## 2 Related Works
### Clustering Optimization Algorithms  
Low Energy Adaptive Clustering Hierarchy (LEACH) was the first clustering protocol for WSNs that achieved low energy dissipation and latency without sacrificing application-specific quality [18]. Each node in the cluster sends its data to a local cluster-head, and the periodic CH selection strategy evenly balances the energy consumption among all the nodes to some extent. However, the size of clusters in LEACH are equal to each other, and each CH transmits data to the sink via a single hop. This causes more energy consumption for communication. For this reason, the uneven clustering model was then proposed in [19] for balancing the energy consumption of CHs. However, the disadvantage of this model is that it can only be applied in WSNs with two-hop inter-cluster communication. In [20], the size of clusters located around the sink is smaller than those far away from the sink, as shown in Figure 1. In this case, the cluster heads near the sink consume less energy while collecting data from their direct children, so they have enough energy to forward data uploaded from other clusters. Although this type of network structure efficiently balances the energy consumption of the whole network and alleviates the energy hole problem near the sink, the workload between the CHs and common nodes is still unbalanced. Moreover, the unsuitable location of the cluster header may also increase the energy consumption for communication between this CH and its members. [PERSON] et al. regarded that inter-cluster energy consumption is more than intra-cluster energy consumption in a large-scale WSN [16]. Therefore, they designed EBCAG to achieve energy balance among CHs and to decrease the total energy consumption of nodes. Each node has a gradient value which determines the optimal radius of the cluster as well as the routing strategy for CHs. Nevertheless, the energy consumption for calculating the optimal radius is still higher, which decreases the energy efficiency of the whole network. To solve the unbalanced energy consumption problem in a randomly distributed network, a self-organized clustering method was proposed in [21]. The cluster radius is calculated according to the density of nodes as well as the average distance between each node and the base station. It effectively balances the energy consumption among clusters with different density. However, each node must maintain a cluster information table, which increases the computational complexity. Moreover, due to the unreasonable local optimal routing strategy, the load difference between cluster heads is still large. In [22], the network is divided into unequal clusters and there are three types of nodes in each cluster. The data collected by the ordinary nodes are no longer sent to the cluster header directly but rather forwarded by the leader nodes to the CH. This effectively saves the intra-cluster energy and prolongs the network lifetime, but the CH selection strategy of this algorithm is a little complicated. [PERSON] et al. employed a non-uniform clustering algorithm to mitigate the energy hole problem. In addition to the hop distance as well as the residual energy, the number of neighbor nodes is also considered during the CH selection process, which prolongs the network lifetime [23]. Moreover, to further save node energy, the CH selection is not executed frequently and a sleep scheduling mechanism is also adopted in clustering. For circular networks, [PERSON] et al. proposed the EBCH method to avoid the energy hole problem [17]. The network is divided into several coronas, and then different sizes of clusters are formed in each sector. An optimum load distribution model is designed in which the CHs send some data to the sink directly and the rest of the data is forwarded to the CHs of the inner coronas to balance the energy consumption among CHs. Unfortunately, this model is not suitable for a large-scale network. The network model proposed in this paper is similar to that in EBCH.