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Automating the solutions of multiple network information theory problems,stretching from fundamental concerns such as determining all informationinequalities and the limitations of linear codes, to applied ones such asdesigning coded networks, distributed storage systems, and caching systems, canbe posed as polyhedral projections. These problems are demonstrated to exhibitmultiple types of polyhedral symmetries. It is shown how these symmetries canbe exploited to reduce the complexity of solving these problems throughpolyhedral projection.

Explicit Polyhedral Bounds on Network Coding Rate Regions via Entropy Function Region: Algorithms, Symmetry, and Computation