 
Summary: lrs: A Revised Implementation of the Reverse Search Vertex Enumeration
Algorithm
David Avis
School of Computer Science
McGill University
3480 University, Montr’eal, Qu’ebec, Canada H3A 2A7
avis@cs.mcgill.ca
January 26, 1999
ABSTRACT
This paper describes an improved implementation of the reverse search ver
tex enumeration/convex hull algorithm for ddimensional convex polyhedra. The
implementation uses a lexicographic ratio test to resolve degeneracy, works on
bounded or unbounded polyhedra and uses exact arithmetic with all integer pivot
ing. It can also be used to compute the volume of the convex hull of a set of
points. For a polyhedron with m inequalities in d variables and known extreme
point, it finds all bases in time O(md 2 ) per basis. This implementation can han
dle problems of quite large size, especially for simple polyhedra (where each
basis corresponds to a vertex and the complexity reduces to O(md) per vertex).
Computational experience is included in the paper, including a comparison with
an earlier implementation.
