# A Survey on an Energy-Efficient and Energy-Balanced Routing Protocol for Wireless Sensor Networks
## 5 Taxonomy for Energy-Efficient and Energy-Balanced Routing Protocols
### Multi-Hop Communication Method
#### 5.1.1 Multi-Hop Clustering Technique
\begin{table}
\begin{tabular}{l c c c c c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Year**} & \multicolumn{2}{c}{**Clustering**} & \multirow{2}{*}{**HAM**} & \multirow{2}{*}{**HT**} & \multirow{2}{*}{**CH Rotation**} & \multicolumn{6}{c}{**Decision Variables (CH Selection)**} & \multirow{2}{*}{**LA**} & \multicolumn{3}{c}{**Decision Variables (Cluster Formation)**} \\ \cline{4-14}  & & & & & & & & & & & & & **RE** & **DDS** & **HCBS** & **TB** & **TPBS** & **Predefined** & **RE** & **DCH** & **HCCH** & **TPCH** & **Others** \\ \hline  
2008 & [60] & ✓ & & ✓ & ✓ & & & & ✓ & & & ✓ & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Decision variables for CH selection and formation in a multi-hop clustering network. Having selected the CH nodes and specified how the nCH nodes should join a cluster, the next load-balanced requirements with the clustering routing protocol technique are (1) how to partition the network into an optimal number of sub-networks or clusters, and (2) the optimal cluster side. Partitioning the WSN into sub-networks is a noteworthy area of research. Some literature simply divides the network randomly into equal sizes while other works attempt to partition the network into different shapes [60; 69; 121]. Besides, some research work divides the network by assuming a virtual grid-based network structure [94; 139]. Much more research is still ongoing in order to proffer a solution on how to efficiently divide the WSN into clusters, whereby the ultimate goal is to prolong the network lifetime. In addition, much literature has focused on determining the number of clusters and the optimal cluster size [75; 86; 101; 108]. These papers strive to distribute the the SNs into clusters so as to have an equal cluster size. A general assumption in some of this literature is that an equal cluster size helps in balancing the traffic load in the network, most especially the intra-cluster traffic load. This might actually be the case but some literature argues otherwise. In [59; 60; 61; 115; 131; 138], the authors explained how an equal cluster size results in an imbalance in the energy consumption by the SNs in the network. Basically, it is perceived that equally distributing the SNs to clusters is a good approach to balance the intra-cluster traffic load; however, this approach suffers during inter-cluster communications. The clusters closer to the BS consume more energy in receiving and forwarding the load traffic from other distant clusters during inter-cluster communications. This results in an imbalance in the energy consumption during inter-cluster communications and can result in early partitioning of the network. This phenomenon is also termed the energy-hole problem [53]. An efficient approach used by researchers to mitigate the energy-hole problem while developing a clustering routing protocol is to divide the network into unequal clusters. The size of each cluster depends on how close the cluster is to the BS. That is, the cluster size increases as the distance of the CH nodes from the BS increases. With this in mind, we classified the studied energy-efficient and energy-balanced clustering routing protocol, based on the clustering formation, into equal or unequal cluster size as shown in Table 3. Besides, some literature strives to mitigate the energy-hole problem by assuming, in the clustering routing protocol, that the BS or sink is mobile. In [139; 140; 141], the authors assume that the BS moves across the sensor field in order to change the direction of the load traffic. In so doing, it is assumed that all the SNs in the network randomly participate in forwarding the load traffic to the BS; thus, the energy consumption is distributed equally among all the SNs. Chiefly, with the mobile BS approach, the BS moves back and forth around the sensor field so as to collect the aggregated information conveyed from each CH.