Algorithm 1 Cluster Tree-Based Routing Algorithm

Input: Coordinates of Node “N”

Output: Number of CH node

Cluster Formation:

1: Calculate the distance between the nodes.

$dist=\sqrt{{{(x}_j{-x}_i)}^2{+(y}_j{-y}_i{)}^2}$

2: Compute the distance matrix for all the nodes.

$dist=\left[\begin{array}{ccc}0& t_{1,2}\dots & t_{1,n}\\ ⋮& 0\dots & ⋮\\ t_{n,1}& t_{n,2\dots }& 0\end{array}\right]$

3: Calculate the centroid of the network nodes

$centroid\left((x_i{-y}_i),(x_j{-y}_j)\right)=(\frac{x_i{+x}_j}{2},\frac{y_i{+y}_j}{2})$

4: Generate the cluster in the network from Equation (7).

5: Calculate the total number of clusters C

$C={\displaystyle {\displaystyle \sum }_{i=1}^x}count(centroid\left(x_i{,y}_i\right))$

6: Obtain a set of “C” clusters.

CH Selection:

7: Compute $E_{RER}$ and $E_{dep}$ of nodes in the cluster.

8: Compute the payoff “p” value for each CM

$p\left({CM}_{ij}\right)=R_{ij}\times RER\left({CM}_j\right)-P_{ij}\times E_{dep}\left({CM}_j\right)+R\left(N_{{CM}_{i,j}}^{CH}\right)$.

9: Compute the Nash equilibrium for deciding the CH node in the cluster

${CH}_i=\underset{i=1tok}{max}p({CM}_i)$

10: Obtain the optimum CH node.

Route Establishment:

11: Compute the DIOC-ETX, DIOC-QU, DIOC-RER, and DIOC-CHNC from the parent CH node.

12: Calculate the quality of the CH parent node using the objective function

${OF}_{\left(QU,ETX\right)}\left(i\right)=w_1\times QU\left(i\right)+w_2\times ETX\left(i\right)+w_1\times RER\left(i\right)+w_2\times CHNC\left(i\right)$

13: Compute the rank for selecting best CH parent node.

${CH}_r\left(X\right)=r_p\left(X\right)+r_i$

$r_i=s_v+r_{min}$

14: Return the best CH parent node.