Matching is as easy as matrix inversion
Combinatorica
Causality: models, reasoning, and inference
Causality: models, reasoning, and inference
Walk-Sums and Belief Propagation in Gaussian Graphical Models
The Journal of Machine Learning Research
The generalized distributive law
IEEE Transactions on Information Theory
The capacity of low-density parity-check codes under message-passing decoding
IEEE Transactions on Information Theory
On the optimality of solutions of the max-product belief-propagation algorithm in arbitrary graphs
IEEE Transactions on Information Theory
Max-Product for Maximum Weight Matching: Convergence, Correctness, and LP Duality
IEEE Transactions on Information Theory
Fast convergence of natural bargaining dynamics in exchange networks
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Belief Propagation for Min-Cost Network Flow: Convergence and Correctness
Operations Research
Combining per-frame and per-track cues for multi-person action recognition
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part I
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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.