{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,9]],"date-time":"2024-09-09T01:47:53Z","timestamp":1725846473752},"publisher-location":"Cham","reference-count":23,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783319284712"},{"type":"electronic","value":"9783319284729"}],"license":[{"start":{"date-parts":[[2015,1,1]],"date-time":"2015-01-01T00:00:00Z","timestamp":1420070400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2015]]},"DOI":"10.1007\/978-3-319-28472-9_1","type":"book-chapter","created":{"date-parts":[[2015,12,31]],"date-time":"2015-12-31T06:22:47Z","timestamp":1451542967000},"page":"1-12","source":"Crossref","is-referenced-by-count":0,"title":["Plane and Planarity Thresholds for Random Geometric Graphs"],"prefix":"10.1007","author":[{"given":"Ahmad","family":"Biniaz","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Evangelos","family":"Kranakis","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Anil","family":"Maheshwari","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Michiel","family":"Smid","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2016,1,1]]},"reference":[{"key":"1_CR1","volume-title":"The Probabilistic Method","author":"N Alon","year":"2007","unstructured":"Alon, N., Spencer, J.H.: The Probabilistic Method, 3rd edn. Wiley, New York (2007)","edition":"3"},{"issue":"4","key":"1_CR2","doi-asserted-by":"publisher","first-page":"351","DOI":"10.1016\/S0167-7152(02)00233-X","volume":"60","author":"MJB Appel","year":"2002","unstructured":"Appel, M.J.B., Russo, R.P.: The connectivity of a graph on uniform points on \n                    \n                      \n                    \n                    $$[0,1]^d$$\n                  . Stat. Prob. Lett. 60(4), 351\u2013357 (2002)","journal-title":"Stat. Prob. Lett."},{"key":"1_CR3","doi-asserted-by":"publisher","first-page":"117","DOI":"10.1007\/978-3-540-69395-6_2","volume-title":"Handbook of Large-Scale Random Networks","author":"P Balister","year":"2008","unstructured":"Balister, P., Sarkar, A., Bollob\u00e1s, B.: Percolation, connectivity, coverage and colouring of random geometric graphs. In: Bollob\u00e1s, B., Kozma, R., Mikl\u00f3s, D. (eds.) Handbook of Large-Scale Random Networks, pp. 117\u2013142. Springer, Heidelberg (2008)"},{"key":"1_CR4","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511814068","volume-title":"Random Graphs","author":"B Bollob\u00e1s","year":"2001","unstructured":"Bollob\u00e1s, B.: Random Graphs. Cambridge University Press, Cambridge (2001)"},{"issue":"1","key":"1_CR5","doi-asserted-by":"publisher","first-page":"35","DOI":"10.1007\/BF02579198","volume":"7","author":"B Bollob\u00e1s","year":"1987","unstructured":"Bollob\u00e1s, B., Thomason, A.: Threshold functions. Combinatorica 7(1), 35\u201338 (1987)","journal-title":"Combinatorica"},{"key":"1_CR6","first-page":"59","volume":"34","author":"J Bourgain","year":"1998","unstructured":"Bourgain, J., Kalai, G.: Threshold intervals under group symmetries. Convex Geom. Anal. MSRI Publ. 34, 59\u201363 (1998)","journal-title":"Convex Geom. Anal. MSRI Publ."},{"key":"1_CR7","unstructured":"Bradonji\u0107, M., Perkins, W.: On sharp thresholds in random geometric graphs. In: Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, APPROX\/RANDOM, pp. 500\u2013514 (2014)"},{"key":"1_CR8","first-page":"17","volume":"5","author":"P Erd\u00f6s","year":"1960","unstructured":"Erd\u00f6s, P., R\u00e9nyi, A.: On the evolution of random graphs. Publ. Math. Inst. Hungar. Acad. Sci. 5, 17\u201361 (1960)","journal-title":"Publ. Math. Inst. Hungar. Acad. Sci."},{"issue":"10","key":"1_CR9","doi-asserted-by":"publisher","first-page":"2993","DOI":"10.1090\/S0002-9939-96-03732-X","volume":"124","author":"E Friedgut","year":"1996","unstructured":"Friedgut, E., Kalai, G.: Every monotone graph property has a sharp threshold. Proc. Am. Math. Soc. 124(10), 2993\u20133002 (1996)","journal-title":"Proc. Am. Math. Soc."},{"issue":"4","key":"1_CR10","doi-asserted-by":"publisher","first-page":"1141","DOI":"10.1214\/aoms\/1177706098","volume":"30","author":"E Gilbert","year":"1959","unstructured":"Gilbert, E.: Random graphs. Ann. Math. Stat. 30(4), 1141\u20131144 (1959)","journal-title":"Ann. Math. Stat."},{"issue":"4","key":"1_CR11","doi-asserted-by":"publisher","first-page":"533","DOI":"10.1137\/0109045","volume":"9","author":"E Gilbert","year":"1961","unstructured":"Gilbert, E.: Random plane networks. J. Soc. Ind. Appl. Math. 9(4), 533\u2013543 (1961)","journal-title":"J. Soc. Ind. Appl. Math."},{"issue":"1\u20132","key":"1_CR12","doi-asserted-by":"publisher","first-page":"137","DOI":"10.1002\/(SICI)1098-2418(199608\/09)9:1\/2<137::AID-RSA9>3.0.CO;2-Y","volume":"9","author":"E Godehardt","year":"1996","unstructured":"Godehardt, E., Jaworski, J.: On the connectivity of a random interval graph. Random Struct. Algorithms 9(1\u20132), 137\u2013161 (1996)","journal-title":"Random Struct. Algorithms"},{"key":"1_CR13","doi-asserted-by":"crossref","unstructured":"Goel, A., Rai, S., Krishnamachari, B.: Sharp thresholds for monotone properties in random geometric graphs. In: Proceedings of STOC, pp. 580\u2013586. ACM (2004)","DOI":"10.1145\/1007352.1007441"},{"key":"1_CR14","first-page":"547","volume-title":"Stochastic Analysis, Control, Optimization and Applications","author":"P Gupta","year":"1998","unstructured":"Gupta, P., Kumar, P.R.: Critical power for asymptotic connectivity in wireless networks. In: McEneaney, W.M., George Yin, G., Zhang, Q. (eds.) Stochastic Analysis, Control, Optimization and Applications, pp. 547\u2013566. Springer, New York (1998)"},{"issue":"3","key":"1_CR15","doi-asserted-by":"publisher","first-page":"991","DOI":"10.1214\/aop\/1176992920","volume":"13","author":"P Hall","year":"1985","unstructured":"Hall, P.: On the coverage of \n                    \n                      \n                    \n                    $$ k $$\n                  -dimensional space by \n                    \n                      \n                    \n                    $$ k $$\n                  -dimensional spheres. Ann. Prob. 13(3), 991\u20131002 (1985)","journal-title":"Ann. Prob."},{"issue":"1","key":"1_CR16","doi-asserted-by":"publisher","first-page":"83","DOI":"10.1007\/BF02399201","volume":"156","author":"S Janson","year":"1986","unstructured":"Janson, S.: Random coverings in several dimensions. Acta Mathematica 156(1), 83\u2013118 (1986)","journal-title":"Acta Mathematica"},{"key":"1_CR17","first-page":"279","volume-title":"Communications, Information and Network Security","author":"B Krishnamachari","year":"2002","unstructured":"Krishnamachari, B., Wicker, S.B., B\u00e9jar, R., Pearlman, M.: Critical density thresholds in distributed wireless networks. In: Bhargava, V.K., Vincent Poor, H., Tarokh, V., Yoon, S. (eds.) Communications, Information and Network Security, vol. 712, pp. 279\u2013296. Springer, USA (2002)"},{"key":"1_CR18","doi-asserted-by":"publisher","first-page":"373","DOI":"10.1017\/S0963548304006121","volume":"13","author":"GL Mccolm","year":"2001","unstructured":"Mccolm, G.L.: Threshold functions for random graphs on a line segment. Comb. Prob. Comput. 13, 373\u2013387 (2001)","journal-title":"Comb. Prob. Comput."},{"key":"1_CR19","unstructured":"Panchapakesan, P., Manjunath, D.: On the transmission range in dense ad hoc radio networks. In: Proceedings of IEEE Signal Processing Communication (SPCOM) (2001)"},{"issue":"2","key":"1_CR20","doi-asserted-by":"publisher","first-page":"340","DOI":"10.1214\/aoap\/1034625335","volume":"7","author":"MD Penrose","year":"1997","unstructured":"Penrose, M.D.: The longest edge of the random minimal spanning tree. Ann. Appl. Prob. 7(2), 340\u2013361 (1997)","journal-title":"Ann. Appl. Prob."},{"issue":"2","key":"1_CR21","doi-asserted-by":"publisher","first-page":"145","DOI":"10.1002\/(SICI)1098-2418(199909)15:2<145::AID-RSA2>3.0.CO;2-G","volume":"15","author":"MD Penrose","year":"1999","unstructured":"Penrose, M.D.: On \n                    \n                      \n                    \n                    $$k$$\n                  -connectivity for a geometric random graph. Random Struct. Algorithms 15(2), 145\u2013164 (1999)","journal-title":"Random Struct. Algorithms"},{"key":"1_CR22","doi-asserted-by":"publisher","DOI":"10.1093\/acprof:oso\/9780198506263.001.0001","volume-title":"Random geometric graphs","author":"MD Penrose","year":"2003","unstructured":"Penrose, M.D.: Random geometric graphs, vol. 5. Oxford University Press, Oxford (2003)"},{"key":"1_CR23","volume-title":"Ten Lectures on the Probabilistic Method","author":"JH Spencer","year":"1987","unstructured":"Spencer, J.H.: Ten Lectures on the Probabilistic Method, vol. 52. SIAM, Philadelphia (1987)"}],"container-title":["Lecture Notes in Computer Science","Algorithms for Sensor Systems"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-319-28472-9_1","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,1]],"date-time":"2019-06-01T03:08:14Z","timestamp":1559358494000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-319-28472-9_1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015]]},"ISBN":["9783319284712","9783319284729"],"references-count":23,"URL":"https:\/\/doi.org\/10.1007\/978-3-319-28472-9_1","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2015]]}}}