A strongly polynomial minimum cost circulation algorithm
Combinatorica
Mathematical Programming: Series A and B
Solving minimum-cost flow problems by successive approximation
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
Matching is as easy as matrix inversion
Combinatorica
Finding minimum-cost circulations by canceling negative cycles
Journal of the ACM (JACM)
Finding minimum-cost flows by double scaling
Mathematical Programming: Series A and B
A faster strongly polynomial minimum cost flow algorithm
Operations Research
Theoretical Improvements in Algorithmic Efficiency for Network Flow Problems
Journal of the ACM (JACM)
Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference
Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference
Introduction to Linear Optimization
Introduction to Linear Optimization
Walk-Sums and Belief Propagation in Gaussian Graphical Models
The Journal of Machine Learning Research
Convergence of min-sum message passing for quadratic optimization
IEEE Transactions on Information Theory
Message passing for maximum weight independent set
IEEE Transactions on Information Theory
Belief propagation for min-cost network flow: convergence & correctness
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Fast convergence of natural bargaining dynamics in exchange networks
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
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
| Hi-index | 0.00 |
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, and machine learning as an attractive, scalable, general-purpose heuristic for a wide class of optimization and statistical inference problems. Despite its empirical success, the theoretical understanding of BP is far from complete. With the goal of advancing the state of art of our understanding of BP, we study the performance of BP in the context of the capacitated minimum-cost network flow problem---a cornerstone in the development of the theory of polynomial-time algorithms for optimization problems and widely used in the practice of operations research. As the main result of this paper, we prove that BP converges to the optimal solution in pseudopolynomial time, provided that the optimal solution of the underlying network flow problem instance is unique and the problem parameters are integral. We further provide a simple modification of the BP to obtain a fully polynomial-time randomized approximation scheme (FPRAS) without requiring uniqueness of the optimal solution. This is the first instance where BP is proved to have fully polynomial running time. Our results thus provide a theoretical justification for the viability of BP as an attractive method to solve an important class of optimization problems.