Convex Hull Calculations: a Matlab Implementation and Correctness Proofs for the lrs-Algorithm

TL;DR

This paper offers a complete Matlab implementation and informal correctness proofs for the lexicographic reverse search algorithm used in convex hull calculations, validated on various polytopes including high-dimensional cases.

Contribution

It provides the first full Matlab code and correctness proofs for the lrs-algorithm, with testing on diverse and complex convex polytopes.

Findings

Successful implementation tested on small and large polytopes

Validated correctness through informal proofs

Demonstrated applicability to high-dimensional polytopes

Abstract

This paper provides full \Matlab-code and informal correctness proofs for the lexicographic reverse search algorithm for convex hull calculations. The implementation was tested on a 1993 486-PC for various small and some larger, partially highly degenerate combinatorial polytopes, one of which (a certain 13-dimensional 24 vertex polyhedron) occurs naturally in the study of a well known problem posed by Professor Graciano de Oliveira: see end of section 1.