# SCMC: An Efficient Scheme for Minimizing Energy in WSNs Using a Set Cover Approach
## 4 Simulation Results  
In order to assess our model, we compared it to the MO-SCP, MDP-MSC, and LEACH models. We performed a set of simulation scenarios in MATLAB [58] using a variable number of sensor nodes (100, 200, 300, 400) deployed randomly in a 1500 m\({}^{2}\) area. This allowed us to evaluate the  
Figure 5: WSN graph representation. effectiveness of our proposed approach and analyze its impact on the energy of the entire network, and thus on the lifetime of the WSN. Parameters used in the simulation are similar to those used in [59], and are shown in Table 1.  
Our experiment consists of two phases of WSN network design: cluster set cover creation and path determination. In both phases, we input the set of SNs, their locations, the required network lifetime, and other parameters to the corresponding SCMC model. We then solved the WSN design model with the IBM(r) ILOG(r) OPL-CPLEX(r) optimization solver. In the first phase the set cover model is used to obtain the optimal number of set covers with their corresponding CH, and the optimal packet transmission path from SNs to the selected CH inside each cluster. In the second phase we use the results obtained from the first phase to derive the optimal path between the CH and the BS using the min-cost max-flow algorithm. The metrics used to test the effectiveness of our proposed approach are based on the percentage of Alive nodes, the round where the First Node Dies (FND), the round where the Last Node Dies (LND), and the network throughput. The results of the first phase are shown in Table 2. The Greedy algorithm creates a number of set covers for each scenario where the number of sensor nodes is varied (\(N\) = 100, 200, 300 and 400)  
In the second phase, the min-cost max-flow model is solved as stated before and a comparison is carried out between the different approaches on the basis of the metrics stated earlier. Tables 3 and 4 summarize the results of these metrics. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Value** \\ \hline Initial energy \(E_{init}\) & 0.5 J \\ Transmitting and receiving energy \(E_{dec}\) & 5 mJ/bit \\ Amplification energy for short distance \(E_{f}\) & 10 P/bit/m\({}^{2}\) \\ Amplification energy for long distance \(E_{amp}\) & 0.013 pJ/bit/m\({}^{4}\) \\ Packet size & 200 bits \\ Operating frequency & 2.4 GHz \\ Initial energy of sensor & 61,560 J \\ Transmit power & 32 mW \\ Reference distance & 3 m \\ Path loss exponent & 4 \\ Signal to Noise Ratio & 2 dB \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation parameters. \begin{table}
\begin{tabular}{c c} \hline \hline
**Number of Nodes** & **Number of Clusters** \\ \hline
100 & 7 \\
200 & 8 \\
300 & 7 \\
400 & 8 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Set covers number created by Greedy algorithm. \begin{table}
\begin{tabular}{c c} \hline \hline
**Number of Nodes** & **Number of Clusters** \\ \hline
100 & 7 \\
200 & 8 \\
300 & 7 \\
400 & 8 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Number of rounds when 10%, 20%, 30%, 40%, 50%, 60%, 70% and 80% of nodes die. Table 3 shows the number of rounds completed by various schemes when 10%, 20%, 30%, 40%, 50%, 60%, 70% and 80% of nodes die for \(N=100\). It is evident, as shown in Table 3, that SCMC has a better performance than its counterpart protocols. For instance, in the case of SCMC the number of rounds when 80% of nodes are dead is 4500 whereas in the case of MO-SCP, MDP-MSC, and LEACH the number is 3785, 3300, and 2987 respectively. Therefore, SCMC extends the lifetime of the WSN and can provide information for a considerably longer period of time. This lifetime increases with node density, where SCMC takes the advantage of the set cover formation and the optimal routing energy.