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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(More)
Distributed, iterative algorithms operating with minimal data structure while performing little computation per iteration are popularly known as message-passing in the recent literature. Belief Propagation (BP), a prototypical message-passing algorithm, has gained a lot of attention across disciplines including communications, statistics, signal processing(More)
The long chain has been an important concept in the design of flexible processes. This design concept, as well as other sparse designs, have been applied by the automotive and other industries as a way to increase flexibility in order to better match available capacities with variable demands. Numerous empirical studies have validated the effectiveness of(More)
Sparse process flexibility and long chain has became an important concept in design flexible manufacturing systems since the seminal paper of Jordan and Graves (1995). In this paper, we study the performance of long chain in comparison to all designs with at most 2n edges over n supply and n demand nodes. We show that, surprisingly, long chain is not(More)
Given a sequence of n independent random variables with common continuous distribution, we propose a simple adaptive online policy that selects a monotone increasing subsequence. We show that the expected number of monotone increasing selections made by such policy is within O(log n) of optimal. Our construction provides a direct and natural way for proving(More)
We study the behavior of strategic customers in an open-routing service network with multiple stations. When a customer enters the network, she is free to choose the sequence of stations that she visits, with the objective of minimizing her expected total system time. For the two-station game with deterministic service times, we prove that the game is(More)