Belief Propagation for Min-Cost Network Flow: Convergence & Correctness
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Shah_Belief propagation.pdf
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Author(s)
Gamarnik, David
Shah, Devavrat
Wei, Yehua
Date Issued
January 2010
Journal
Proceedings of the Twenty-First Annual ACM-SIAM Symposium on Discrete Algorithms (SODA '10)
Publisher
Society for Industrial and Applied Mathematics
Citation
David Gamarnik, Devavrat Shah, and Yehua Wei. 2010. Belief propagation for min-cost network flow: convergence \& correctness. In Proceedings of the Twenty-First Annual ACM-SIAM Symposium on Discrete Algorithms (SODA '10). Society for Industrial and Applied Mathematics, Philadelphia, PA, USA, 279-292. Copyright © 2010, Society for Industrial and Applied Mathematics
Version
Final published version
Abstract
We formulate a Belief Propagation (BP) algorithm in the context of the capacitated minimum-cost network flow problem (MCF). Unlike most of the instances of BP studied in the past, the messages of BP in the context of this problem are piecewise-linear functions. We prove that BP converges to the optimal solution in pseudo-polynomial time, provided that the optimal solution is unique and the problem input is integral. Moreover, we present a simple modification of the BP algorithm which gives a fully polynomial-time randomized approximation scheme (FPRAS) for MCF. This is the first instance where BP is proved to have fully-polynomial running time.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Massachusetts Institute of Technology. Operations Research Center
Sloan School of Management
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
http://dl.acm.org/citation.cfm?id=1873625
