{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T04:27:28Z","timestamp":1750307248931,"version":"3.41.0"},"reference-count":28,"publisher":"Association for Computing Machinery (ACM)","issue":"4","license":[{"start":{"date-parts":[[2011,2,1]],"date-time":"2011-02-01T00:00:00Z","timestamp":1296518400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"DOI":"10.13039\/100007567","name":"City University of Hong Kong","doi-asserted-by":"publisher","award":["7008041"],"award-info":[{"award-number":["7008041"]}],"id":[{"id":"10.13039\/100007567","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["6.06E+15"],"award-info":[{"award-number":["6.06E+15"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Sen. Netw."],"published-print":{"date-parts":[[2011,2]]},"abstract":"<jats:p>\n            In this article, we study the critical sensor density for partial connectivity of a large area sensor network. We assume that sensor deployment follows the Poisson distribution. For a given partial connectivity requirement \u03c1, 0.5 &lt; \u03c1 &lt; 1, we prove that there exists a critical sensor density \u03bb\n            <jats:sub>0<\/jats:sub>\n            , around which the probability that at least a fraction \u03c1 of sensors are connected in the network increases sharply from \u03b5 to 1-\u03b5 within a short interval of sensor density \u03bb. The length of this interval is in the order of\n            <jats:italic>O<\/jats:italic>\n            (-log \u03b5\/log\n            <jats:italic>A<\/jats:italic>\n            ) as\n            <jats:italic>A<\/jats:italic>\n            \u2192 \u221e, where\n            <jats:italic>A<\/jats:italic>\n            is the area of the sensor field, and the location of \u03bb\n            <jats:sub>0<\/jats:sub>\n            is at the sensor density where the aforesaid probability is about 1\/2. We prove the preceding theoretical results in the hexagonal model. We also extend our results to the disk model that models transmission range of sensors as disks. Simulations are performed to confirm the analytical results.\n          <\/jats:p>","DOI":"10.1145\/1921621.1921629","type":"journal-article","created":{"date-parts":[[2011,3,2]],"date-time":"2011-03-02T18:19:53Z","timestamp":1299089993000},"page":"1-23","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":14,"title":["Critical sensor density for partial connectivity in large area wireless sensor networks"],"prefix":"10.1145","volume":"7","author":[{"given":"Haiyan","family":"Cai","sequence":"first","affiliation":[{"name":"University of Missouri-St. Louis, St. Louis, MO"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaohua","family":"Jia","sequence":"additional","affiliation":[{"name":"City University of Hong Kong, Kowloon, Hong Kong"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mo","family":"Sha","sequence":"additional","affiliation":[{"name":"Washington University in St. Louis, St. Louis, MO"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2011,2,4]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1145\/1132905.1132921"},{"volume-title":"Proceedings of the 28th IEEE Conference on Computer Communications (InfoCom). 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