On the exactness of the cavity method for Weighted b-Matchings on Arbitrary Graphs and its Relation to Linear Programs
Statistical Mechanics
2009-11-13 v1 Disordered Systems and Neural Networks
Abstract
We consider the general problem of finding the minimum weight b-matching on arbitrary graphs. We prove that, whenever the linear programming 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.
Cite
@article{arxiv.0807.3159,
title = {On the exactness of the cavity method for Weighted b-Matchings on Arbitrary Graphs and its Relation to Linear Programs},
author = {M. Bayati and C. Borgs and J. Chayes and R. Zecchina},
journal= {arXiv preprint arXiv:0807.3159},
year = {2009}
}