The largest small Polytopes
نویسنده
چکیده
The aim of this paper is the determination of the largest n-dimensional polytope with n+3 vertices of unit diameter. This is a special case of a more general problem Graham proposes in [2].
منابع مشابه
Phase Transition in Random Integer Programs
We study integer programming instances over polytopes P (A, b) = {x : Ax ≤ b} where the constraint matrices A are random – the rows of the constraint matrices are chosen i.i.d. from a spherically symmetric distribution. We address the radius of the largest inscribed ball that guarantees integer feasibility of such random polytopes with high probability. We show that for m = 2 √ , there exist co...
متن کاملLinear Programming, the Simplex Algorithm and Simple Polytopes
In the first part of the paper we survey some far reaching applications of the basis facts of linear programming to the combinatorial theory of simple polytopes. In the second part we discuss some recent developments concurring the simplex algorithm. We describe sub-exponential randomized pivot roles and upper bounds on the diameter of graphs of polytopes.
متن کاملEuler Polytopes and Convex Matroid Optimization
Del Pia and Michini recently improved the upper bound of kd due to Kleinschmidt and Onn for the largest possible diameter of the convex hull of a set of points in dimension d whose coordinates are integers between 0 and k. We introduce Euler polytopes which include a family of lattice polytopes with diameter (k + 1)d/2, and thus reduce the gap between the lower and upper bounds. In addition, we...
متن کاملMinkowski Length of 3D Lattice Polytopes
We study the Minkowski length L(P ) of a lattice polytope P , which is defined to be the largest number of non-trivial primitive segments whose Minkowski sum lies in P . The Minkowski length represents the largest possible number of factors in a factorization of polynomials with exponent vectors in P , and shows up in lower bounds for the minimum distance of toric codes. In this paper we give a...
متن کاملInteger Feasibility of Random Polytopes
We study integer programming instances over polytopes P (A, b) = {x : Ax ≤ b} where the constraint matrix A is random, i.e., its entries are i.i.d. Gaussian or, more generally, its rows are i.i.d. from a spherically symmetric distribution. The radius of the largest inscribed ball is closely related to the existence of integer points in the polytope. We show that for m = 2 √ , there exist consta...
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 2008