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The problem of\n            <jats:italic>k<\/jats:italic>\n            -coverage in WSNs is even more challenging. In this article, we investigate the\n            <jats:italic>k<\/jats:italic>\n            -coverage problem in planar (or two-dimensional) WSNs, where each point in a field of interest (FoI) is covered by at least\n            <jats:italic>k<\/jats:italic>\n            sensors simultaneously, where\n            <jats:italic>k<\/jats:italic>\n            \u2265 1. Our contribution is four-fold: First, we determine the optimal planar convex tile that maximizes the usage of the sensors\u2019 sensing range. Then, we propose a few sensor placement strategies based on the degree of coverage\n            <jats:italic>k<\/jats:italic>\n            using a hexagonal tiling-based approach. In addition, we compute the sensor density (i.e., number of sensors per unit area) for each of the above sensor placement strategies. Second, we propose a generalized one using irregular hexagons, which are denoted by\n            <jats:italic>IRH(r\/n)<\/jats:italic>\n            , where\n            <jats:italic>r<\/jats:italic>\n            stands for the radius of the sensors\u2019 sensing range and\n            <jats:italic>n<\/jats:italic>\n            \u2265 2 is a natural number. Also, we derive the corresponding sensor density. Moreover, we prove that\n            <jats:italic>IRH(r\/n)<\/jats:italic>\n            are capable of tiling the Euclidean plane using a mathematical induction proof. Third, we compute the relationship between the sensing range\n            <jats:italic>r<\/jats:italic>\n            of the sensors and their communication range\n            <jats:italic>R<\/jats:italic>\n            for the above sensor placement strategies. Fourth, we corroborate our analysis with simulation results.\n          <\/jats:p>","DOI":"10.1145\/3564272","type":"journal-article","created":{"date-parts":[[2022,9,26]],"date-time":"2022-09-26T12:56:08Z","timestamp":1664196968000},"page":"1-42","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":23,"title":["A Computational Geometry-based Approach for Planar\n            <i>k<\/i>\n            -Coverage in Wireless Sensor Networks"],"prefix":"10.1145","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3529-2862","authenticated-orcid":false,"given":"Habib M.","family":"Ammari","sequence":"first","affiliation":[{"name":"Texas A&amp;M University-Kingsville, Kingsville, Texas"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2023,2,3]]},"reference":[{"key":"e_1_3_2_2_1","doi-asserted-by":"crossref","DOI":"10.1016\/j.inffus.2015.11.005","article-title":"A centralized immune-Voronoi deployment algorithm for coverage maximization and energy conservation in mobile wireless sensor networks","author":"Abo-Zahhad Mohammed","year":"2016","unstructured":"Mohammed Abo-Zahhad, Nabil Sabor, Shigenobu Sasaki, and Sabah M. 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Metaheuristics for maximization of obstacles constrained area coverage in heterogeneous wireless sensor networks. Applied Soft Computing 86, January 2020 (2020), 105939. https:\/\/www.sciencedirect.com\/science\/article\/abs\/pii\/S1568494619307203.","journal-title":"Applied Soft Computing"},{"key":"e_1_3_2_9_1","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511816574","volume-title":"The Art of Mathematics: Coffee Time in Memphis","author":"Bollob\u00e1s Bela","year":"2006","unstructured":"Bela Bollob\u00e1s. 2006. The Art of Mathematics: Coffee Time in Memphis. Cambridge University Press."},{"key":"e_1_3_2_10_1","doi-asserted-by":"crossref","DOI":"10.1016\/j.adhoc.2018.07.003","article-title":"Connectivity and coverage based protocols for wireless sensor networks","author":"Boukerche Azzedine","year":"2018","unstructured":"Azzedine Boukerche and Peng Sun. 2018. Connectivity and coverage based protocols for wireless sensor networks. 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In Proceedings of the Time Travel and Other Mathematical Bewilderments. New York: W. H. Freeman, 162\u2013176."},{"key":"e_1_3_2_24_1","article-title":"Solving energy issues for sweep coverage in wireless sensor networks","author":"Gorain Barun","year":"2017","unstructured":"Barun Gorain, Partha Sarathi Mandal. 2017. Solving energy issues for sweep coverage in wireless sensor networks. Discrete Applied Mathematics 228, September 2017 (2017), 130--139. https:\/\/www.sciencedirect.com\/science\/article\/pii\/S0166218X16304346.","journal-title":"Discrete Applied Mathematics"},{"issue":"3","key":"e_1_3_2_25_1","doi-asserted-by":"crossref","first-page":"951","DOI":"10.1090\/S0273-0979-1980-14827-2","article-title":"Tilings with congruent tiles","volume":"3","author":"Grunbaum Branko","year":"1980","unstructured":"Branko Grunbaum and G. C. Shephard. 1980. Tilings with congruent tiles. Bulletin of the American Mathematical Society 3, 3 (1980), 951\u2013973.","journal-title":"Bulletin of the American Mathematical Society"},{"key":"e_1_3_2_26_1","article-title":"Genetic algorithm approach for k-coverage and m-connected node placement in target based wireless sensor networks","author":"Kumar Gupta Suneet","year":"2016","unstructured":"Suneet Kumar Gupta, Pratyay Kuila, and Prasanta K. Jana. 2016. Genetic algorithm approach for k-coverage and m-connected node placement in target based wireless sensor networks. Computers and Electrical Engineering 56, November 2016 (2016), 544--556. https:\/\/www.sciencedirect.com\/science\/article\/pii\/S0045790615003651.","journal-title":"Computers and Electrical Engineering"},{"issue":"1","key":"e_1_3_2_27_1","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1109\/TNET.2005.863478","article-title":"Connected sensor cover: Self-organization of sensor networks for efficient query execution","volume":"14","author":"Gupta Himanshu","year":"2006","unstructured":"Himanshu Gupta, Zongheng Zhou, Samir Das, and Quinyi Gu. 2006. Connected sensor cover: Self-organization of sensor networks for efficient query execution. 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Information Sciences 488, July 2019 (2019), 58\u201375. https:\/\/www.sciencedirect.com\/science\/article\/pii\/S0020025519301823?via%3Dihub.","journal-title":"Information Sciences"},{"issue":"4","key":"e_1_3_2_29_1","doi-asserted-by":"crossref","first-page":"660","DOI":"10.1109\/TWC.2002.804190","article-title":"An application-specific protocol architecture for wireless microsensor networks","volume":"1","author":"Heinzelman Wendi","year":"2002","unstructured":"Wendi Heinzelman, A. Chandrakasan, and H. Balakrishnan. 2002. An application-specific protocol architecture for wireless microsensor networks. IEEE Transactions on Wireless Communications 1, 4 (2002), 660\u2013670.","journal-title":"IEEE Transactions on Wireless Communications"},{"key":"e_1_3_2_30_1","doi-asserted-by":"crossref","DOI":"10.1090\/S0002-9904-1902-00923-3","article-title":"Mathematische problem","author":"Hilbert David","year":"1902","unstructured":"David Hilbert. 1901--1902. Mathematische problem. Bull. Amer. 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Energy efficiency optimization for multiple chargers in wireless rechargeable sensor networks. Elsevier Theoretical Computer Science 922, June 2022 (2022), 193--205. https:\/\/www.sciencedirect.com\/science\/article\/abs\/pii\/S0304397522002468.","journal-title":"Elsevier Theoretical Computer Science"},{"issue":"4","key":"e_1_3_2_33_1","doi-asserted-by":"crossref","first-page":"519","DOI":"10.1007\/s11036-005-1564-y","article-title":"The coverage problem in a wireless sensor network","volume":"10","author":"Huang Chi-Fu","year":"2005","unstructured":"Chi-Fu Huang and Yu-Chee Tseng. 2005. The coverage problem in a wireless sensor network. Springer Mobile Networks and Applications 10, 4 (2005), 519\u2013528.","journal-title":"Springer Mobile Networks and Applications"},{"key":"e_1_3_2_34_1","doi-asserted-by":"publisher","DOI":"10.1145\/1210669.1210674"},{"key":"e_1_3_2_35_1","doi-asserted-by":"crossref","DOI":"10.1016\/j.adhoc.2018.11.005","article-title":"Sensor and sink placement, scheduling and routing algorithms for connected coverage of wireless sensor networks","author":"Kabakulak Banu","year":"2019","unstructured":"Banu Kabakulak. 2019. Sensor and sink placement, scheduling and routing algorithms for connected coverage of wireless sensor networks. Ad Hoc Networks 86, April 2019 (2019), 83--102. https:\/\/www.sciencedirect.com\/science\/article\/pii\/S1570870518308199.","journal-title":"Ad Hoc Networks"},{"key":"e_1_3_2_36_1","doi-asserted-by":"crossref","unstructured":"Richard B. Kershner. 1968. On paving the plane. The American Mathematical Monthly 75 8 (1968) 839\u2013844.","DOI":"10.1080\/00029890.1968.11971075"},{"issue":"3","key":"e_1_3_2_37_1","doi-asserted-by":"crossref","first-page":"665","DOI":"10.2307\/2371320","article-title":"The number of circles covering a set","volume":"1","author":"Kershner Richard B.","year":"1939","unstructured":"Richard B. Kershner. 1939. The number of circles covering a set. American Journal of Mathematics 1, 3 (1939), 665\u2013671.","journal-title":"American Journal of Mathematics"},{"key":"e_1_3_2_38_1","doi-asserted-by":"crossref","DOI":"10.1016\/j.jnca.2015.08.010","article-title":"Critical density for coverage and connectivity in two-dimensional fixed-orientation directional sensor networks using continuum percolation","author":"Khanjary Mohammad","year":"2015","unstructured":"Mohammad Khanjary, Masoud Sabaei, and Mohammad Reza Meybodi. 2015. 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ACM New York, 144\u2013158."},{"key":"e_1_3_2_40_1","doi-asserted-by":"crossref","first-page":"102","DOI":"10.1016\/j.procs.2017.06.126","article-title":"Adaptive trap coverage in mobile sensor networks","volume":"110","author":"Kuo Chia-Hsu","year":"2017","unstructured":"Chia-Hsu Kuo, Tzung-Shi Chen, and Siou-Ci Syu. 2017. Adaptive trap coverage in mobile sensor networks. Procedia Computer Science 110 (2017), 102\u2013109. https:\/\/www.sciencedirect.com\/science\/article\/pii\/S1877050917313054.","journal-title":"Procedia Computer Science"},{"issue":"6","key":"e_1_3_2_41_1","doi-asserted-by":"crossref","first-page":"1699","DOI":"10.1016\/j.adhoc.2013.03.005","article-title":"Best and worst-case coverage problems for arbitrary paths in wireless sensor networks","volume":"11","author":"Lee Chunseok","year":"2013","unstructured":"Chunseok Lee, Donghoon Shin, Sang Won Bae, and Sunghee Choi. 2013. Best and worst-case coverage problems for arbitrary paths in wireless sensor networks. 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IEEE Transactions on Mobile Computing 4, 1 (2005), 84\u201392.","journal-title":"IEEE Transactions on Mobile Computing"},{"key":"e_1_3_2_50_1","first-page":"1380","volume-title":"Proceedings of the 20th Annual Joint Conference of the IEEE Computer and Communications Societies","author":"Megerian Seapahn","year":"2001","unstructured":"Seapahn Megerian, Farinaz Koushanfar, Miodrag Potkonjak, and Mani Srivastava. 2001. Coverage problems in wireless ad-hoc sensor networks. In Proceedings of the 20th Annual Joint Conference of the IEEE Computer and Communications Societies, 1380\u20131387."},{"key":"e_1_3_2_51_1","volume-title":"Proceedings of the Symposia of Pure Mathematics, 28, Bulletin of the American Mathematical Society","author":"Milnor John W.","year":"1976","unstructured":"John W. Milnor. 1976. Hilbert's problem 18. In Proceedings of the Symposia of Pure Mathematics, 28, Bulletin of the American Mathematical Society."},{"key":"e_1_3_2_52_1","article-title":"Coverage in mobile wireless sensor networks (M-WSN): A survey","author":"Mohamed Shaimaa M.","year":"2017","unstructured":"Shaimaa M. Mohamed, Haitham S. Hamza, and Iman Aly Saroit. 2017. Coverage in mobile wireless sensor networks (M-WSN): A survey. Computer Communications 110, September 2017 (2017), 133--150. https:\/\/www.sciencedirect.com\/science\/article\/pii\/S0140366417307235.","journal-title":"Computer Communications"},{"key":"e_1_3_2_53_1","doi-asserted-by":"crossref","first-page":"200","DOI":"10.1016\/j.compeleceng.2016.12.024","article-title":"A node failure and battery-aware coverage protocol for wireless sensor networks","volume":"64","author":"More Avinash","year":"2017","unstructured":"Avinash More and Vijay Raisinghani. 2017. A node failure and battery-aware coverage protocol for wireless sensor networks. Computers and Electrical Engineering 64, November 2017 (2017), 200\u2013219. https:\/\/www.sciencedirect.com\/science\/article\/pii\/S0045790616311570.","journal-title":"Computers and Electrical Engineering"},{"key":"e_1_3_2_54_1","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1016\/j.engappai.2017.07.020","article-title":"Game theory based node scheduling as a distributed solution for coverage control in wireless sensor networks","volume":"65","author":"Movassagh Mahdi","year":"2017","unstructured":"Mahdi Movassagh and Hadi S. Aghdasi. 2017. Game theory based node scheduling as a distributed solution for coverage control in wireless sensor networks. Engineering Applications of Artificial Intelligence 65, October 2017 (2017), 137\u2013146. https:\/\/www.sciencedirect.com\/science\/article\/abs\/pii\/S0952197617301689.","journal-title":"Engineering Applications of Artificial Intelligence"},{"key":"e_1_3_2_55_1","article-title":"Node placement for connected target coverage in wireless sensor networks with dynamic sinks","author":"Le Nguyen Phi","year":"2019","unstructured":"Phi Le Nguyen, Nguyen Thi Hanh, Nguyen Tien Khuong, Huynh Thi Thanh Binh, and Yusheng Ji. 2019. Node placement for connected target coverage in wireless sensor networks with dynamic sinks. Pervasive and Mobile Computing 59, October 2019 (2019), 101070. https:\/\/www.sciencedirect.com\/science\/article\/abs\/pii\/S1574119219301415.","journal-title":"Pervasive and Mobile Computing"},{"key":"e_1_3_2_56_1","doi-asserted-by":"crossref","DOI":"10.1090\/surv\/152","volume-title":"Combinatorial Geometry and Its Algorithmic Applications, Chapter 8","author":"Pach Janos","year":"2008","unstructured":"Janos Pach and Micha Sharir. 2008. Combinatorial Geometry and Its Algorithmic Applications, Chapter 8. American Mathematical Society."},{"key":"e_1_3_2_57_1","volume-title":"Uber die Zerlegung der Ebene in Polygone","author":"Reinhardt Karl","year":"1918","unstructured":"Karl Reinhardt. 1918. Uber die Zerlegung der Ebene in Polygone. Dissertation der Naturwiss. Fakultat. Universitat Frankfurt\/Main, Borna."},{"key":"e_1_3_2_58_1","doi-asserted-by":"crossref","DOI":"10.1016\/j.adhoc.2017.04.001","article-title":"Maximizing the wireless sensor networks lifetime through energy efficient connected coverage","author":"Roselin J.","year":"2017","unstructured":"J. Roselin, P. Latha, and S. Benitta. 2017. Maximizing the wireless sensor networks lifetime through energy efficient connected coverage. Ad Hoc Networks 62, July 2017 (2017), 1--10. https:\/\/www.sciencedirect.com\/science\/article\/pii\/S1570870517300689.","journal-title":"Ad Hoc Networks"},{"issue":"6","key":"e_1_3_2_59_1","doi-asserted-by":"crossref","first-page":"702","DOI":"10.1016\/j.adhoc.2004.02.001","article-title":"Unreliable sensor grids: Coverage, connectivity and diameter","volume":"3","author":"Shakkottai Sanjay","year":"2005","unstructured":"Sanjay Shakkottai, Rayadurgam Srikant, and Ness Shroff. 2005. Unreliable sensor grids: Coverage, connectivity and diameter. Ad Hoc Networks 3, 6 (2005), 702\u2013716.","journal-title":"Ad Hoc Networks"},{"key":"e_1_3_2_60_1","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1016\/j.comcom.2017.05.011","article-title":"\u03b1-Overlapping area coverage for clustered directional sensor networks","volume":"1091","author":"Sharmin Selina","year":"2017","unstructured":"Selina Sharmin, Fernaz Narin Nur, Md. Abdur Razzaque, Md. Mustafizur Rahman, and Sk. Md. Mizanur Rahman. 2017. \u03b1-Overlapping area coverage for clustered directional sensor networks. Computer Communications 1091, September 2017 (2017), 89\u2013103. https:\/\/www.sciencedirect.com\/science\/article\/pii\/S0140366417306072.","journal-title":"Computer Communications"},{"key":"e_1_3_2_61_1","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1016\/j.automatica.2018.03.014","article-title":"Coverage control for mobile sensor networks with limited communication ranges on a circle","volume":"92","author":"Song and Yuan Fan Cheng","year":"2018","unstructured":"Cheng Song and Yuan Fan. 2018. Coverage control for mobile sensor networks with limited communication ranges on a circle. Automatica 92, June 2018 (2018), 155\u2013161. https:\/\/www.sciencedirect.com\/science\/article\/pii\/S0005109818301018.","journal-title":"Automatica"},{"key":"e_1_3_2_62_1","article-title":"A novel connectivity and coverage algorithm based on shortest path for wireless sensor networks","author":"Sun Geng","year":"2018","unstructured":"Geng Sun, Yanheng Liu, Han Li, Aimin Wang, Shuang Liang, and Ying Zhang. 2018. A novel connectivity and coverage algorithm based on shortest path for wireless sensor networks. Computers and Electrical Engineering 71, October 2018 (2018), 1025--1039. https:\/\/www.sciencedirect.com\/science\/article\/pii\/S0045790617312983.","journal-title":"Computers and Electrical Engineering"},{"key":"e_1_3_2_63_1","volume-title":"Regular Figures","author":"Fejes Toth Laszlo","year":"1964","unstructured":"Laszlo Fejes Toth. 1964. Regular Figures. Oxford: Pergamon Press."},{"issue":"9","key":"e_1_3_2_64_1","doi-asserted-by":"crossref","first-page":"1280","DOI":"10.1109\/TPDS.2007.70808","article-title":"Distributed deployment schemes for mobile wireless sensor networks to ensure multi-level coverage","volume":"19","author":"Wang You-Chiun","year":"2008","unstructured":"You-Chiun Wang and Yu-Chee Tseng. 2008. Distributed deployment schemes for mobile wireless sensor networks to ensure multi-level coverage. IEEE Transactions on Parallel and Distributed Systems 19, 9 (2008), 1280\u20131294.","journal-title":"IEEE Transactions on Parallel and Distributed Systems"},{"key":"e_1_3_2_65_1","doi-asserted-by":"crossref","DOI":"10.1016\/j.compeleceng.2017.12.031","article-title":"An optimized Bidding-based coverage improvement algorithm for hybrid wireless sensor networks","author":"Vatankhah Ayda","year":"2018","unstructured":"Ayda Vatankhah and Shahram Babaie. 2018. An optimized Bidding-based coverage improvement algorithm for hybrid wireless sensor networks. Computers and Electrical Engineering 65, January 2018 (2018), 1--17. https:\/\/www.sciencedirect.com\/science\/article\/pii\/S0045790617322164.","journal-title":"Computers and Electrical Engineering"},{"key":"e_1_3_2_66_1","doi-asserted-by":"crossref","first-page":"200","DOI":"10.1016\/j.comnet.2017.05.008","article-title":"Coverage problem with uncertain properties in wireless sensor networks: A survey","author":"Wang Yang","year":"2017","unstructured":"Yang Wang, Shuang Wu, Zhiyin Chen, Xiaofeng Gao, and Guihai Chen. 2017. Coverage problem with uncertain properties in wireless sensor networks: A survey. Computer Networks 123, August 2017 (2017), 200\u2013232. https:\/\/www.sciencedirect.com\/science\/article\/pii\/S1389128617301998.","journal-title":"Computer Networks"},{"issue":"1","key":"e_1_3_2_67_1","doi-asserted-by":"crossref","first-page":"36","DOI":"10.1145\/1077391.1077394","article-title":"Integrated coverage and connectivity configuration for energy conservation in sensor networks","volume":"1","author":"Xing Guoliang","year":"2005","unstructured":"Guoliang Xing, Xiaorui Wang, Yuanfang Zhang, Chenyang Lu, Robert Pless, and Christopher Gill. 2005. Integrated coverage and connectivity configuration for energy conservation in sensor networks. ACM Transactions on Sensor Networks 1, 1 (2005), 36\u201372.","journal-title":"ACM Transactions on Sensor Networks"},{"key":"e_1_3_2_68_1","doi-asserted-by":"crossref","first-page":"268","DOI":"10.1016\/j.asoc.2018.03.053","article-title":"Hybrid multi-objective evolutionary algorithms based on decomposition for wireless sensor network coverage optimization","volume":"68","author":"Xu Ying","year":"2018","unstructured":"Ying Xu, Ou Ding, Rong Qu, Keqin Li. 2018. Hybrid multi-objective evolutionary algorithms based on decomposition for wireless sensor network coverage optimization. Applied Soft Computing 68, July 2018 (2018), 268\u2013282. https:\/\/www.sciencedirect.com\/science\/article\/abs\/pii\/S1568494618301868.","journal-title":"Applied Soft Computing"},{"issue":"4","key":"e_1_3_2_69_1","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1007\/s10776-006-0036-z","article-title":"On connected multiple point coverage in wireless sensor networks","volume":"13","author":"Yang S.","year":"2006","unstructured":"S. Yang, F. Dai, M. Cardei, and J. Wu. 2006. On connected multiple point coverage in wireless sensor networks. International Journal of Wireless Information Networks 13, 4 (2006), 289\u2013301.","journal-title":"International Journal of Wireless Information Networks"},{"key":"e_1_3_2_70_1","volume-title":"Proceedings of the 10th IEEE International Conference on Network Protocols","author":"Ye Fan","year":"2002","unstructured":"Fan Ye, Geng Zhong, Songwu Lu, and Lixia Zhang. 2002. PEAS: A robust energy conserving protocol for long-lived sensor networks. In Proceedings of the 10th IEEE International Conference on Network Protocols. DOI: 10.1109\/ICNP.2002.1181406"},{"key":"e_1_3_2_71_1","doi-asserted-by":"publisher","DOI":"10.1007\/s11276-006-5875-0"},{"issue":"11","key":"e_1_3_2_72_1","doi-asserted-by":"crossref","first-page":"937","DOI":"10.1016\/j.aeue.2013.05.004","article-title":"CWSC: Connected k-coverage working sets construction algorithm in wireless sensor networks","volume":"67","author":"Yu Jiguo","year":"2013","unstructured":"Jiguo Yu, Xiu Deng, Dongxiao Yu, Guanghui Wang, and Xin Gu. 2013. CWSC: Connected k-coverage working sets construction algorithm in wireless sensor networks. International Journal of Electronics and Communications 67, 11 (2013), 937\u2013946.","journal-title":"International Journal of Electronics and Communications"},{"issue":"1","key":"e_1_3_2_73_1","first-page":"89","article-title":"Maintaining sensing coverage and connectivity in large sensor networks","volume":"1","author":"Zhang Honghai","year":"2005","unstructured":"Honghai Zhang and Jennifer C. Hou. 2005. Maintaining sensing coverage and connectivity in large sensor networks. Ad Hoc and Sensor Wireless Networks Journal 1, 1\u20132 (2005), 89\u2013124.","journal-title":"Ad Hoc and Sensor Wireless Networks Journal"},{"issue":"2","key":"e_1_3_2_74_1","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1145\/1149283.1149287","article-title":"Models and solutions for radio irregularity in wireless sensor networks","volume":"2","author":"Zhou Gang","year":"2006","unstructured":"Gang Zhou, Tian He, Sudha Krishnamurthy, and John A. Stankovic. 2006. Models and solutions for radio irregularity in wireless sensor networks. ACM Transactions on Sensor Networks 2, 2 (2006), 221\u2013262.","journal-title":"ACM Transactions on Sensor Networks"},{"key":"e_1_3_2_75_1","first-page":"373","volume-title":"Proceedings of the 24th International Conference on Computer Communications and Networks","author":"Zhou Zongheng","year":"2004","unstructured":"Zongheng Zhou, Samir Das, and Himanshu Gupta. 2004. Connected k-coverage problem in sensor networks. In Proceedings of the 24th International Conference on Computer Communications and Networks. Rosemont, Illinois, 373\u2013378."},{"issue":"8","key":"e_1_3_2_76_1","doi-asserted-by":"crossref","first-page":"978","DOI":"10.1109\/TC.2005.123","article-title":"A distributed coverage- and connectivity-centric technique for selecting active nodes in wireless sensor networks","volume":"54","author":"Zou Yi","year":"2005","unstructured":"Yi Zou and Krishnendu Chakrabarty. 2005. A distributed coverage- and connectivity-centric technique for selecting active nodes in wireless sensor networks. IEEE Transactions on Computers 54, 8 (2005), 978\u2013991.","journal-title":"IEEE Transactions on Computers"},{"key":"e_1_3_2_77_1","first-page":"594","volume-title":"Proceedings of the 1st Annual IEEE Communications Society Conference on Sensor, Mesh, and Ad Hoc Communications and Networks","author":"Zhou Zongheng","year":"2005","unstructured":"Zongheng Zhou, Samir Das, and Himanshu Gupta. 2005. Fault tolerant connected sensor cover with variable sensing and transmission ranges. In Proceedings of the 1st Annual IEEE Communications Society Conference on Sensor, Mesh, and Ad Hoc Communications and Networks. California, 594\u2013604."},{"key":"e_1_3_2_78_1","unstructured":"Wilson. 2022. 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