A node-weight equalization problem with circuit-based computations

Circuit-based computation has contributed to designing efficient, highly-scalable, and reliable distributed control systems. As in load-balancing problems, uniform assignment of node weights is an important function in this domain. Intuitively, iterative computation for balancing workloads based on graph circuit structure seems to always converge to an optimal solution. However, no previous literature provides a proof that circuit-based computation for load balancing guarantees to average all the weights in a given mesh network topology. We therefore analyze the property of circuit-based computations for a node-weight equalization problem (NWEP) whose objective is making the average deviation of graph weights converge on zero. This paper provides a graph theory-based verification of circuit-based computations for NWEP, and a way to shorten the computation time required to solve the NWEP.