Convergence and correctness of belief propagation for the Chinese postman problem

Guowei Dai, Fengwei Li, Yuefang Sun, Dachuan Xu and Xiaoyan Zhang ()
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Guowei Dai: Nanjing Normal University
Fengwei Li: Shaoxing University
Yuefang Sun: Shaoxing University
Dachuan Xu: Beijing University of Technology
Xiaoyan Zhang: Nanjing Normal University

Journal of Global Optimization, 2019, vol. 75, issue 3, No 9, 813-831

Abstract: Abstract Belief Propagation (BP), a distributed, message-passing algorithm, has been widely used in different disciplines including information theory, artificial intelligence, statistics and optimization problems in graphical models such as Bayesian networks and Markov random fields. Despite BP algorithm has a great success in many application fields and many progress about BP algorithm has been made, the rigorous analysis about the correctness and convergence of BP algorithm are known in only a few cases for arbitrary graph. In this paper, we will investigate the correctness and convergence of BP algorithm for determining the optimal solutions of the Chinese postman problem in both undirected and directed graphs. As a main result, we prove that BP algorithm converges to the optimal solution of the undirected Chinese postman problem within O(n) iterations where n represents the number of vertices, provided that the optimal solution is unique. For the directed case, we consider the directed Chinese postman problem with capacity and show that BP algorithm also converges to its optimal solution after O(n) iterations, as long as its corresponding linear programming relaxation has the unique optimal solution.

Keywords: Belief propagation (BP); Message-passing algorithm; Min-sum algorithm; Convergence; Undirected Chinese postman problem; Directed Chinese postman problem (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s10898-019-00749-2

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