Connected Spatial Networks over Random Points and a Route-Length Statistic
We review mathematically tractable models for connected networks on random points in the plane, emphasizing the class of proximity graphs which deserves to be better known to applied probabilists and statisticians. We introduce and motivate a particular statistic R measuring shortness of routes in a...
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| Veröffentlicht in: | Statistical science 2010-08, Vol.25 (3), p.275-288 |
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| container_title | Statistical science |
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| creator | Aldous, David J. Shun, Julian |
| description | We review mathematically tractable models for connected networks on random points in the plane, emphasizing the class of proximity graphs which deserves to be better known to applied probabilists and statisticians. We introduce and motivate a particular statistic R measuring shortness of routes in a network. We illustrate, via Monte Carlo in part, the trade-off between normalized network length and R in a one-parameter family of proximity graphs. How close this family comes to the optimal trade-off over all possible networks remains an intriguing open question. The paper is a write-up of a talk developed by the first author during 2007-2009. |
| doi_str_mv | 10.1214/10-sts335 |
| format | Article |
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The paper is a write-up of a talk developed by the first author during 2007-2009.</description><subject>Cities</subject><subject>Determinism</subject><subject>geometric graph</subject><subject>Geometric planes</subject><subject>Graphs</subject><subject>Mathematical models</subject><subject>Monte Carlo simulation</subject><subject>Network access lines</subject><subject>Proximity graph</subject><subject>random graph</subject><subject>Roads</subject><subject>Spacetime</subject><subject>spatial network</subject><subject>Spatial points</subject><subject>Statistics</subject><subject>Triangulation</subject><subject>Vertices</subject><issn>0883-4237</issn><issn>2168-8745</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2010</creationdate><recordtype>article</recordtype><recordid>eNo9kF9LwzAUxYMoOKcPfgAh-OZD9aZJk_RJpPiXorJuzyVtUm3dmpmkit_ejo09He7ld889HITOCVyTmLAbApEPntLkAE1iwmUkBUsO0QSkpBGLqThGJ953AJBwwiboJbN9b-pgNC7WKrRqiV9N-LXuy2P7YxyeqV7bFX63bR88Hges8MwOwUS56T_CJy7CeOZDW5-io0YtvTnb6RQtHu7n2VOUvz0-Z3d5VDOahKjRla4MZZJoRhrVSAMaeMpiw6k0sgLFNdEUDOUs4bJhKQGoaioaQgUYQ6foduu7drbbRB_qZavLtWtXyv2VVrVltsh32514X5I4ZYSLlMPocLl3-B6MD2VnB9ePoUspYpKkIhYjdLWFame9d6bZfyBQbrreaDEvxq5H9mLLdj5YtwcZgUSmTNJ_yUF7Wg</recordid><startdate>20100801</startdate><enddate>20100801</enddate><creator>Aldous, David J.</creator><creator>Shun, Julian</creator><general>Institute of Mathematical Statistics</general><general>The Institute of Mathematical Statistics</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20100801</creationdate><title>Connected Spatial Networks over Random Points and a Route-Length Statistic</title><author>Aldous, David J. ; Shun, Julian</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c435t-fdbdbe3481d41faf8e0d06942e638e8b0a6d1d30e364568f49100bc37f1370ee3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2010</creationdate><topic>Cities</topic><topic>Determinism</topic><topic>geometric graph</topic><topic>Geometric planes</topic><topic>Graphs</topic><topic>Mathematical models</topic><topic>Monte Carlo simulation</topic><topic>Network access lines</topic><topic>Proximity graph</topic><topic>random graph</topic><topic>Roads</topic><topic>Spacetime</topic><topic>spatial network</topic><topic>Spatial points</topic><topic>Statistics</topic><topic>Triangulation</topic><topic>Vertices</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Aldous, David J.</creatorcontrib><creatorcontrib>Shun, Julian</creatorcontrib><collection>CrossRef</collection><jtitle>Statistical science</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Aldous, David J.</au><au>Shun, Julian</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Connected Spatial Networks over Random Points and a Route-Length Statistic</atitle><jtitle>Statistical science</jtitle><date>2010-08-01</date><risdate>2010</risdate><volume>25</volume><issue>3</issue><spage>275</spage><epage>288</epage><pages>275-288</pages><issn>0883-4237</issn><eissn>2168-8745</eissn><abstract>We review mathematically tractable models for connected networks on random points in the plane, emphasizing the class of proximity graphs which deserves to be better known to applied probabilists and statisticians. 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| fulltext | fulltext |
| identifier | ISSN: 0883-4237 |
| ispartof | Statistical science, 2010-08, Vol.25 (3), p.275-288 |
| issn | 0883-4237 2168-8745 |
| language | eng |
| recordid | cdi_projecteuclid_primary_oai_CULeuclid_euclid_ss_1294167960 |
| source | JSTOR Mathematics & Statistics; JSTOR Archive Collection A-Z Listing; EZB-FREE-00999 freely available EZB journals; Project Euclid Complete |
| subjects | Cities Determinism geometric graph Geometric planes Graphs Mathematical models Monte Carlo simulation Network access lines Proximity graph random graph Roads Spacetime spatial network Spatial points Statistics Triangulation Vertices |
| title | Connected Spatial Networks over Random Points and a Route-Length Statistic |
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