A decentralized algorithm for Network Flow Optimization in mesh networks

In order to evaluate total throughput against given traffics in an entire network, we formulate a minimum cost flow problem with quadratic edge functions, which we call Network Flow Optimization (NFO) problem in this paper. The problem with quadratic flow costs has been proved to be NP-complete. However, by dividing a network into a set of loops that represents a linear vector space, the problem can efficiently be solved. The theory that deals with the nature of loops of a graph is called tie-set graph theory where a tie-set represents a set of edges that constitute a loop. The theory of tie-sets has played a significant role in solving core problems in the domain of circuits and power systems as in applications of Kirchhoff's theory. Therefore, we propose a novel decentralized algorithm based on tie-set graph theory to optimize network flows in a mesh network. Global optimization can be achieved by iterative distributed computation where flows within a loop are locally optimized. Simulation results demonstrate the optimal allocation of network flows and show the superiority over the multi-path routing method.