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Netw."],"published-print":{"date-parts":[[2025,3,31]]},"abstract":"<jats:p>\n            Coverage and connectivity are the major performance metrics that reflect the quality of service provided by heterogeneous planar wireless sensor networks (PWSNs) monitoring a planar field of interest (PFoI), where the deployed sensors may not necessarily have the same capabilities in terms of their sensing range, communication range, and maximum battery-power capacity. Precisely, coverage is considered as the main functionality of PWSNs, which is meaningful only when connectivity is guaranteed. Therefore, it is important that both coverage and connectivity be jointly considered in the deployment of heterogeneous PWSNs. In order to account for joint coverage and connectivity, we propose to solve the problem of connected\n            <jats:italic>k<\/jats:italic>\n            -coverage in heterogeneous PWSNs, where every point in a PFoI is covered by at least\n            <jats:italic>k<\/jats:italic>\n            sensors simultaneously, while all the deployed sensors are mutually connected, either directly or indirectly, with\n            <jats:italic>k<\/jats:italic>\n            &gt; 1. While most existing studies of this problem focus on homogeneous sensors, which have the same above-mentioned capabilities (i.e., initial energy, sensing range, and communication range), our study in this article considers heterogeneous ones. More specifically, we propose a hierarchical (or multitier) deployment of heterogeneous sensors in a square FoI, which is divided into concentric square bands with the same width difference to achieve\n            <jats:italic>k<\/jats:italic>\n            -coverage of this PFoI. Based on this multitier sensor deployment and the slicing of a square FoI into square bands for\n            <jats:italic>k<\/jats:italic>\n            -coverage, we establish the necessary relationship for connectivity among the sensors located in adjacent bands. Finally, we propose our heterogeneous\n            <jats:italic>k<\/jats:italic>\n            -coverage protocol and validate our theoretical analysis using simulation results. We find that the deployment of heterogeneous sensors helps achieve much better results compared to those obtained using homogeneous sensors. Furthermore, our proposed protocol outperforms an existing connected\n            <jats:italic>k<\/jats:italic>\n            -coverage protocol for heterogeneous PWSNs with respect to various performance metrics.\n          <\/jats:p>","DOI":"10.1145\/3713074","type":"journal-article","created":{"date-parts":[[2025,1,21]],"date-time":"2025-01-21T11:23:11Z","timestamp":1737458591000},"page":"1-27","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":3,"title":["Hierarchical Deployment and Square Tessellation for Connected k-Coverage in Heterogeneous Planar Wireless Sensor Networks"],"prefix":"10.1145","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3916-0939","authenticated-orcid":false,"given":"Kalyan","family":"Nakka","sequence":"first","affiliation":[{"name":"Texas A&amp;M University, College Station, United States"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3529-2862","authenticated-orcid":false,"given":"Habib M.","family":"Ammari","sequence":"additional","affiliation":[{"name":"WiSeMAN Research Center \/ School of Engineering \/ College of Arts and Sciences, Texas A&amp;M International University, Laredo, United States"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2025,3,22]]},"reference":[{"key":"e_1_3_1_2_2","doi-asserted-by":"publisher","DOI":"10.1109\/98.878533"},{"key":"e_1_3_1_3_2","doi-asserted-by":"publisher","DOI":"10.1109\/twc.2002.804190"},{"key":"e_1_3_1_4_2","article-title":"PEAS: A robust energy conserving protocol for long-lived sensor networks","author":"Ye Fan","year":"2003","unstructured":"Fan Ye, G. 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