Open Access
December 2014 Belief propagation for optimal edge cover in the random complete graph
Mustafa Khandwawala, Rajesh Sundaresan
Ann. Appl. Probab. 24(6): 2414-2454 (December 2014). DOI: 10.1214/13-AAP981


We apply the objective method of Aldous to the problem of finding the minimum-cost edge cover of the complete graph with random independent and identically distributed edge costs. The limit, as the number of vertices goes to infinity, of the expected minimum cost for this problem is known via a combinatorial approach of Hessler and Wästlund. We provide a proof of this result using the machinery of the objective method and local weak convergence, which was used to prove the $\zeta(2)$ limit of the random assignment problem. A proof via the objective method is useful because it provides us with more information on the nature of the edge’s incident on a typical root in the minimum-cost edge cover. We further show that a belief propagation algorithm converges asymptotically to the optimal solution. This can be applied in a computational linguistics problem of semantic projection. The belief propagation algorithm yields a near optimal solution with lesser complexity than the known best algorithms designed for optimality in worst-case settings.


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Mustafa Khandwawala. Rajesh Sundaresan. "Belief propagation for optimal edge cover in the random complete graph." Ann. Appl. Probab. 24 (6) 2414 - 2454, December 2014.


Published: December 2014
First available in Project Euclid: 26 August 2014

zbMATH: 1318.60016
MathSciNet: MR3262507
Digital Object Identifier: 10.1214/13-AAP981

Primary: 60C05
Secondary: 68Q87 , 82B44

Keywords: belief propagation , edge cover , Local weak convergence , objective method , semantic projection

Rights: Copyright © 2014 Institute of Mathematical Statistics

Vol.24 • No. 6 • December 2014
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