Bounding the diameter of a polyhedron with respect to its dimension d and the number n of its facets is one of the most important open problems in convex geom...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2014