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Belief-Propagation for Weighted b-Matchings on Arbitrary Graphs and its Relation to Linear Programs with Integer Solutions”, ArXiv: 0709.1190 (2007)
| Content Provider | CiteSeerX |
|---|---|
| Author | Borgs, Christian Riccardo Chayes, Jennifer Bayati, Mohsen |
| Abstract | Abstract. We consider the general problem of finding the minimum weight b-matching on arbitrary graphs. We prove that, whenever the linear programming (LP) relaxation of the problem has no fractional solutions, then the belief propagation (BP) algorithm converges to the correct solution. We also show that when the LP relaxation has a fractional solution then the BP algorithm can be used to solve the LP relaxation. Our proof is based on the notion of graph covers and extends the analysis of [5, 27]. These results are notable in the following regards: (1) It is one of a very small number of proofs showing correctness of BP without any constraint on the graph structure. (2) Variants of the proof work for both synchronous and asynchronous BP; it is the first proof of convergence and correctness of an asynchronous BP algorithm for a combinatorial optimization problem. |
| File Format | |
| Publisher Date | 2007-01-01 |
| Access Restriction | Open |
| Subject Keyword | Asynchronous Bp Algorithm Graph Structure First Proof Algorithm Converges Following Regard Lp Relaxation Combinatorial Optimization Problem Proof Work Minimum Weight B-matching Arbitrary Graph General Problem Integer Solution Belief Propagation Linear Program Bp Algorithm Weighted B-matchings Fractional Solution Asynchronous Bp Graph Cover Correct Solution Linear Programming |
| Content Type | Text |
| Resource Type | Article |
