2014/12/16 by Sejun Park, Jinwoo Shin, Park, Sejun +1
Computer Science · Decision Sciences · #Artificial Intelligence (cs.AI) #Bayesian Modeling and Causal Inference #Error Correcting Code Techniques #FOS: Computer and information sciences #Machine Learning and Algorithms #Multi-Criteria Decision Making
paper · pdf · doi:10.48550/arxiv.1412.4972
openalex publication_date 2014/12/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The max-product belief propagation (BP) is a popular message-passing heuristic for approximating a maximum-a-posteriori (MAP) assignment in a joint distribution represented by a graphical model (GM). In the past years, it has been shown that BP can solve a few classes of linear programming (LP) formulations to combinatorial optimization problems including maximum weight matching, shortest path and network flow, i.e., BP can be used as a message-passing solver for certain combinatorial optimizations. However, those LPs and corresponding BP analysis are very sensitive to underlying problem setups, and it has been not clear what extent these results can be generalized to. In this paper, we obtain a generic criteria that BP converges to the optimal solution of given LP, and show that it is satisfied in LP formulations associated to many classical combinatorial optimization problems including maximum weight perfect matching, shortest path, traveling salesman, cycle packing, vertex/edge cover and network flow.