Algorithm 1 Shortest Routes in a Wireless Network

Step: 1  $\mathbf{Input}\mathbf{data}:$ $X_u,Y_u\leftarrow \mathrm{Meter}\mathrm{coordinates}$ $X_d,Y_d\leftarrow \mathrm{UDAP}\mathrm{coordinates}$ $X_{eb},Y_{eb}\leftarrow \mathrm{Base}\mathrm{station}\mathrm{coordinates}$ $X_c,Y_c\leftarrow \mathrm{Head}\mathrm{Office}\mathrm{Coordinates}$ $N=card\left(X_u\right);M=card\left(X_d\right)$ $K=card\left(X_{eb}\right);P=card\left(X_c\right)$ $X_T=[X_u,X_d,X_{eb},X_c];Y_T=[Y_u,Y_d,Y_{eb},Y_c]$ Step: 2  $\mathbf{Calculation}\mathbf{of}\mathbf{distances}:$ for  $i=1:card\left(X_T\right)$ $\hspace{1em}$for  $j=1:card\left(Y_T\right)$ $\hspace{1em}\hspace{1em}$$D(i,j)\leftarrow Haversine(\left[Y_i{X}_i\right],\left[Y_j{X}_j\right])$ $\hspace{1em}$endfor endfor $D(D=0)\leftarrow \infty$ $\alpha =N+M+K+P;D_{max}=\delta \forall \delta \in {\mathbb{Q}}^{+}$ $G_{\alpha ,\alpha }\leftarrow \mathrm{ceros};G(D\le D_{max})\leftarrow \mathrm{unos}$ Step: 3  $\mathbf{Minimum}\mathbf{roads}\mathbf{and}\mathbf{route}\mathbf{costs}:$ $\left[rpciai\right]\leftarrow \mathrm{compress}\mathrm{sparse}\mathrm{matrix}\left(G\right)$ $A=\left[rpciai\right]$ $pred\leftarrow Dijkstra(A,\alpha )$ $CostT\leftarrow RouteCost(\alpha ,pred)$