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 | |
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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