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.

中文翻译：

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VaLiPro：集群计算系统的线性规划验证器

本文介绍并评估了一种可扩展的算法，用于验证集群计算系统上线性规划问题的解决方案。该方法的主要思想是在以验证解的点为中心的小半径超球面上生成规则的点集（验证集）。为验证集的每个点计算属于可行域的目标函数。如果所有这些值都小于或等于验证点的目标函数值，则该点是正确的解决方案。VaLiPro 算法的并行实现是通过并行 BSF 框架在 C++ 中执行的，它封装了与基于 MPI 的程序并行化相关的所有方面。