## 4 Problem Formulation
\begin{table}
\begin{tabular}{c l} \hline \hline \(X_{u},Y_{u}\) & Geographic coordinates of users (Lat., Long.) \\ \hline \(X_{d},Y_{d}\) & Geographic coordinates of UDAP (Lat., Long.) \\ \hline \(X_{eb},Y_{eb}\) & Geographic coordinates of base stations (Lat., Long.) \\ \hline \(X_{e},Y_{c}\) & Head office geographic coordinates (Lat., Long.) \\ \hline \(N\) & Number of users \\ \hline \(M\) & Number of UDAP \\ \hline \(K\) & Number of base stations \\ \hline \(P\) & Number of base stations \\ \hline \(X_{T},Y_{T}\) & Geographic coordinates of all nodes (Lat., Long.) \\ \hline \(D\) & Distance between nodes \\ \hline \(G\) & Logical matrix of links between nodes \\ \hline \(D_{max}\) & Range in kilometers of the devices \\ \hline \(A\) & Compressed matrix of \(G\) \\ \hline \(rp\) & Row indicator of the compressed matrix \\ \hline \(ci\) & Column index of the compressed matrix \\ \hline \(ai\) & Compressed array value index \\ \hline \(pred\) & Path predecessor tree function, Dijkstra \\ \hline \(node\) & Device Index \\ \hline \(path\) & Tree Path Set \\ \hline \(CostR\) & Cost of each route \\ \hline \(Cost\) & Cumulative vector of costs per route \\ \hline \(CostT\) & Tree Path Adder \\ \hline \(CapNodo\) & Maximum capacity of each node \\ \hline \(Coverage\) & Maximum distance in kilometers of reach of the nodes \\ \hline \(B\) & Logical matrix of connections between users and UDAP \\ \hline \(tmp\) & Time vector of users connected to concentrators, Prim \\ \hline \(s\) & User count per UDAP \\ \hline \(L\) & Matrix of users connected to each UDAP \\ \hline \(ind\) & Matrix of users not connected to UDAP \\ \hline \(solC\) & Resulting transposed logic matrix, Greedy SCP \\ \hline \(solL\) & Optimal UDAP matrix, Greedy SCP \\ \hline \(R\) & SoIL ordered array without repeating UDAP \\ \hline \(X_{el},Y_{cl}\) & Geographical coordinates of optimal concentrators (Lat., Long.) \\ \hline \(G2\) & Matrix of weights per link between nodes \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Notation of model variables. In the second stage of the model, a new capacity constraint is added for the nodes and their respective scope to establish the actual condition of a device to establish a simultaneous connection with other devices in the network. As shown in Algorithm 2, the determination of the topology is made using [PERSON]'s algorithm, from which some devices connected and not connected to the UDAP is obtained, with which we proceed to discard those meters not connected from the set of initial users. With the number of meters defined, the SCP is solved using the Greedy SCP algorithm, referred to as the Chvatal heuristic, from which the concentrators chosen for further processing are obtained. Having redefined the number of nodes in the system, the proposed model recalculates the distances through Haversine to form a new graph. In addition, the model proposes the assignment of weights to establish the routing criteria of the devices, so the Algorithm 3 is established within the model to restrict and enforce the connection between devices in NAN and WAN. Finally, through [PERSON] again, the shortest path between the nodes of the system is created to determine the spanning tree that is established as the final topology resulting from the heterogeneous wireless network.