## 2 Related Work  
In the choice of CHs, the criteria of existing clustering algorithms are different. We summarize the previous work about the selection methods of CHs as follows. Low energy adaptive clustering hierarchy (LEACH) [23, 24] randomly rotates the CHs to distribute the energy load among all of the sensor nodes in the network. The CHs' selection of them uses a probability scheme by which each node determines whether it is selected to be the CH based on the random number generated by itself. Although LEACH is simple and does not require a large communication overhead, it does not consider the energy and the distribution of CHs, which makes the algorithm energy-inefficient. Different from LEACH, DCHSintroduces the residual energy of nodes into the probability threshold, which improves the energy efficiency of the entire network and can extend the network lifetime effectively. Some other similar cluster head election algorithms based on the residual energy of nodes are also proposed in [25, 26, 27, 28, 29]. The algorithms proposed in [26, 30, 31] are the centralization version of LEACH. They improve LEACH by using central control, that is the BS collects information, such as node energy and location, from all sensor nodes and selects the optimal CHs. The defects of these are that the clustering process may be very complex and can generate more overhead. Thus, the centralized clustering algorithm has poor scalability and is only suitable for small or medium-sized networks. For this reason, most of the effective clustering algorithms are all distributed. Hybrid energy efficient distributed clustering (HEED) [32] is a distributed clustering algorithm, in which CHs are selected from the sensor nodes based on a certain probability related to a hybrid of energy and communication cost. Only sensor nodes with high residual energy and lower intra-communication costs can become CHs. Clusters generated by HEED are more well-distributed than LEACH. However, it cannot guarantee the optimal number of elected CHs and the network connectivity. A similar, but improved, clustering algorithm, EEDC, is proposed in [33], which can reduce the number of iterations and prolong the network lifetime efficiently. An energy-aware data gathering protocol for wireless sensor networks ( EADEEG) [34] is a novel distributed clustering algorithm. It elects cluster heads based on the ratio between the average residual energy of neighbor nodes and the residual energy of the node itself, which can achieve a good CH distribution and prolong the network lifetime. However, in some cases, there are \"isolate points\" in EADEEG, which influence the monitoring performance and lifetime of networks. In addition, it chooses \(2R_{a}\) as the inter-cluster communication radius, where \(R_{a}\) denotes the cluster radius, which cannot ensure the connectivity among CHs. Similar to EADEEG, but improved, cluster head election algorithms are adopted in the cluster setup phase of clustering algorithms [35, 36, 37], which can effectively solve the \"isolate points\" problem existing in EADEEG, and the CHs generated by them can cover all the nodes in the network. For the disconnected problem, two energy-efficient clustering algorithms, called a distributed algorithm of clustering technology based on parameters used for electing CHs (BPEC) [38]and energy-efficient cluster formation protocol (EECF) [39], can keep all of the CHs connected by choosing 3\(R_{a}\) as the inter-cluster communication radius. Besides the node degree, location and energy, there still exist many other considerable influencing factors when designing clustering algorithms, such as coverage, connectivity, mobility, and so on. [PERSON] _et al._ in [40] proposed some good cluster head election techniques. However, this paper focuses on coverage preservation, while the energy consumption and network lifetime is on the back burner. As a consequence, many hybrid control algorithms are also widely used in CHs selection.