## 3 Algorithm Description and Process  
### Problem Description  
Some scholars have already researched the node self-deployment problem for move-restricted underwater sensor nodes. However, these algorithms are suitable only for the node deployment of underwater sensor nodes with a fixed communication radius and only consider the criterion of network coverage or the network connectivity rate without considering the network reliability problem and the energy consumption balance of the network. In existing algorithms, adjacent nodes are far away from one another as much as possible to minimize the overlapping area among themselves and to maximize the network coverage rate. Consequently, the probability that nodes are deployed near the sink node decreases to some degree, and the number of nodes within a certain range around the sink node cannot be guaranteed. Even the use of a topology control method with a good effect cannot improve network performance after deployment. In addition, in the process of adjusting the node depth, algorithms only focus on the _CRR_ of the position wherein the overlapping area of one node with a specific node is the smallest and ignores the _CRR_ of the position where the overlapping area is not the smallest. Therefore, the network coverage rate should be improved. Moreover, existing algorithms that consider the network connectivity rate (_i.e._, CDA) do not consider the balance of network energy consumption during network operations. When the number of nodes is dense, the network formed by CDA can modify the network topology by a routing protocol to achieve energy consumption balance. By contrast, when the number of nodes is relatively sparse, the network formed by CDA may have no other connected topology or ineffectively route protocols because the number of nodes is insufficient. At this time, an operated network can only use the topological structure formed during the process of node deployment. Furthermore, the energy consumption balance of the topological structure performs badly, _i.e._, the energy consumption balance of the network formed by CDA is poor when the number of nodes is relatively sparse. Therefore, this study defines the following problem: \"After \(N\) nodes are randomly and uniformly scattered on the water surface of the target area, a node self-deployment algorithm with an adjustable communication radius is designed to adjust the depth of nodes, improve network reliability, balance, reduce energy consumption, and maximize network coverage on the premise of maintaining network connectivity\". To solve the defined problem, this study proposes a distributed self-deployment algorithm for underwater sensor nodes (_i.e._, URSA). After all nodes are scattered on the water surface randomlyand uniformly, each node firstly begins the process of uneven clustering according to the distance to the sink node. This process forms a layout wherein the number of cluster head nodes in an area close to the sink node becomes large and the scale of the cluster in that area becomes small. Second, every cluster head node uses the hybrid radius path-selection method to select its next-hop node concurrently according to the principle of minimizing the energy consumption of sending a message from itself to the sink node. The cluster head node then forms a connected path to the sink node. The feature of the connected path is that if the cluster head node is far away from the sink node, its path to the next-hop node is long, thus ensuring network connectivity and saving and balancing energy consumption in network operations. Third, each cluster begins to adjust the depth in an iterative manner, and the corresponding cluster head node selects its own adjusting position with the principle that the distance between itself and its next-hop node after adjustment is 1 m longer than that before adjustment.