A task-based approach to parallel parametric linear programming solving, and application to polyhedral computations

TL;DR

This paper introduces a task-based parallel approach to parametric linear programming, significantly improving efficiency for large problems and including a redundancy elimination algorithm, with thorough performance analysis.

Contribution

It presents a novel task-based parallel scheme for parametric linear programming with redundancy elimination, enhancing scalability and performance in polyhedral computations.

Findings

Achieved quasi-linear speedup on large problems

Developed a parallel redundancy elimination algorithm

Provided comprehensive performance analysis

Abstract

Parametric linear programming is a central operation for polyhedral computations, as well as in certain control applications.Here we propose a task-based scheme for parallelizing it, with quasi-linear speedup over large problems.This type of parallel applications is challenging, because several tasks mightbe computing the same region. In this paper, we are presenting thealgorithm itself with a parallel redundancy elimination algorithm, andconducting a thorough performance analysis.