VaLiPro: Linear Programming Validator for Cluster Computing Systems

TL;DR

This paper introduces VaLiPro, a scalable parallel algorithm for validating solutions to linear programming problems on cluster systems, using a hypersphere-based validation set to ensure solution correctness.

Contribution

The paper presents a novel parallel validation algorithm for linear programming solutions that is scalable and implemented with MPI on cluster systems.

Findings

Demonstrates scalability of VaLiPro on large cluster systems.

Validates solutions efficiently using hypersphere-based sampling.

Provides performance results from large-scale experiments.

Abstract

The article presents and evaluates a scalable algorithm for validating solutions of linear programming problems on cluster computing systems. The main idea of the method is to generate a regular set of points (validation set) on a small-radius hypersphere centered at the point of the solution under validation. The objective function is calculated for each point of the validation set that belongs to the feasible region. If all these values are less than or equal to the value of the objective function at the point under validation, then this point is the correct solution. The parallel implementation of the VaLiPro algorithm is performed in C++ through the parallel BSF-skeleton, which encapsulates all aspects related to the MPI-based parallelization of the program. We provide the results of large-scale computational experiments on a cluster computing system to study the scalability of the VaLiPro algorithm.