On Modelling of Computer Cluster Optimization Problem With Applications

A decision-making problem of reasonability of upgrading a computer network by adding new connections between nodes is investigated. As a basic topology, a well-known hypercube topology is chosen. The expediency of its upgrading by links corresponding to edge sets of hypercube cuts by parallel hyperplanes is investigated. It is done by graph-theoretic approaches and tolls of polyhedral combinatorics. In the course of solving the problem, key structural characteristics of a new graph Q'n, which is a complemented by edges the hypercube graph, are studied. The offered methodology can be applied to other problems of optimization of computer networks, aiming to improve their reliability and efficiency.