Message Passing for Max-weight Independent Set

We investigate the use of message-passing algorithms for the problem of finding the max-weight independent set (MWIS) in a graph. First, we study the perfor- mance of loopy max-product belief propagation. We show that, if it converges, the quality of the estimate is closely related to the tightness of an LP relaxation of the MWIS problem. We use this relationship to obtain sufficient conditions for correctness of the estimate. We then develop a modification of max-product – one that converges to an optimal solution of the dual of the MWIS problem.