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


 
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1. Title Title of document Belief propagation for minimum weight many-to-one matchings in the random complete graph
 
2. Creator Author's name, affiliation, country Mustafa Khandwawala; Indian Institute of Science; India
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) belief propagation; local weak convergence; many-to-one matching; objective method; random graph
 
3. Subject Subject classification 60C05; 68Q87
 
4. Description Abstract In a complete bipartite graph with vertex sets of cardinalities $n$ and $n^\prime$, assign random weights from exponential distribution with mean 1, independently to each edge. We show that, as $n\rightarrow\infty$, with $n^\prime=\lceil n/\alpha\rceil$ 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.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) Department of Science and Technology, Government of India; TCS
 
7. Date (YYYY-MM-DD) 2014-12-11
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/3491
 
10. Identifier Digital Object Identifier 10.1214/EJP.v19-3491
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 19
 
12. Language English=en en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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