Type of Publication: Journal Articles
Authors: Khaled.Elbassioni, Zvi Lotker, Raimund.Seidel
Title: Upper bound on the number of vertices of polyhedra with 0, 1-constraint matrices
Name of the Journal: Information Processing Letters
Year: 2006
Volume: 100
Issue: 2
Pages: 69 - 71
Abstract: In this note we give upper bounds for the number of vertices of the polyhedron P (A, b) = {x is a member of the set of Rd : A x [less-than or equal to] b} when the m × d constraint matrix A is subjected to certain restriction. For instance, if A is a 0/1-matrix, then there can be at most d! vertices and this bound is tight, or if the entries of A are non-negative integers so that each row sums to at most C, then there can be at most Cd vertices. These bounds are consequences of a more general theorem that the number of vertices of P (A, b) is at most d ! s W / D, where W is the volume of the convex hull of the zero vector and the row vectors of A, and D is the smallest absolute value of any non-zero d × d subdeterminant of A. © 2006 Elsevier B.V. All rights reserved.
Keywords: Constraint theory;Computational geometry;Integer programming;Number theory;Linear programming; ,
Last Updated: 9/4/2007 12:00:00 AM
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