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Poster
Linear programming analysis of loopy belief propagation for weighted matching
Sujay Sanghavi · Dmitry Malioutov · Alan S Willsky

Mon Dec 03 10:30 AM -- 10:40 AM (PST) @ None #None

Loopy belief propagation has been employed in a wide variety of applications with great empirical success, but it comes with few theoretical guarantees. In this paper we investigate the use of the max-product form of belief propagation for weighted matching problems on general graphs. We show that max-product converges to the correct answer if the linear programming (LP) relaxation of the weighted matching problem is tight and does not converge if the LP relaxation is loose. This provides an exact characterization of max-product performance and reveals connections to the widely used optimization technique of LP relaxation. In addition, we demonstrate that max-product is effective in solving practical weighted matching problems in a distributed fashion by applying it to the problem of self-organization in sensor networks.

Author Information

Sujay Sanghavi (UT-Austin)
Dmitry Malioutov (DE Shaw Group)
Alan S Willsky (Massachusetts Institute of Technology)

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