Interacting Urns Processes for Clustering of Large-Scale Networks of Tiny Artifacts
We analyze a distributed variation on the Pólya urn process in which a network of tiny artifacts manages the individual urns. Neighboring urns interact by repeatedly adding the same colored ball based on previous random choices. We discover that the process rapidly converges to a definitive random r...
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| Format: | Article |
| Language: | English |
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Wiley
2010-07-01
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| Series: | International Journal of Distributed Sensor Networks |
| Online Access: | https://doi.org/10.1155/2010/936195 |
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| _version_ | 1832555312332144640 |
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| author | Pierre Leone Elad M. Schiller |
| author_facet | Pierre Leone Elad M. Schiller |
| author_sort | Pierre Leone |
| collection | DOAJ |
| description | We analyze a distributed variation on the Pólya urn process in which a network of tiny artifacts manages the individual urns. Neighboring urns interact by repeatedly adding the same colored ball based on previous random choices. We discover that the process rapidly converges to a definitive random ratio between the colors in every urn. Moreover, the rate of convergence of the process at a given node depends on the global topology of the network. In particular, the same ratio appears for the case of complete communication graphs. Surprisingly, this effortless random process supports useful applications, such as clustering and computation of pseudo-geometric coordinate. We present numerical studies that validate our theoretical predictions. |
| format | Article |
| id | doaj-art-73f6a3f94fc24008a79036e4f71ec429 |
| institution | Kabale University |
| issn | 1550-1477 |
| language | English |
| publishDate | 2010-07-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Distributed Sensor Networks |
| spelling | doaj-art-73f6a3f94fc24008a79036e4f71ec4292025-02-03T05:48:34ZengWileyInternational Journal of Distributed Sensor Networks1550-14772010-07-01610.1155/2010/936195Interacting Urns Processes for Clustering of Large-Scale Networks of Tiny ArtifactsPierre Leone0Elad M. Schiller1 Computer Science Department, Centre Universitaire d'Informatique Battelle Bâtiment, University of Geneva, A route de Drize 7, 1227 Carouge, Geneva, Switzerland Distributed Computing and Systems Research Group, Department of Computing Science, Chalmers University of Technology and Göteborg University Rännvägen, 6B S-412 96 Göteborg, SwedenWe analyze a distributed variation on the Pólya urn process in which a network of tiny artifacts manages the individual urns. Neighboring urns interact by repeatedly adding the same colored ball based on previous random choices. We discover that the process rapidly converges to a definitive random ratio between the colors in every urn. Moreover, the rate of convergence of the process at a given node depends on the global topology of the network. In particular, the same ratio appears for the case of complete communication graphs. Surprisingly, this effortless random process supports useful applications, such as clustering and computation of pseudo-geometric coordinate. We present numerical studies that validate our theoretical predictions.https://doi.org/10.1155/2010/936195 |
| spellingShingle | Pierre Leone Elad M. Schiller Interacting Urns Processes for Clustering of Large-Scale Networks of Tiny Artifacts International Journal of Distributed Sensor Networks |
| title | Interacting Urns Processes for Clustering of Large-Scale Networks of Tiny Artifacts |
| title_full | Interacting Urns Processes for Clustering of Large-Scale Networks of Tiny Artifacts |
| title_fullStr | Interacting Urns Processes for Clustering of Large-Scale Networks of Tiny Artifacts |
| title_full_unstemmed | Interacting Urns Processes for Clustering of Large-Scale Networks of Tiny Artifacts |
| title_short | Interacting Urns Processes for Clustering of Large-Scale Networks of Tiny Artifacts |
| title_sort | interacting urns processes for clustering of large scale networks of tiny artifacts |
| url | https://doi.org/10.1155/2010/936195 |
| work_keys_str_mv | AT pierreleone interactingurnsprocessesforclusteringoflargescalenetworksoftinyartifacts AT eladmschiller interactingurnsprocessesforclusteringoflargescalenetworksoftinyartifacts |