{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,23]],"date-time":"2025-10-23T09:35:21Z","timestamp":1761212121440,"version":"build-2065373602"},"reference-count":11,"publisher":"World Scientific Pub Co Pte Ltd","issue":"08","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2025,11]]},"abstract":"<jats:p>In wireless sensor networks (WSNs), barrier coverage is used to detect objects crossing a protected area or to monitor an area of interest. It is a critical application within WSNs. Due to cost considerations, sensor nodes are often randomly deployed along the boundary of the monitoring area, constructing multiple barriers to maximize network lifetime. These barriers operate based on a sleep-wakeup schedule. However, a new security issue, known as the barrier-breach problem, can arise during this schedule. In this paper, we propose a novel barrier coverage construction algorithm (BCC_VL) that addresses the barrier-breach problem using Virtual Lines (VLs), a concept that has not been explored before. By employing VLs, our algorithm can construct a barrier coverage without any breaches. We conducted simulations to validate the proposed method, and the results were compared and verified against the MaxFlow model. In the MaxFlow_RM method, our approach demonstrated superior performance in identifying barrier coverage.<\/jats:p>","DOI":"10.1142\/s1793830924501246","type":"journal-article","created":{"date-parts":[[2024,11,13]],"date-time":"2024-11-13T21:14:12Z","timestamp":1731532452000},"source":"Crossref","is-referenced-by-count":0,"title":["Barrier coverage construction without barrier-breach using virtual lines"],"prefix":"10.1142","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1978-2105","authenticated-orcid":false,"given":"Joong-Lyul","family":"Lee","sequence":"first","affiliation":[{"name":"Department of Mathematics and Computer Science, University of North Carolina at Pembroke, Pembroke NC 28372, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0004-1666-2807","authenticated-orcid":false,"given":"Ke","family":"Su","sequence":"additional","affiliation":[{"name":"Department of Computer Science, University of Texas at Dallas, Richardson, TX 75080, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yisheng","family":"Zhou","sequence":"additional","affiliation":[{"name":"Department of Computer Science, University of Texas at Dallas, Richardson, TX 75080, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2024,12,26]]},"reference":[{"key":"S1793830924501246BIB001","first-page":"63","volume-title":"Proc. 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