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lrs: A Revised Implementation of the Reverse Search Vertex Enumeration School of Computer Science
 

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.

  

Source: Avis, David - School of Computer Science, McGill University

 

Collections: Computer Technologies and Information Sciences