## 2 Literature Review  
Hierarchical Routing Protocols (HRPs) for WSN were introduced in the literature for energy-efficient routing protocols. HRPs in WSN show higher energy and bandwidth efficiency over conventional routing protocols. Unlike flat routing protocols, where sensors transmit their data to the BS directly, HRPs allow sensors to transmit data via mediators. HRPs are either cluster based or chain based. In cluster-based HRPs, sensors are organized into clusters, and transmissions go through cluster heads, while in chain-based HRPs, sensors are organized as chains through which the transmissions pass [14]. LEACH [12] is the pioneering and the most referenced HRP; it achieves a tremendous performance regarding WSN useful lifetime and energy consumption balancing [18]. LEACH is a distributed cluster-based HRP that utilizes randomized rotation of CHs based on a probabilistic threshold to distribute the energy load evenly among the sensors in the network. LEACH-C (LEACH-Centralized) [19] is one of the most popular versions of LEACH; it is a cluster-based centralized approach in which the CH election and distribution over the WSN are controlled by the BS using simulated annealing. LEACH-C utilize nodes' residual energies and positions from the BS [20]. LEACH-C has better performance over LEACH in useful network lifetime and energy dissipation [19; 20]. The authors of TEEN [21] classify sensor networks as proactive or reactive networks based on their functional mode. In reactive mode, nodes respond immediately to the changes of relevant parameters of interest, while sensor nodes in proactive mode respond to the changes of relevant parameters of interest periodically. TEEN is an energy-efficient routing protocol for reactive WSN; it reduces unnecessary or redundant transmissions. TEEN outperforms existing conventional WSN protocols in energy efficiency. [PERSON] et al. [22] introduced APTEENs an extension to TEEN for both transmitting periodic data and reacting to time-critical situations [23]. APTEEN allows three types of queries: historical, on-time, and persistent, which are used in hybrid networks. Moreover, it introduces QoS requirements for the on-time queries by minimum delay using the TDMA schedule with a special time slot assignment [23]. HEED (Hybrid Energy-Efficient Distributed clustering) [6] periodically performs clustering of WSN and CH selection for each cluster based on nodes' residual energy as a primary parameter and the proximity of a given node to its neighbors as a secondary parameter. HEED achieves uniform CH distribution across the network, increases network scalability and lifetime, and balances load on sensor nodes. Simulation results prove the effectiveness of HEED in prolonging network lifetime and supporting scalable data aggregation. PEGASIS (Power-Efficient Gathering in Sensor Information Systems) [7] is a chain-based HRP, where each node communicates only with a close neighbor to reduce energy spent per round by transmitting to the BS in rounds. PEGASIS outperforms LEACH by 100-300% when 1%, 20%, 50%, and 100% of nodes die for different network sizes and topologies [7]. [PERSON] et al. [24] propose a way to confine the election range of CHs in LEACH by exploiting residual energy, the relative density of surrounding nodes, and centroid distance. Thereby, longer sensor nodes' lifetime is achieved according to the authors. A novel approach of adopting the \(k\)-means clustering algorithm in WSN routing protocols has been proposed in [25]. It achieves higher network lifetime over the existing LEACH and HEED, as their simulation results demonstrated. In [26], the authors proposed the Load-balancing Cluster-based Protocol (LCP) to increase network lifetime by the selection of the highest residual energy node in each round to be CH in each cluster. A modification to LEACH considering residual energy and node location to distribute CHs evenly was proposed in [27]. As the simulation results demonstrated, LEACH was improved by 40% in survival time.