Message-passing for Maximum Weight Independent Set

Abstract--In this paper, we investigate the use of messagepassing algorithms for the problem of finding the max-weight independent set (MWIS) in a graph. First, we study the performance of the classical loopy max-product belief propagation. We show that each fixed-point estimate of max product can be mapped in a natural way to an extreme point of the linear programming (LP) polytope associated with the MWIS problem. However, this extreme point may not be the one that maximizes the value of node weights; the particular extreme point at final convergence depends on the initialization of max product. We then show that if max product is started from the natural initialization of uninformative messages, it always solves the correct LP, if it converges. This result is obtained via a direct analysis of the iterative algorithm, and cannot be obtained by looking only at fixed points. The tightness of the LP relaxation is thus necessary for max-product optimality, but it is not sufficient. Motiv...

• Type: Journal
• Year: 2008
• Where: CORR
• Authors: Sujay Sanghavi, Devavrat Shah, Alan S. Willsky
• Keywords: Algorithms, CORR 2008, Education, Extreme Point, Max Product