Parallel Redundancy Removal in lrslib with Application to Projections

TL;DR

This paper introduces a parallel algorithm in lrslib for efficiently removing redundant halfspaces in convex polyhedra, significantly improving the speed of Fourier-Motzkin elimination, especially on highly redundant data.

Contribution

The paper presents a novel parallel implementation for redundancy removal in convex polyhedra, applicable to both H- and V-representations, enhancing computational efficiency.

Findings

Parallel implementation speeds up redundancy removal

Comparison shows improved performance over Clarkson's algorithm on redundant inputs

Effective for Fourier-Motzkin elimination in convex polyhedra

Abstract

We describe a parallel implementation in lrslib for removing redundant halfspaces and finding a minimum representation for an H-representation of a convex polyhedron. By a standard transformation, the same code works for V-representations. We use this approach to speed up the redundancy removal step in Fourier-Motzkin elimination. Computational results are given including a comparison with Clarkson's algorithm, which is particularly fast on highly redundant inputs.