## 5 Analysis of Prominent Clustering Routing Protocols in WSNs
### Cluster-Construction Based Clustering Routing Protocols
#### 5.1.7 Eecs  
Energy Efficient Clustering Scheme (EECS), proposed by [PERSON] _et al._[21, 22], is a clustering algorithm which better suits the periodical data gathering applications. EECS is a LEACH-like scheme, where the network is partitioned into several clusters and single-hop communication between the CH and the BS is performed. In EECS, CH candidates compete for the ability to elevate to CH for a given round. This competition involves candidates broadcasting their residual energy to neighboring candidates. If a given node does not find a node with more residual energy, it becomes a CH. Different  
Figure 6: Pie Shaped Clusters Arranged in Two Layers in UCS.  
from LEACH for cluster formation, EECS extends LEACH by dynamic sizing of clusters based on cluster distance from the BS.  
In EECS, a node chooses the CH by considering not only saving its own energy but also balancing the workload of CHs, _i.e._, two distance factors: \(d(P_{j}\), \(CH_{j})\) and \(d(CH_{i}\), \(BS)\). A weighted function \(cost(j,i)\) is introduced in EECS for the ordinary node \(P_{j}\) to make a decision, which is:  
\[cost(j,i)=((1-w(P_{j}))w\times f(P_{j},CH_{i})+w(P_{j})\times g(CH_{i}) \tag{6}\]  
and node \(P_{j}\), chooses cluster head \(CH_{i}\) with the minimal \(\{cost\}\)to join. In Equation (6), \(f\) and \(g\) are two normalized functions for the distance \(d(P_{j}\), \(CH_{i})\) and \(d(CH_{i}\), \(BS)\), respectively:  
\[f(P_{j},CH_{i})=\frac{d(P_{j},CH_{i})}{d_{f\_max}} \tag{7}\]  
\[g(CH_{i})=\frac{d(CH_{i},BS)-d_{g\_min}}{d_{g\_max}-d_{g\_min}} \tag{8}\]  
where \(d_{f\_max}=\exp(\max\{d(P_{j}\), \(CH_{i})\})\), \(d_{g\_max}=\max\{d(CH_{i}\), \(BS)\}\) and \(d_{g\_min}=\min\{d(CH_{i}\), \(BS)\}\). \(w\) is the function of \(P_{j}\) as follows:  
\[w(P_{j})=c+(1-c)\sqrt{\frac{d(P_{j},BS)}{(d_{g\_max}-d_{g\_min})}} \tag{9}\]  
Function \(f\) in \(cost\) guarantees that nodes choose the closest CH in order to minimize the intra-cluster communication cost, while function \(g\) makes the nodes join the CH with small \(d(CH_{i}\), \(BS)\)\(\}\) to alleviate the workload of the CHs farther from the BS. Function \(w\) is the weighted factor for the tradeoff between \(f\) and \(g\). Furthermore, the optimal value of weighted factor \(c\) in the function \(w\) depends on the specific network scale.  
The advantages of EECS are summarized as follows: (1) Based on energy and distance, EECS constructs balancing point between intra-cluster energy consumption and inter-cluster communication load; (2) Clustering is performed by dynamic sizing based on cluster distance from the BS. This addresses the problem that clusters with a larger distance to the BS require more energy for transmission than those with a shorter distance, and bring about low message overheads and uniform distribution of CHs compared to LEACH.  
However, there exist a few advantages in EECS as follows: (1) Account of single-hop communications in EECS, long-range transmissions directly from CHs to the BS can lead to much energy consumption. Hence it is not suitable for large-range networks; (2) EECS requires more global knowledge about the distances between the CHs and the BS, and the task of global data aggregation adds overheads to all sensor nodes; (3) EECS produces much more control overhead complexity because all nodes must compete for becoming CHs.