## 2 Related Work  
Clustering routing protocols have been widely researched in WSNs, and have achieved very fruitful results. In the clustering network structure, sensor nodes are divided into several clusters; each cluster is a node set of a cluster head (CH) and a plurality of member sensor nodes. The CH is not only accountable for managing member sensor nodes, but it also presides over data aggregation and data forwarding between clusters. The earliest classical clustering protocol of WSNs is the LEACH protocol [11], which optimizes the network energy expenditure by creating clusters dynamically. It was proposed initially as a distributed and single-hop clustering protocol, where sensor nodes made autonomous decisions without any centralized control. CHs are randomly selected by a predefined probability \(p\) (i.e., the desired percentage of CHs in WSNs), which forms clusters accordingly. However, the randomized process fails to select certain sensor nodes (such as those with more residual energy or in a better position) as CHs, which results in unevenly distributed CHs and premature energy depletion of these sensor nodes [12]. Consequently, the key step is the election of CHs, which requires taking into consideration plenty of factors, such as the node energy property, the node distance property, etc. In the past decades, many classical WSN routing protocols utilizing the node energy property to search for the optimal clustering structure have arisen. A representative routing protocol is the stable election protocol (SEP) [13], which is a heterogeneous-aware protocol prolonging the time interval before the death of the first sensor node. The death of the first sensor node is crucial for many applications in which the feedback from WSNs must be reliable. Considering the node residual energy, the SEP algorithm selects CHs by using weighted election probabilities. Later, developed distributed energy-efficient clustering (DDEEC) [14] improved upon the SEP algorithm by selecting CHs with a probability based on the ratio between the residual energy of each sensor node and the average energy of the network. In the DDEEC algorithm, sensor nodes with a high residual energy have more chances to be CHs than low-residual energy nodes. Recently, differently to the previous WSN clustering protocols, [PERSON] et al. [15] proposed an analytic model to estimate WSNs' lifetimes, and developed the DCFR protocol that selects the next hop based on the node residual energy and the energy consumption rate. SEP, DDEEC, and DCFR algorithms pay attention to the node energy property and ignore other key factors of sensor nodes (i.e., the node distance property, etc), which is not optimal to maximize the WSNs longevity. Alternatively, the node distance property is another significant aspect of developments upon the LEACH algorithm. At present, a great many efficient routing protocols based on the node distance property have arisen, such as the power-efficient gathering in sensor information systems (PEGASIS), energy-efficient unequal clustering (EEUC), and gateway based energy-efficient routing protocol (M-GEAR) algorithms. PEGASIS [16] is an optimal chain-based protocol that is an improvement upon the LEACH algorithm. In the PEGASIS algorithm, the sensor node chain for each sensor node is formed by communicating with a closer neighbor, and sensor nodes of a cluster rotate to transmit data to the BS. Similarly, in [17], [PERSON] et al. proposed an EEUC mechanism partitioning sensor nodes into clusters of unequal size. In the EEUC algorithm, clusters closer to the BS have smaller sizes than those farther away, which can preserve energy for WSNs. Like the EEUC algorithm, M-GEAR [18] is also a location-based protocol, and divides sensor nodes into four logical regions on the basis of their location in the sensing field.