Inverse and Direct Maxflow Problem Study on the Free-Oriented ST-Planar Network Graph

Abstract

The issues of telecommunication network engineering are considered in the context of digital flows optimal scheduling. Introduced the concept of the free-oriented network graph as an enhanced math model of the modern software defined networking technologies with dynamic channel configuration. Normalized the framework of ST-planar network graph for the MaxFlow problem analysis. Formulated the inverse and direct tasks of network MaxFlow problem on the ST-planar free-oriented network graph concerning conventional Ford-Fulkerson approach and SDN virtual infrastructure design respectively. The inverse MaxFlow problem is formalized in terms of discrete optimization on Pontryagin maximum principle. The direct MaxFlow problem exhibited as graph templates generation combinatorial procedure by alternative criteria of flow paths shortest lengths or maximal diversity of paths. Specified the terms of "topology" and "metrics" for open twopole software defined network in the form of vertices' relation matrix, along with the tensors of ST-paths and ST-flows. The properties of planar graph have been studied as functions of vertices number, including the edges quantity, ST-flows tensor dimensions and paths' length distribution. The direct MaxFlow problem formalism can be used for automated testing the algorithms of classical inverse MaxFlow task, as well as generation the comprehensive teaching sequence for artificial intellect machine learning

Keywords

• telecommunication network
• maximal flow
• free oriented planar graph
• sdn