## 3 Proposed Techniques
### Initial Phase
#### 3.1.2 Independent Nodes (INs)  
The result of the previous assumption is that a large part of the nodes has joined the existing clusters of the network. The remaining part of sensor nodes have not been able to join any cluster and they will be called INs. The proposed protocol grants the INs the ability to route their data to the BS through other INs or CHs. Moreover, any IN can aid other INs or CHs to route their data to the BS. Conversely, the INs are unable to contact the regular nodes like the CHs [12]. Finally, the detail procedure of the clustering process, which takes place at the beginning of every round, is given by the pseudo-code in Algorithm 1. ```
1\(X\in\) group of the deployed sensor nodes
2\(R\) a random number between 0 and 1
3\(T^{\prime}\)(i) threshold value
4\(N^{\prime}\) number of the nodes that joined to the CH
5\(N_{o}\) maximum number of the member nodes that can join to the CH
6 ST selection table
7
8 begin
9 begin
10 begin
11 begin
12 for each (\(X\))
13\(X\) selects \(R\)
14 if (\(R<T^{\prime}(i)\)) then
15\(X\) becomes CH in this round;
16 else
17\(X\) remains a regular node waiting to join a cluster;
18 end if

#### 3.1.3 Network Leveling

According to the proposed approach, the whole architecture of a sensor network is split into a number of levels around the BS, the length of each level being \(d_{o}/2\). All the CHs and the INs will be distributed into levels based on their distances to the BS (Figure 2). For example, the CH located at a distance less than \(d_{o}/2\) from the BS will belong to the first level, whereas the CH with a distance equal or larger than \(d_{o}/2\) but less than \(d_{o}\) will belong to the second level and so on. Furthermore, it supposes that each cluster will be divided also into two levels around the CH, using the same procedure (Figure 2). By doing so, all the CHs, INs, and Ns will have their specific levels, and most of the data transmissions, which occur between the sensor nodes in any two successive levels, will stay within transmission distances less than \(d_{o}\). We expect this solution will positively reflect on the amount of consumed energy, which can be calculated using Equation (2). Additionally, we suppose that each cluster owns a cluster ID, which distinguishes it from other clusters. Usually, the Ns use the cluster ID to forward the sensed data to their CH. Figure 2 shows a general topology of a WSN using the proposed approach. Indeed, the proposed technique can be applied into deployment areas of sensor nodes of different shapes (parts of the general topology) and regardless of the BS position either inside or outside of the deployment area. For example, the deployment areas A and B represent two different situations that could be encountered in practice. So, even if we suppose that the sensor nodes are only deployed on the rectangular area (A) or on the triangular area (B), the same general leveling approach to distribute the nodes into levels based on their distances to the BS is used. ### Announcement Phase

During the network lifetime, all the CHs, INs, and Ns are regularly declaring themselves to each other by broadcasting announcement messages. In the static approach, it is assumed that the different kinds of nodes use different types of broadcasting messages. Usually, they only use the messages at the beginning of every round. Hence, the Ns broadcast messages that include their IDs, cluster IDs, levels, and coordinates, is shown in Figure 2(a). Furthermore, the CHs and INs broadcast announcement messages containing their IDs, levels, and coordinates, is shown in Figure 2(b). The dynamic approach specifies two types of broadcasting messages. The first one is used at the beginning of the round. Thus, the Ns of all clusters broadcast message comprising their IDs, cluster IDs, levels, coordinates, and residual energy, is shown in Figure 3(a). In turn, the CHs and INs broadcast messages containing their IDs, levels, coordinates, and residual energy, is shown in Figure 3(b).