{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,29]],"date-time":"2026-06-29T06:45:19Z","timestamp":1782715519689,"version":"3.54.5"},"reference-count":38,"publisher":"MDPI AG","issue":"13","license":[{"start":{"date-parts":[[2026,6,27]],"date-time":"2026-06-27T00:00:00Z","timestamp":1782518400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The deployment of three-dimensional Wireless Sensor Networks (3D WSNs) in complex environments demands robust topological control to ensure both reliable and fault-tolerant sensing and communication. In order to simultaneously achieve the two objectives over time, an even distribution of the sensors\u2019 energy consumption is essential. Achieving optimal sensor distribution on non-planar surfaces (3D shapes), such as spheres, while maintaining reliable network routes is a significant algorithmic challenge. While many approaches effectively and efficiently addressed the aforementioned goals in 2D environments, and there exists a significant body of work on coverage, connectivity, or energy efficiency in 3D sensor networks, the solutions for either can not straightforwardly be adapted to the 3D case (e.g., some coverage problems are optimally solved for 2D but are still open problems in the 3D case), or the solutions to the individual problems in the 3D case are not integrated gracefully to solve the entire problem. Moreover, these problems have not been address for the realistic spherical 3D case. This paper presents a novel holistic algorithm designed to generate energy-efficient, optimal sensor topologies over spherical 3D sensor networks that guarantee redundant coverage to deal with sensor failures, connectivity with controlled redundancy support for more efficient communication, and the creation of a hierarchy over the flat network to deal with energy issues, at would be appropriate for real-world tasks. The proposed methodology is executed in three primary phases. First, it approaches the geometric part of the problem to determine the optimal placement of sensor nodes on the surface of a sphere, guaranteeing k-coverage for the target area. Second, it creates a reliable inner-layer backbone network of sensors that establishes k-connectivity ensuring a reliable network for data transmission and distribution of total power in the whole network. Finally, after formulating sensors into clusters, a mathematical formula to change each cluster head is created so that we achieve even distribution of energy consumption across the network. To validate the proposed approach, a 3D WSN software simulator was developed. This tool provides a dynamic visual simulation of the network, enabling the execution, visualization and simulation of the hybrid algorithm and any other 3D WSN.<\/jats:p>","DOI":"10.3390\/s26134085","type":"journal-article","created":{"date-parts":[[2026,6,29]],"date-time":"2026-06-29T05:49:33Z","timestamp":1782712173000},"page":"4085","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Topology Control in Spherical 3D Sensor Networks"],"prefix":"10.3390","volume":"26","author":[{"ORCID":"https:\/\/orcid.org\/0009-0005-0775-7983","authenticated-orcid":false,"given":"Nikolaos","family":"Zarifis","sequence":"first","affiliation":[{"name":"Department of Electrical & Computer Engineering, University of Thessaly, 38334 Volos, Greece"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3473-4187","authenticated-orcid":false,"given":"Dimitrios","family":"Katsaros","sequence":"additional","affiliation":[{"name":"Department of Electrical & Computer Engineering, University of Thessaly, 38334 Volos, Greece"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,6,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"32","DOI":"10.1145\/1978802.1978811","article-title":"Coverage problems in sensor networks: A survey","volume":"43","author":"Wang","year":"2011","journal-title":"ACM Comput. 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