{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,16]],"date-time":"2026-02-16T08:51:59Z","timestamp":1771231919364,"version":"3.50.1"},"reference-count":54,"publisher":"Association for Computing Machinery (ACM)","issue":"1","license":[{"start":{"date-parts":[[2013,11,1]],"date-time":"2013-11-01T00:00:00Z","timestamp":1383264000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"DOI":"10.13039\/100000144","name":"Division of Computer and Network Systems","doi-asserted-by":"publisher","award":["CNS-0917089 and CNS-1054935"],"award-info":[{"award-number":["CNS-0917089 and CNS-1054935"]}],"id":[{"id":"10.13039\/100000144","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100007270","name":"University of Michigan","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100007270","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Sen. Netw."],"published-print":{"date-parts":[[2013,11]]},"abstract":"<jats:p>\n            Coverage is one of the fundamental concepts in the design of wireless sensor networks (WSNs) in the sense that the monitoring quality of a phenomenon depends on the quality of service provided by the sensors in terms of how well a field of interest is covered. It enables the sensors to detect any event that may occur in the field, thus, meeting the application-specific requirements. Several applications require\n            <jats:italic>k<\/jats:italic>\n            -\n            <jats:italic>coverage<\/jats:italic>\n            , where each point in the field is covered by at least\n            <jats:italic>k<\/jats:italic>\n            sensors, which helps increase data availability to ensure better data reliability. Achieving\n            <jats:italic>k<\/jats:italic>\n            -coverage of a field of interest becomes a more challenging issue in sparsely deployed WSNs. Though the problem of coverage in WSNs has been well studied in the literature, only little research efforts have been devoted to the case of sparsely deployed WSNs. Thus, in this article, we investigate the problem of\n            <jats:italic>k<\/jats:italic>\n            -coverage in sparse WSNs using static and mobile sensors, which do not necessarily have the same communication range, sensing range, and energy supply. Precisely, we propose an optimized, generalized framework for\n            <jats:italic>k<\/jats:italic>\n            -coverage in sparsely deployed WSNs, called\n            <jats:italic>k<\/jats:italic>\n            -SCHEMES, which exploits sensor heterogeneity and mobility. First, we characterize\n            <jats:italic>k<\/jats:italic>\n            -coverage using heterogeneous sensors based on\n            <jats:italic>Helly<\/jats:italic>\n            's Theorem. Second, we introduce our energy-efficient four-tier architecture to achieve mobile\n            <jats:italic>k<\/jats:italic>\n            -coverage of a region of interest in a field. Third, on top of this architecture, we suggest two data-gathering protocols, called direct data-gathering and forwarding chain-based data-gathering, using the concept of mobile proxy sink. We found that the second data-gathering protocol outperforms the first one. For energy-efficient forwarding, we compute the minimum transmission distance between any pair of consecutive mobile proxy sinks forming the forwarding chain as well as the corresponding optimum number of mobile proxy sinks in this chain. We corroborate our analysis with several simulation results.\n          <\/jats:p>","DOI":"10.1145\/2529978","type":"journal-article","created":{"date-parts":[[2013,12,10]],"date-time":"2013-12-10T13:28:12Z","timestamp":1386682092000},"page":"1-33","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":10,"title":["Joint\n            <i>k<\/i>\n            -coverage and data gathering in sparsely deployed sensor networks -- Impact of purposeful mobility and heterogeneity"],"prefix":"10.1145","volume":"10","author":[{"given":"Habib M.","family":"Ammari","sequence":"first","affiliation":[{"name":"WiSeMAN Research Lab., University of Michigan-dearborn, Dearborn, Michigan"}]}],"member":"320","published-online":{"date-parts":[[2013,12,6]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10878-006-5975-x"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00454-009-9238-3"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1109\/TC.2011.82"},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.1109\/ICDCS.2009.67"},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1145\/1132905.1132921"},{"key":"e_1_2_1_6_1","doi-asserted-by":"crossref","unstructured":"Bollob\u00e1s B. 2006. The Art of Mathematic: Coffee Time in Memphis. Cambridge University Press.  Bollob\u00e1s B. 2006. The Art of Mathematic: Coffee Time in Memphis. Cambridge University Press.","DOI":"10.1017\/CBO9780511816574"},{"key":"e_1_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.1109\/98.878533"},{"key":"e_1_2_1_8_1","doi-asserted-by":"publisher","DOI":"10.1109\/MPRV.2004.1269130"},{"key":"e_1_2_1_9_1","unstructured":"Cao G. Kesidis G. La Porta T. Yao B. and Phoha S. 2006. Purposeful mobility in tactical sensor networks. In Sensor Network Operations Wiley-IEEE Press 113.  Cao G. Kesidis G. La Porta T. Yao B. and Phoha S. 2006. Purposeful mobility in tactical sensor networks. 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