## 2 Related Works  
The most classical hierarchical routing protocol in WSN is Low Energy Adaptive Clustering Hierarchy (LEACH), proposed by [PERSON] [13]. In this protocol, cluster heads are randomly selected using a threshold and other nodes choose the nearest cluster heads to form clusters. LEACH incorporates data fusion into the routing protocol to reduce the amount of information that must be transmitted to the base station. However, since the rotation method may cause the hot spot problem, a number of new protocols based on LEACH has been proposed to balance energy consumption and prolong the lifetime of WSNs. Threshold sensitive Energy Efficient sensor Network (TEEN) [22] is a routing protocol for enhanced efficiency in wireless sensor networks. It sets two thresholds: a hard and a soft threshold. The hard threshold tries to reduce the number of transmissions by allowing the nodes to transmit only when the sensed attribute is in the range of interest. The soft threshold further reduces the number of transmissions by eliminating all the transmissions which might occur when there is little or no change in the sensed attribute according to the hard threshold. Power-efficient gathering in sensor information systems (PEGASIS) [15] is a chain-based protocol that is an improvement over LEACH. In PEGASIS, each node communicates only with a close neighbor and takes turns transmitting to the base station, thus reducing the amount of energy spent per round. To avoid uneven distribution problem of cluster heads and cluster sizes in LEACH, reference [14] proposed the LEACH-Centralized (LEACH-C) algorithm. LEACH-C uses a centralized clustering algorithm and the same steady-state phase as LEACH. During the set-up phase of LEACH-C, each node sends information about its current location and residual energy level to the sink node. Thus, it can choose cluster heads with high residual energy. However, both of them are centralized approaches and not suitable for large-scale networks. To avoid cluster heads' premature death in LEACH, reference [23] proposes the V-LEACH algorithm. V-LEACH is a new version of LEACH protocol to reduce energy consumption. The main concept of V-LEACH is that, besides having a cluster head in the cluster, there is a vice-cluster head that takes the role of the cluster head when the cluster head dies, so cluster nodes can send data to the base station without the need to select a new cluster head each time, which can prolong network lifetime. On the other hand, some heterogeneity-aware protocols such as SEP [16] and DEEC [24] are specially designed for heterogeneous WSNs. SEP is aimed at prolonging the stability period of two-level heterogeneous networks, which consist of two types of nodes according to the initial energy, i.e., normal nodes and advanced nodes. SEP works in the same way as LEACH, but for SEP, the CH rotating epoch and election probability are directly related to the initial energy of nodes. As opposed to SEP, DEEC further improves the functions of election probability by considering both the initial and residual energy of the network. It achieves better performance than SEP and LEACH in a multi-level heterogeneous WSN. Unfortunately, DEEC can't be used when the sink node is located far from the sensor nodes since it is working under the assumption that sink node is located in the center of the WSN. In recent years, there have been lots of improvements on the original LEACH protocol. ALEACH [17], C-LEACH [18] and K-LEACH [19] improve the cluster head selection, which take nodes' residual energy, initial energy or optimal cluster numbers into consideration. [PERSON] and [PERSON] proposed the Self-Organized Tree-Based Energy-Balance (STEB) routing protocol [25] in which a sink node assigns a root node and broadcasts this selection to all sensor nodes. Each node selects its parent by considering only itself and its neighbors' information. STEB outperforms LEACH in terms of rounds and remaining energy.