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83views more  MOC 1998»
12 years 3 months ago
A sweep-plane algorithm for generating random tuples in simple polytopes
Abstract. A sweep-plane algorithm of Lawrence for convex polytope computation is adapted to generate random tuples on simple polytopes. In our method an affine hyperplane is swept ...
Josef Leydold, Wolfgang Hörmann
71views more  DCG 2002»
12 years 3 months ago
A Polytope Related to Empirical Distributions, Plane Trees, Parking Functions, and the Associahedron
The volume of the n-dimensional polytope nx := fy 2 Rn : yi 0 and y1 + + yi x1 + + xi for all 1 i ng for arbitrary x := x1; : : : ; xn with xi 0 for all i de nes a polyn...
Richard P. Stanley, Jim Pitman
75views more  DCG 2000»
12 years 3 months ago
Cutting Polytopes and Flag f-Vectors
We show how the flag f -vector of a polytope changes when cutting off any face, generalizing work of Lee for simple polytopes. The result is in terms of explicit linear operators o...
Richard Ehrenborg, D. Johnston, R. Rajagopalan, Ma...
122views more  JCT 2007»
12 years 3 months ago
h-Vectors of Gorenstein polytopes
We show that the Ehrhart h-vector of an integer Gorenstein polytope with a unimodular triangulation satisfies McMullen’s g-theorem; in particular it is unimodal. This result gen...
Winfried Bruns, Tim Römer
167views more  SIAMSC 2008»
12 years 3 months ago
Low-Dimensional Polytope Approximation and Its Applications to Nonnegative Matrix Factorization
In this study, nonnegative matrix factorization is recast as the problem of approximating a polytope on the probability simplex by another polytope with fewer facets. Working on th...
Moody T. Chu, Matthew M. Lin
119views more  SIAMDM 2008»
12 years 3 months ago
On the Graph Bisection Cut Polytope
Given a graph G = (V, E) with node weights v N {0}, v V , and some number F N{0}, the convex hull of the incidence vectors of all cuts (S), S V with (S) F and (V \ S) F is ...
Michael Armbruster, Christoph Helmberg, Marzena F&...
73views more  ORL 2008»
12 years 3 months ago
Polytopes and arrangements: Diameter and curvature
By analogy with the conjecture of Hirsch, we conjecture that the order of the largest total curvature of the central path associated to a polytope is the number of inequalities de...
Antoine Deza, Tamás Terlaky, Yuriy Zinchenk...
69views more  DCG 2007»
12 years 3 months ago
Realizations of the Associahedron and Cyclohedron
Abstract. We describe many different realizations with integer coordinates for the associahedron (i.e. the Stasheff polytope) and for the cyclohedron (i.e. the Bott-Taubes polyto...
Christophe Hohlweg, Carsten E. M. C. Lange
105views more  IPL 2008»
12 years 3 months ago
Hausdorff approximation of 3D convex polytopes
Let P be a convex polytope in Rd , d = 3 or 2, with n vertices. We present linear time algorithms for approximating P by simpler polytopes. For instance, one such algorithm select...
Mario A. Lopez, Shlomo Reisner
65views more  COMBINATORICA 2006»
12 years 3 months ago
A Linear Bound On The Diameter Of The Transportation Polytope
We prove that the combinatorial diameter of the skeleton of the polytope of feasible solutions of any m
Graham Brightwell, Jan van den Heuvel, Leen Stougi...