###### Abstract  
Numerous protocols have emerged to address the energy depletion problem in Wireless Sensor Networks (WSNs). Among these protocols, the Dynamic Multi-Hop Routing (DMR) protocol adopts a dynamic technique for routing data across the network. The use of the DMR protocol has shown promising results in reducing energy consumption, prolonging the network lifetime, and increasing throughput. To improve the performance of WSNs, this paper proposes the Enhanced Dynamic Multi-Hop Routing (EDMR) protocol as a modification of the DMR protocol. The EDMR protocol introduces an effective sleeping mechanism that selectively deactivates clusters that do not generate significantly updated data for a specific duration. This mechanism reduces redundant transmissions, thereby saving energy and prolonging the network lifetime. The EDMR protocol incorporates static and dynamic approaches to support two major categories of applications: monitoring and event-driven applications. The proposed protocol is evaluated against the DMR protocol, the Enhanced Dynamic Multi-Hop Technique (EMDHT-LEACH) protocol, and the Low-Energy Adaptive Clustering Hierarchy (LEACH) protocol. The simulation results demonstrate that the EDMR protocol mitigates energy depletion, extends the network lifetime, increases stability, and improves network throughput toward the Base Station (BS), while reducing packet redundancy compared with the other protocols. 11 June 202514 July 202514  
faces various challenges that affect the network's performance. Energy depletion in the sensor nodes is one of these challenges; in most cases, it is not possible to replenish energy from another source, especially when these nodes are deployed in extensive and harsh environments. Most of the sensor nodes' energy is consumed during data transmission to the BS [3]. Hence, much research has focused on minimizing the energy required for data transmission, which in turn prolongs the network's lifetime and increases its efficiency. Several routing protocols have been introduced to manage data transmission across the network area--specifically, the transmissions from the sensor nodes to the BS. Generally, routing protocols are categorized into three groups based on the wireless network architecture: flat routing protocols, location-based routing protocols, and hierarchical routing protocols [4]. Each category has a specific technique for forwarding data from sensor nodes to the BS. Among these, the hierarchical category is the most common. It provides a routing mechanism based on grouping all sensor nodes. An example of a protocol in this category is the LEACH protocol [5]. The main idea of the LEACH protocol is based on distributing all the sensor nodes into clusters. Each cluster comprises a number of nodes responsible for gathering data from the environment, which are then transmitted to an aggregator sensor node called the Cluster Head (CH). Afterwards, all the CHs send the collected data to the BS. The LEACH protocol divides the lifespan of the network into rounds. Each round is split into two phases: the setup phase and the steady-state phase. The setup phase is dedicated to forming the clusters and electing the CHs. At the start of each round, all sensor nodes select a random number between 0 and 1. This random value is compared with a threshold value, \(T(n)\). If it is lower than \(T(n)\), the sensor node is selected as the CH for that round. \(T(n)\) is calculated according to Equation (1) [5]:  
\[T(n)= \begin{cases}\frac{p}{1-p(r\;md\;\frac{1}{p})}&\quad\text{if }n\in G\\ 0&\quad\text{otherwise}\end{cases}  \tag{1}\]  
In this context, the parameter \(p\) represents the percentage of CHs in each round, the parameter \(r\) denotes the index of the current round, and the parameter \(G\) identifies the group of sensor nodes that have not been elected as CHs in the previous \(1/p\) rounds.