Belief Propagation for Min-Cost Network Flow: Convergence & Correctness Citation
نویسندگان
چکیده
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
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