## 1 Introduction  
Nowadays, Wireless Sensor Networks (WSNs) are attracting the considerable attention of many researchers thanks to their participation in a variety of practical applications [1; 2; 3]. WSNs have a number of characteristics that make them distinctive from other conventional networks. For instance, the energy sources, the computational capabilities, and the data storages are limited [4; 5]. Hence, the characteristics of WSNs must be taken into account during their use. Many routing protocols have been introduced to convey the collected data of WSN to a Base Station (BS), which in turn, forwards it to the end-user [6; 7]. In this context, a group of these protocols adopted hierarchical mechanisms for delivering the sensor data to the BS. The Low Energy Adaptive Clustering Hierarchy (LEACH) protocol [8] is one of these protocols which has attained widespread acceptance in this domain. The main concept of the LEACH protocol is to split the whole area of the sensor network into clusters. Thus, every cluster combines an aggregator called a Cluster Head (CH) that is able to collect sensed data from other cluster member nodes. Figure 1 presents the topology of the sensor network within the LEACH protocol. In the LEACH protocol, the network's lifespan is also divided into specific durations called rounds and each round includes two phases. The first phase is the set-up process, which is dedicated to picking out the network's CHs and forming the clusters. For this reason, the whole sensor nodes choose in advance a random number between 0 and 1. Then, every node compares its random  
level in the nodes. Such problems will negatively affect the lifetime and the performance of the sensor network [9]. The Improved MHT-LEACH (IMHT-LEACH) protocol was proposed in [10] to provide an approach for transmitting the CH data from sensors over an unlimited number of levels toward the BS. The length of each level is \(d_{o}/2\). The IMHT-LEACH protocol is also considered as an improvement approach for the Multi-Hop LEACH (MHT-LEACH) protocol [11]. It supposes that the network lifetime is split into rounds and each round comprises of three primary phases: the initial phase, the announcement phase and the routing phase. In the initial phase, the clusters are formed by using the same approach that is used in the LEACH protocol. Thus, the CHs of the network will be elected and other sensor nodes will join to their clusters. In the announcement phase, all the CHs of the network declare themselves to each other. The previous phase gives sufficient information to the CHs in order to create their routing tables (RTs). In the routing phase, each CH decides to route its data directly or through another CH toward the BS based on the available routes distances in its RT. Obviously, the routes that have lowest distances will be chosen. The IMHT-LEACH protocol achieved advantages related to reducing the energy consumption and arranging the data transmitting process from the CHs to the BS. On the other side, it did not show interest in: the clusters formation, the transmitting the data within the clusters and the energy load that will appear due to using the same routes along the round. The Enhancing DMHT-LEACH (EDMHT-LEACH) protocol was proposed in [12]. The main purpose of the EDMHT-LEACH protocol is to upgrade the performance of the Dynamic Multi-Hop LEACH (DMHT-LEACH) protocol [13]. Similar to the IMHT-LEACH protocol, the sensor nodes are distributed over the levels around the BS and the length of each level is \(d_{o}/2\). Further, it splits the network lifetime into rounds. The main idea of the EDMHT-LEACH approach is built on dividing each round into four phases: the initial phase, the announcement phase, the selection phase and the routing phase. In the initial phase, an approach was proposed to control the number of sensor nodes within the clusters in order to relieve energy loads on the CHs. Moreover, a new designation (Independent Nodes--INs) and tasks have been given to the sensor nodes that can't join any network cluster.