On the Convergence and Optimality of Reweighted Message Passing for Channel Assignment Problems

Many assignment problems, and channel allocation in OFDMA networks is a typical example, can be formulated as bipartite weighted b-matching (BWBM) problems. In this letter we provide a proof of the convergence and the optimality of the reweighted message passing (ReMP) algorithm when applied to solve BWBM problems in a distributed fashion. To this aim, we first show that the ReMP rule is a contraction mapping under a maximum mapping norm. Then, we show that the fixed convergence point is an optimal solution for the original assignment problem.