On validation of solutions to linear programming problems on cluster computing systems

The paper presents and evaluates a scalable algorithm for validating solutions to linear programming (LP) 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 solution point submitted to validation. The objective function is computed at each point of the validation that belongs to the feasible region. If all the values are less than or equal to the value of the objective function at the point that is to be validated, then this point is the correct solution. The parallel implementation of the VaLiPro algorithm is written 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.