Khandwawala, Mustafa and Sundaresan, Rajesh (2014) BELIEF PROPAGATION FOR OPTIMAL EDGE COVER IN THE RANDOM COMPLETE GRAPH. In: ANNALS OF APPLIED PROBABILITY, 24 (6). pp. 2414-2454.
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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 Wastlund. We provide a proof of this result using the machinery of the objective method and local weak convergence, which was used to prove the (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.
| Item Type: | Journal Article |
|---|---|
| Publication: | ANNALS OF APPLIED PROBABILITY |
| Publisher: | INST MATHEMATICAL STATISTICS |
| Additional Information: | Copy right for this article belongs to the INST MATHEMATICAL STATISTICS, 3163 SOMERSET DR, CLEVELAND, OH 44122 USA |
| Department/Centre: | Division of Electrical Sciences > Electrical Communication Engineering |
| Date Deposited: | 20 Nov 2014 05:08 |
| Last Modified: | 20 Nov 2014 05:08 |
| URI: | http://eprints.iisc.ac.in/id/eprint/50318 |
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