On the exactness of the cavity method for weighted b-matchings on arbitrary graphs and its relation to linear programs
Mohsen Bayati, Christian Borgs, Jennifer Chayes, Riccardo Zecchina · Journal of Statistical Mechanics Theory and Experiment · 2008
We consider the general problem of finding the minimum weight b-matching on arbitrary graphs. We prove that, whenever the linear programing relaxation of the problem has no fractional solutions, then the cavity or belief propagation equations converge to the correct solution both for synchronous and asynchronous updating.