{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:39:46Z","timestamp":1760243986493,"version":"build-2065373602"},"reference-count":19,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2009,9,14]],"date-time":"2009-09-14T00:00:00Z","timestamp":1252886400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>Wireless sensor networks are a relatively new area where technology is developing fast and are used to solve a great diversity of problems that range from museums\u2019 security to wildlife protection. The geometric optimisation problem solved in this paper is aimed at minimising the sensors\u2019 range so that every point on a polygonal region R is within the range of at least two sensors. Moreover, it is also shown how to minimise the sensors\u2019 range to assure the existence of a path within R that stays as close to two sensors as possible.<\/jats:p>","DOI":"10.3390\/a2031137","type":"journal-article","created":{"date-parts":[[2009,9,15]],"date-time":"2009-09-15T11:19:31Z","timestamp":1253013571000},"page":"1137-1154","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Optimal 2-Coverage of a Polygonal Region in a Sensor Network"],"prefix":"10.3390","volume":"2","author":[{"given":"Manuel","family":"Abellanas","sequence":"first","affiliation":[{"name":"Facultad de Inform\u00e1tica, Universidad Polit\u00e9cnica de Madrid, Campus de Montegancedo, 28660 Boadilla del Monte, Madrid, Spain"}]},{"given":"Antonio L.","family":"Bajuelos","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1tica & CEOC, Universidade de Aveiro, Campus Universit\u00e1rio de Santiago, 3810-193 Aveiro, Portugal"}]},{"given":"In\u00eas","family":"Matos","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1tica & CEOC, Universidade de Aveiro, Campus Universit\u00e1rio de Santiago, 3810-193 Aveiro, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2009,9,14]]},"reference":[{"key":"ref_1","unstructured":"Meguerdichian, S., Koushanfar, F., Potkonjak, M., and Srivastava, M.B. (2001, January April). Coverage problems in wireless ad-hoc sensor networks. Proceedings of the Twentieth Annual Joint Conference of the IEEE Computer and Communications Societies, Anchorage, AK, USA."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Boukerche, A., Fei, X., and Araujo, R.B. (2005, January October). An energy aware coverage-preserving scheme for wireless sensor networks. Proocedings of the 2nd ACM international Workshop on Performance Evaluation of Wireless ad hoc, Sensor and Ubiquitous Networks, Montreal, Canada.","DOI":"10.1145\/1089803.1089987"},{"key":"ref_3","unstructured":"Gomez, J., Campbell, A.T., Naghshineh, M., and Bisdikian, C. (2001, January November). Conserving transmission power in wireless ad hoc networks. Proceedings of the 9th International Conference on Network Protocols, Riverside, CA, USA."},{"key":"ref_4","unstructured":"Sack, J.R., and Urrutia, J. (2000). Handbook of Computational Geometry, Elsevier Science. Chapter 5."},{"key":"ref_5","first-page":"478","article-title":"On k-nearest neighbor voronoi diagrams in the plane","volume":"31","author":"Lee","year":"1982","journal-title":"IEEE Trans. Comput."},{"key":"ref_6","unstructured":"Abellanas, M., and Hern\u00e1ndez, G. (2007, January June). Optimizaci\u00f3n de rutas de evacuaci\u00f3n. Proceedings of the XII Encuentros de Geometr\u00eda Computacional, Valladolid, Spain."},{"key":"ref_7","unstructured":"Mehta, D.P., Lopez, M.A., and Lin, L. (2003, January May). Optimal coverage paths in ad-hoc sensor networks. Proceedings of the ICC \u201903, IEEE International Conference on Communications, Anchorage, Alaska, USA."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1423","DOI":"10.1016\/j.cor.2008.02.013","article-title":"Covering a line segment with variable radius discs","volume":"36","author":"Agnetis","year":"2009","journal-title":"Comput. Oper. Res."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"753","DOI":"10.1109\/TC.2003.1204831","article-title":"Coverage in wireless ad-hoc sensor networks","volume":"52","author":"Li","year":"2003","journal-title":"IEEE Trans. Comput."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1007\/s11276-007-0021-1","article-title":"Localized algorithms for coverage boundary detection in wireless sensor networks","volume":"15","author":"Zhang","year":"2009","journal-title":"Wireless Netw."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1145\/1464420.1464428","article-title":"Variable radii connected sensor cover in sensor networks","volume":"5","author":"Zhou","year":"2009","journal-title":"ACM Trans. Sens. Netw."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1353","DOI":"10.1016\/j.jpdc.2006.05.004","article-title":"Efficient algorithm for Placing a given number of base stations to cover a convex region","volume":"66","author":"Das","year":"2006","journal-title":"J. Paral. Distrib. Comput."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Stoyan, Y.G., and Patsuk, V.M. (2008). Covering a compact polygonal set by identical circles. Comput. Opt. Appl.","DOI":"10.1007\/s10589-008-9191-8"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1023\/A:1004275121878","article-title":"Circle covering with a margin","volume":"34","author":"Bezdek","year":"1997","journal-title":"Period. Math. Hung."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"768","DOI":"10.1016\/j.ipl.2009.03.016","article-title":"2-Covered paths by a set of antennas with minimum power transmission range","volume":"109","author":"Abellanas","year":"2009","journal-title":"Inf. Processing Lett."},{"key":"ref_16","unstructured":"Chazelle, B. (1980). computational geometry and convexity. [PhD Thesis, Yale University]."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"799","DOI":"10.1137\/0214056","article-title":"Decomposing a polygon into simpler components","volume":"14","author":"Keil","year":"1985","journal-title":"SIAM J. Comput."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"516","DOI":"10.1145\/321296.321300","article-title":"Backtrack programming","volume":"12","author":"Golomb","year":"1965","journal-title":"JACM"},{"key":"ref_19","unstructured":"Abellanas, M., Bajuelos, A.L., and Matos, I. (2009, January March). Safe routes on a street graph with minimum power transmission range. Proceedings of the 25th European Workshop on Computational Geometry, Brussels, Belgium."}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/2\/3\/1137\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T22:11:10Z","timestamp":1760220670000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/2\/3\/1137"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,9,14]]},"references-count":19,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2009,9]]}},"alternative-id":["a2031137"],"URL":"https:\/\/doi.org\/10.3390\/a2031137","relation":{},"ISSN":["1999-4893"],"issn-type":[{"type":"electronic","value":"1999-4893"}],"subject":[],"published":{"date-parts":[[2009,9,14]]}}}