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Summary: Living with lrs
David Avis
School of Computer Science
McGill University
3480 University, Montreal, Quebec, Canada H3A 2A7
avis@cs.mcgill.ca
ABSTRACT
This paper describes the development of lrs, an implementation of
the reverse search method to the vertex enumeration/convex hull prob
lem for convex polyhedra. We describe an important and difficult class
of polyhedra, called configuration polytopes, that have application to
determining the ground states of alloy phase diagrams. Experience
gained while trying to solve these problems lead to a number of
improvements to the original implementation.
1. Introduction
A classic result is that a convex polyhedron P can be represented in two ways.
An Hrepresentation is given by an m × d matrix A = (a i, j ) and mvector b = (b i ):
P = {yÎR d | b + Ay ³ 0}. (1)
We assume throughout that P is full dimensional and has at least one vertex, which
implies that m ³ d . If A is minimal, that is no row can be deleted without changing P,
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