## 1 Introduction  
The modern era of electronics engineering, aviation, defense, robotics, computers, biomedical engineering, and meteorology enables researchers to design a variety of intelligent wireless sensors. The set of diminutive, low-cost, energy-efficient, self-organized, and programmable sensors are allied together to form a wireless sensor network (WSN). These networks are generally used to accumulate valuable information without human interaction in the domains of medical research, disaster management, engineering, tracking, industrial operations, and surveillance in battlefields [1]. Recent applications of WSNs introduced in the last decade include wave monitoring [2], ocean water monitoring [3], cattle herding [4], wildlife monitoring [5], landslide detection [6], and living and residential monitoring [7]. One of the main limitations of WSNs is the limited power available at the sensor nodes because of their minuscule sizes, which cannot embed with massive capacity batteries, as shown in Figure 1. In most WSN applications, nodes are randomly deployed in the target environment, so it is impossible to collect and recharge them. Most of the prior literature on WSNs focuses on different techniques to conserve the available energy during computations and communications while collecting more valued data with stretched network stability. Figure 2 describes the phase-wise energy consumption of a sensor node. It shows that the communication phase's energy dissipation is much higher than the energy consumption during internal computations and other internal operations. There are different energy-efficient routing techniques used in WSNs to gain enhanced performance. Each technique has its limitations, and the selection of appropriate topology depends upon the target application. Some common techniques are presented in Figure 3. The critical challenge of WSN is to adopt a technique that consumes the least energy and delivers accurate data collected from sensors to the sink node. Several algorithms have been proposed to reduce the computational complexities in data collection, aggregation, and delivery, and reduce the overall energy consumption of the sensor node [8]. The stability of WSNs depends upon the communication time period. That is only possible with efficient use of limited energy due to the architectural and communication restrictions of sensor nodes [9]. With the increase in the number of sensor nodes, and the  
Figure 1: Layout of a node with multiple sensors. Figure 3: Classification of routing protocols in WSNs. Figure 2: Average energy consumption in sensor node. coverage area of WSN, congestion in communication occurs. This congestion affects the delivery ratio of communication packets which can reduce their performance. Therefore, an efficient routing and congestion management are important to achieve effective performance. Several energy-efficient data routing algorithms have been proposed in the past. Such algorithms are categorized into three classes: (a) flat routing [10], (b) location-based routing [11], and (c) hierarchical routing [12]. Further extensions with geographic routing algorithms have also been proposed to improve network stability [13; 14; 15; 16]. The hierarchical clustering technique is more effective than the centralized or flat routing in WSNs. In this technique, the whole network is comprised of multiple clusters. A node is selected as the cluster head (CH) from each cluster using computational and probabilistic operations. The higher residual energy of a node results in higher chances of being selected as a cluster head. These CHs are responsible for collecting data from their respective clusters and transmitting the aggregated data to the BS. Some clustering schemes such as cluster formation, selection of CHs, and cluster size were always motivating the authors to research with new computational parameters. In static clustering, cluster formation is done only once that remains permanent until the entire network's termination.