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Sen. Netw."],"published-print":{"date-parts":[[2015,3,2]]},"abstract":"<jats:p>\n            We investigate the condition on transmission radius needed to achieve connectivity in duty-cycled wireless sensor networks (briefly, DC-WSNs). First, we settle a conjecture of Das et al. [2012] and prove that the connectivity condition on random geometric graphs (RGGs), given by Gupta and Kumar [1989], can be used to derive a weakly sufficient condition to achieve connectivity in DC-WSNs. To find a stronger result, we define a new vertex-based random connection model that is of independent interest. Following a proof technique of Penrose [1991], we prove that when the density of the nodes approaches infinity, then a finite component of size greater than 1 exists with probability 0 in this model. We use this result to obtain an optimal condition on node transmission radius that is both necessary and sufficient to achieve connectivity and is hence\n            <jats:italic>optimal<\/jats:italic>\n            . The optimality of such a radius is also tested via simulation for two specific duty-cycle schemes, called the\n            <jats:italic>contiguous<\/jats:italic>\n            and the\n            <jats:italic>random selection<\/jats:italic>\n            duty-cycle schemes. Finally, we design a minimum-radius duty-cycling scheme that achieves connectivity with a transmission radius arbitrarily close to the one required in random geometric graphs. The overhead in this case is that we have to spend some time computing the schedule.\n          <\/jats:p>","DOI":"10.1145\/2663353","type":"journal-article","created":{"date-parts":[[2014,12,16]],"date-time":"2014-12-16T13:39:54Z","timestamp":1418737194000},"page":"1-37","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":5,"title":["Optimal Radius for Connectivity in Duty-Cycled Wireless Sensor Networks"],"prefix":"10.1145","volume":"11","author":[{"given":"Amitabha","family":"Bagchi","sequence":"first","affiliation":[{"name":"IIT, Delhi, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sainyam","family":"Galhotra","sequence":"additional","affiliation":[{"name":"IIT, Delhi, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tarun","family":"Mangla","sequence":"additional","affiliation":[{"name":"IIT, Delhi, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Cristina M.","family":"Pinotti","sequence":"additional","affiliation":[{"name":"University of Perugia, Perugia, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2014,12,12]]},"reference":[{"key":"e_1_2_2_1_1","doi-asserted-by":"crossref","unstructured":"N. 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