CONVERGENCE AND CORRECTNESS OF MAX-PRODUCT BELIEF PROPAGATION FOR LINEAR PROGRAMMING

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The max-product belief propagation (BP) is a popular message-passing heuristic for approximating a maximum-a-posteriori assignment in a joint distribution represented by a graphical model. 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.
Publisher
SIAM PUBLICATIONS
Issue Date
2017
Language
English
Article Type
Article
Keywords

ARBITRARY GRAPHS; ALGORITHM

Citation

SIAM JOURNAL ON DISCRETE MATHEMATICS, v.31, no.3, pp.2228 - 2246

ISSN
0895-4801
DOI
10.1137/15M1042565
URI
http://hdl.handle.net/10203/226745
Appears in Collection
EE-Journal Papers(저널논문)
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