# Multilayer Backbones for Internet of Battlefield Things +
## 4 Performance Evaluation
### Experimental Evaluation
#### 4.1.1 Impact of Topology Density  
Firstly, we consider the impact of topology density on the performance of each competitor. In Figure 2 we evaluate, for medium skewness, the _per layer_ size of the \(CDS\). The main conclusion is that the size of the CDS is practically a decreasing function of the node density. This happens because the higher the network density is, the greater the coverage capability of the network nodes becomes, and therefore the size of the \(CDS\) gets smaller. In the case we succeed medium skewness, there is no clear winner between \(CCDS\) and \(FAST\)-\(CMDSM\) as the topology becomes denser (degree \(\geq\) 6) and both competitors present similar performance (\(<\)10% variance). The explanation is that in such topologies, there exist multiple redundant paths towards nodes, and thus both pruning mechanisms work equally well. On the contrary, in sparse topologies (degree = 3) \(FAST\)-\(CMDSM\) is up to 15% more efficient. This is due to the fact that during the pruning process, the redundant paths are less in sparse topologies, and their discovery requires knowledge of the topology further away than 2-hops, which is beyond the capabilities of localized algorithms deployed in wireless ad hoc networks. Apparently, the centralized nature of \(FAST\)-\(CMDSM\) provides a clear advantage, since its pruning task has a broader overview of the topology. If we exclude the pruning task, then \(CCDS^{*}\) and \(FAST\)-\(CMDSM^{*}\) present similar performance (less than 10% variance) when degree \(\leq\)10, and the performance of the latter is up to 15% better to the former when degree \(>\)10. However, these results are not good news, because both algorithms do not perform well in terms of the--_per layer_--CDS size; i.e., the--_per layer_--\(CDS\) size is up to 98% of that of the total number of nodes in that layer. This is considered natural in multilayer networks when the traditional methods are used (2-hop neighborhood coverage). \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Range** & **Default** \\ \hline avg. node degree (D) & 3, 6, 10, 16, 20 & 6 \\ network diameter (H) & 3, 5, 8, 12, 17 & 5 \\ number of network layers (L) & 2, 3, 4, 5, 7 & 4 \\ size of a layer relative to its adjacent layers & 10\%, 20\%, 30\%, 50\%, 70\% & - \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Experimentation parameters values. \(DS\) redundancy justifies the use of the pruning mechanism (up to 88% and 85% \(CDS\) size reduction for \(CCDS\) and \(FAST\)-\(CMDSM\), respectively, in this particular case). We expanded our experiments in case of low skewness. The results, depicted in Figure 3 show that there are no important differences regarding the efficiency, between \(CCDS\) and \(FAST\)-\(CMDSM\), when topology becomes denser (degree \(\geq\) 6). As mentioned above, this happens because pruning mechanisms work well, when nodes have multiple ways to connect with one another. When degree = 3 (sparse topologies), \(CCDS\) is about 10% less efficient than \(FAST\)-\(CMDSM\), something which is justified due to the centralized control of the \(FAST\)-\(CMDSM\). In this case, the reduction size of \(CDS\) is about 90% for \(CCDS\) algorithm and up to 88%. In case of high skewness (see Figure 4), when degree \(\geq\) 10, both the proposed algorithms behaves in a quite similar way (less than 10% variance), too, regarding the size of \(CDS\). Here, \(FAST\)-\(CMDSM\) outperforms \(CCDS\), due to the centralized control of the first one which makes the procedure of finding surplus paths easier inside the Multilayer network. Examining the case when topology is sparse (degree = 3), we see that \(CCDS\) is less efficient than the other pruning proposed algorithm, bearing in mind that due to the lack of enough connections, it is more difficult for a distributed algorithm to find minimum \(DS\). Also, when degree = 6, \(CCDS\) continues to outperform \(FAST\)-\(CMDSM\), but both algorithms create \(DS\) with smaller size than the above implementations do.