# A Robust and Energy-Efficient Weighted Clustering Algorithm on Mobile Ad Hoc Sensor Networks +
## 3 Description of RE2 WCA Algorithm
### The Process of Cluster Establishment  
In mobile Ad hoc sensor network, this stage constitutes the final step of our novel weight algorithm and represents the construction of the cluster members' set. Each cluster defines its neighbors at one hop maximum, which forms the member of the cluster. Firstly, all nodes are distributed in a network range and assigned with typically identical energy. In the network, each node broadcasts Hello messages packets which will consume a little of energy. Nodes will move towards different direction with different velocity, which will also cost various energy. When nodes are stable in first round, it is time to cluster through calculating the weight value of each node. Those nodes with large weight value will be elected as \(CH\). Since the cluster is only restricted to manage its one hop neighbor, the process of cluster establishment will be accomplished quickly. Eventually, when all CHs connect with each other, the network is initialized. In order to display the process clearly, we give an explanatory example to clarify the clustering process. Firstly, we give some relevant parameters. For example, we render \(a=0.7\), \(b=0.3\). It implies that the residual energy attaches more significance than mobility. Actually, the mobility will not very large in sensor network. It is only a small range of displacement; therefore, the history cache operations will not be very frequent. More clearly and directly, only those displacements of nodes beyond \(D_{thr}\), the record will be entered into cache and is used to calculate the next moment displacement. Additionally, the \(CH\) is typically identical with cluster members. Hence, it also needs same computing with cluster members. Then, \(CHSD\) of one node will be calculated by Equations (5)-(7). This process actually need no data transmission except for the computing of \(CHSD\). The data transmission needs only \(n\) times (if the number of cluster members is \(n\)). Of course, the weighted value can be adjusted according to different needs in application. For example, if the protocol is used in VANET, \(b\) can be adjusted larger since the energy is not a vital factor for sensor network. When the initialization of the network, the ratio of residual energy to average energy is equal and speed, directions are same, hence the weighted summation of \(CHSD\) and ratio of energy is 1. By Equation (8), we assume \(C_{prob}\) is an appropriate value that can reduce the iterations as much as possible. Then all nodes start to announce to form a cluster. Since we consider the cost of AMRP, therefore, each node need to broadcast a packet {ID, \(CH_{prob}\), cost (AMRP)}. According to the cost of broadcasting, the left nodes join in a cluster according to the minimum cost. In Figure 2a, nodes (A, B, C, D) announce their tentative \(CH\) and display their connection with nodes in the first iteration. In Figure 2b, tentative CHs (B, C) quit the job of \(CH\) and join in cluster because the cost (AMRP) or \(CH_{prob}\) is not suitable. Tentative \(CH\) (A, D) is still keeping their job for the group mobility feature (\(CHSD\)) is relatively greater. In Figure 2c, more tentative CHs are announced. Actually, AMRP will control the hops minimized in order to energy efficiency. After the first iteration, the \(CH_{prob}\) will double. Therefore, if \(CH_{prob}\) of one tentative \(CH\) is greater than 1 or greater, this \(CH\) will be the formal \(CH\) and does not participate the iteration process but allows another node to join in. This example shows three iterations in \(CH\) selection. Actually in the next round, the process will keep longer and will even trigger \(p_{thr}\) to finish the iteration forcibly. Figure 2: The \(CH\) selection process in RE\({}^{2}\)WCA. (**a**) Tentative CHs (A, B, C, D, E) form. There are some nodes fail to join a cluster. (**b**) The tentative CHs (A, D, E, F, G, H, I) are updated and increased, so only a few nodes are at free state.