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The algorithm includes two stages: routing establishment and data transmission. During the first stage, a mathematical model is constructed for transmission distance to find the neighbors at the optimal distances and the underwater network links are established. In addition, IEBR will select relays based on the depth of the neighbors, minimize the hops in a link based on the depth threshold, and solve the problem of data transmission loop. During the second stage, the links built in the first stage are dynamically changed based on the energy level (EL) differences between the neighboring nodes in the links, so as to achieve energy balance of the entire network and extend the network lifetime significantly. Simulation results show that compared with other typical energy-balanced routing algorithms, IEBR presents superior performance in network lifetime, transmission loss, and data throughput.<\/jats:p>","DOI":"10.1186\/s13638-019-1533-y","type":"journal-article","created":{"date-parts":[[2019,9,11]],"date-time":"2019-09-11T23:04:05Z","timestamp":1568243045000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":25,"title":["Improved energy-balanced algorithm for underwater wireless sensor network based on depth threshold and energy level partition"],"prefix":"10.1186","volume":"2019","author":[{"given":"Pan","family":"Feng","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5829-6121","authenticated-orcid":false,"given":"Danyang","family":"Qin","sequence":"additional","affiliation":[]},{"given":"Ping","family":"Ji","sequence":"additional","affiliation":[]},{"given":"Min","family":"Zhao","sequence":"additional","affiliation":[]},{"given":"Ruolin","family":"Guo","sequence":"additional","affiliation":[]},{"given":"Teklu Merhawit","family":"Berhane","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2019,9,12]]},"reference":[{"key":"1533_CR1","first-page":"1","volume":"6","author":"L Xin","year":"2018","unstructured":"L Xin, J Min, Z Xueyan, et al., A novel multi-channel Internet of Things based on dynamic spectrum sharing in 5G communication[J]. 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