## 2 Related Work  
Low-Energy Adaptive Clustering Hierarchy (LEACH) is a classic clustering algorithm for WSNs. It is a clustering-based protocol that utilizes randomized rotation of local cluster heads to evenly distribute the energy load among the sensors in the network. As the authors claimed, LEACH reduces communication energy by as much as 8 times compared with direct transmission and minimum-transmission-energy routing [9]. Its advantages can be summarized as follows: first, it can prolong the network lifetime compared to the original plane routing protocol and static clustering algorithms. Second, the cluster heads fuse the data collected from the corresponding areas, and transfer it to the sink node, which could effectively raise the energy use ratio. Finally, LEACH distributes the task among every sensor node, reducing the overload of individual nodes. LEACH-C was proposed in [10] to cope with the disadvantages of LEACH. It uses a central control algorithm to form clusters, which distributes cluster heads more evenly throughout the network. To make sure the energy load is evenly distributed among all nodes, the base station computes the average node energy. Nodes with energy below the average cannot be used as cluster heads for the current round [10]. However, LEACH-type protocols have some disadvantages. First, the algorithm offers no guarantee about the placement and number of cluster head nodes. Second, if the cluster head dies in round \(n\), the whole cluster is unable to transfer its data to the base station until the next round. This intermittent failure of clusters could be a disaster when monitoring a region in real-time. Third, the individual sensor nodes  
Figure 1: Clustering network topology. transfer their data to the cluster head through single-hops, which is not suitable for large-scale networks. Therefore, further research has been undertaken into some of these issues. The main idea in Power-Efficient GAthering in Sensor Information System (PEGASIS) is to make the energy load distribution more even among sensors for WSNs. Each node will receive from and transmit to close neighbors and take turns being the leader for transmissions to the base station [11]. It assumes that all nodes have global knowledge of the network; the base station is fixed at a far distance from the sensor nodes; the sensor nodes are homogeneous and energy constrained with uniform energy; and the energy cost for transmitting a packet depends on the distance of transmission. PEGASIS builds a chain to ensure that all nodes have close neighbors. When a node dies, the chain is reconstructed to bypass the dead node. The Hybrid Energy-Efficient Distributed (HEED) [12] algorithm selects cluster heads according to a hybrid of node residual energy and a secondary parameter, such as node proximity or node degree. There is a tradeoff between extending the time until the first node dies (FND) and the time until the last node dies (LND). In [13], an evolutionary-based routing protocol has been proposed to obtain a better compromise between stability and network lifetime. It can guarantee a better tradeoff between the lifespan and the stability period of the network with efficient energy utilization. As the tradeoff that exists between network lifetimes and sensing coverage is the major problem in fixed sink networks, the authors in [31] proposed an energy-aware coverage-preserving hierarchical (ECHR) algorithm which accommodates energy-balance and coverage-preservation. In [14], a distance aware intelligent clustering (DAIC) was proposed. The key concept is dividing the network into tiers and selecting the high energy CHs at the nearest distance from the base station. In [15], an Energy-Efficient Unequal Clustering (EEUC) mechanism for periodical data gathering in WSNs is proposed to address the hot spots problem. It partitions the nodes into clusters of unequal size, and clusters closer to the base station have smaller sizes than those farther away from the base station.