Belief propagation for minimum weight many-to-one matchings in the random complete graph

Khandwawala, Mustafa (2014) Belief propagation for minimum weight many-to-one matchings in the random complete graph. In: ELECTRONIC JOURNAL OF PROBABILITY, 19 .

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Abstract

In a complete bipartite graph with vertex sets of cardinalities n and n', assign random weights from exponential distribution with mean 1, independently to each edge. We show that, as n -> infinity, with n' = n/alpha] for any fixed alpha > 1, the minimum weight of many-to-one matchings converges to a constant (depending on alpha). Many-to-one matching arises as an optimization step in an algorithm for genome sequencing and as a measure of distance between finite sets. We prove that a belief propagation (BP) algorithm converges asymptotically to the optimal solution. We use the objective method of Aldous to prove our results. We build on previous works on minimum weight matching and minimum weight edge cover problems to extend the objective method and to further the applicability of belief propagation to random combinatorial optimization problems.

Item Type:	Journal Article
Publication:	ELECTRONIC JOURNAL OF PROBABILITY
Publisher:	UNIV WASHINGTON, DEPT MATHEMATICS
Additional Information:	Copy right for this article belongs to the UNIV WASHINGTON, DEPT MATHEMATICS, BOX 354350, SEATTLE, WASHINGTON 98195-4350 USA
Keywords:	belief propagation; local weak convergence; many-to-one matching; objective method; random graph
Department/Centre:	Division of Electrical Sciences > Electrical Communication Engineering
Date Deposited:	01 Apr 2015 12:12
Last Modified:	01 Apr 2015 12:12
URI:	http://eprints.iisc.ac.in/id/eprint/51155

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