## 1 Introduction
This algorithm adopts relevant concepts (graph coloring problem or connected dominating set) of graph theory to adjust the depth of nodes through the depth-adjustment to reduce redundant coverage, thus completing the overall 3D coverage. [PERSON] et al. [14] proposed a self-deployment depth adjustment algorithm that mainly focuses on maximizing network coverage by constantly adjusting node depths to reduce coverage overlaps between two neighboring nodes. Meanwhile, this algorithm adopts graph coloring problem to solve the distribution of network group IDs, based on coverage overlaps of intra-cluster nodes for different node assigned with different group IDs, and the cluster head node applies the centralized approach to nodes executing depth adjustment, decreasing coverage overlaps and thus increasing overall network coverage for the 3D monitoring space. [PERSON] et al. [15] proposed depth adjustment algorithms based on a connected dominating set, and this algorithm is derived from [14]. Compared with the latter algorithm, the former algorithm initially constitutes a connected backbone, and then the dominant node respectively optimizes its non-dominators located inside their connected dominating set in an iterative way. Moreover, the algorithm ensures the full network connectivity, maximizes network overall coverage rate, and reduces the deployment energy consumption. Meanwhile, many scholars have proposed deployment algorithms based on computational geometry for traditional sensor networks and supported many applications in real industrial markets. [PERSON] et al. [22] proposed a self-deployment algorithm based on Voronoi diagrams. The algorithm constant constructs Voronoi diagrams of all nodes to reflect the nodes' movement state and optimize the location of nodes, thus improving network operator performance. [PERSON] et al. [23] used Voronoi diagrams to detect network coverage holes and to control the movement of nodes to repair coverage holes. The algorithm argues that calculating the correct Voronoi polygons can help to optimize its healing efficiency of coverage holes, if they exist. However, network connectivity is not considered. The construction of the Voronoi diagram needs to execute global computation, so the communication costs are large. In recent years, some scholars have transferred the concept of computational geometry deployment strategies to UWSN applications. [PERSON] et al. [24] proposed Voronoi-based depth-adjustment algorithm (VBDA) for UWSNs. First, all of the nodes are randomly deployed on the water surface through the formation of the Voronoi polygon of each node to calculate the network coverage redundancy, the Voronoi region area of each node in same layer to determine the depth-adjustment distance, and then the iterative operating process of depth adjustment until the last layer network deployment arrives at the water bottom threshold. The VBDA is first proposed based on the Vonoroi deployment strategy for UWSNs. Through the vertical depth adjustment of the nodes to reduce the network coverage redundancy, the 3D network coverage is increased. However, the algorithm does not consider the network connectivity between two neighboring layers, which makes the network connectivity performance very poor with a small \(\alpha\) (the ratio of node communication radius to sensing radius). Moreover, as the process of network deployment proceeds, fewer nodes are available to execute network deployment when the process of depth-adjustment reaches the water bottom threshold, then its network coverage performance is relatively inferior. Meantime, the VBDA is a centralized algorithm, and all nodes have more communication costs and then consume more communication energy, thereby affecting network operator performance. The deployment issues mentioned above, considering the above-proposed deployment algorithms of UWSNs based on computational geometry consisting of vertical movement deployment strategy, the VBDA cannot improve network coverage performance while ensuring full network connectivity.