## 2 Related Works  
In recent years, in the field of sensing coverage, many solutions have been proposed by scholars for the purpose of accurately detecting the position of coverage holes and using effective repair methods to repair holes, thus improving the QoS of WSNs. Among them, the swarm intelligence optimization algorithm is used for coverage hole detection and repair in a two-dimensional environment. [PERSON] et al. [17] presented a multi-objective fault-tolerant routing identification approach combined with a particle swarm algorithm and a genetic algorithm. It integrates coverage, communication cost, proximity, and other factors and uses particle swarm technology to monitor the nodes in the cluster for faults and a genetic algorithm to determine fault-free status. [PERSON] et al. [18] divided the specific region based on the static node density deployed in the network, used a round robin working mechanism for the overlap between nodes, and finally added nodes to repair the holes by using a locust optimization algorithm combined with the objective function of the size of the holes and the node movement distance. However, connectivity and the minimum transmission path during the node repair process were not considered. The authors of [19] constructed auxiliary lines to detect underground monitoring area holes by mathematical methods and used tree seeding algorithms with randomness, optimality, and spiral generation techniques to generate new nodes to repair the blind zones; however, the effectiveness of the algorithm complexity was not demonstrated in comparative experiments. [PERSON] et al. [20] proposed consideration of the mobile state of nodes as the motion of artificial fish to repair the holes. Based on a comparison with a correlation threshold, the algorithm introduced jumping and respawning behavior when the population fell into local extremes. It extended the search range of the population, and effectively improved network coverage, which did not demonstrate the performance of the nodes in the aspect of energy consumption as well as connectivity. Some scholars have proposed a strategy to prioritize the use of boundary nodes to address the coverage hole problem in a two-dimensional scenario. [PERSON] et al. [21] focused on the phenomenon of coverage blind zones due to the node failure, the algorithm divided the nodes in the region into the edge and interior nodes, where the nodes are moved by the perceived gravity of the surrounding environment. By calculating the direction and distance of movement, as well as energy consumption, priority is given to moving edge nodes, which effectively reduces unnecessary movement energy consumption. [PERSON] et al. [22] used unsupervised machine learning to identify interior and boundary nodes, and a social spider optimization algorithm was used to adjust Gaussian mixture modelling parameters with maximized expectation to improve the detection rate of coverage holes. The authors of [23] proposed an enhanced hole-boundary detection algorithm for the detection of node failures in networks and connectivity reconstruction after node failures, which effectively avoids network congestion during data transmission and thus improves energy efficiency, but it is difficult to accurately detect the hole boundary when the hole range is large. Some scholars have also effectively combined mathematical thinking with the coverage hole problem. [PERSON] et al. [24] proposed the development of a prioritization strategy in hybrid heterogeneous networks based on mathematical geometric approaches to determine the size of hole regions and use a limited quantity of mobile nodes to repair the holes, which reduces the redundancy of mobile nodes in the area, with a lack of analysis of the mobile nodes' energy consumption aspects.