Optimality of belief propagation for random assignment problem
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Belief Propagation: An Asymptotically Optimal Algorithm for the Random Assignment Problem
Mathematics of Operations Research
Effective bidding and deal identification for negotiations in highly nonlinear scenarios
Proceedings of The 8th International Conference on Autonomous Agents and Multiagent Systems - Volume 2
Loopy Substructural Local Search for the Bayesian Optimization Algorithm
SLS '09 Proceedings of the Second International Workshop on Engineering Stochastic Local Search Algorithms. Designing, Implementing and Analyzing Effective Heuristics
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
Convergence of min-sum message-passing for convex optimization
IEEE Transactions on Information Theory
Avoiding the prisoner's dilemma in auction-based negotiations for highly rugged utility spaces
Proceedings of the 9th International Conference on Autonomous Agents and Multiagent Systems: volume 1 - Volume 1
Belief propagation for min-cost network flow: convergence & correctness
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
An FPTAS for bargaining networks with unequal bargaining powers
WINE'10 Proceedings of the 6th international conference on Internet and network economics
Autonomous Agents and Multi-Agent Systems
Fast convergence of natural bargaining dynamics in exchange networks
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
An auction based pre-processing technique to determine detour in global routing
Proceedings of the International Conference on Computer-Aided Design
Efficient rank aggregation using partial data
Proceedings of the 12th ACM SIGMETRICS/PERFORMANCE joint international conference on Measurement and Modeling of Computer Systems
Belief Propagation for Min-Cost Network Flow: Convergence and Correctness
Operations Research
A multithreaded algorithm for network alignment via approximate matching
SC '12 Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis
Optimizing social welfare for network bargaining games in the face of unstability, greed and spite
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
A message passing graph match algorithm based on a generative graphical model
AMT'12 Proceedings of the 8th international conference on Active Media Technology
Approximating the permanent with fractional belief propagation
The Journal of Machine Learning Research
Hi-index | 754.90 |
Max-product "belief propagation" (BP) is an iterative, message-passing algorithm for finding the maximum a posteriori (MAP) assignment of a discrete probability distribution specified by a graphical model. Despite the spectacular success of the algorithm in many application areas such as iterative decoding and combinatorial optimization, which involve graphs with many cycles, theoretical results about both the correctness and convergence of the algorithm are known in only a few cases (see section I for references). In this paper, we prove the correctness and convergence of max-product for finding the maximum weight matching (MWM) in bipartite graphs. Even though the underlying graph of the MWM problem has many cycles, somewhat surprisingly we show that the max-product algorithm converges to the correct MWM as long as the MWM is unique. We provide a bound on the number of iterations required and show that for a graph of size n, the computational cost of the algorithm scales as O(n3), which is the same as the computational cost of the best known algorithms for finding the MWM. We also provide an interesting relation between the dynamics of the max-product algorithm and the auction algorithm, which is a well-known distributed algorithm for solving the MWM problem.