# Multilayer Backbones for Internet of Battlefield Things +
## 4 Performance Evaluation
### Experimental Evaluation
#### 4.1.2 Impact of Network Diameter  
In Figures 6-8, we evaluate the effect of the network diameter in the size of the \(CDS\). The main conclusion is that as the network diameter increases the size of the resulting \(CDS\) increases, and this observations is valid for all competitors. In case of medium skewness (Figure 6), the diameter increases and also the topology gets sparser. So, we have fewer, longer (in hops), and less redundant paths. In that way, the selection of 1-hop neighbor nodes that cover the \(N^{2}\) neighborhood of a particular node requires more 1-hop neighbors. Now, in terms of the competitors' performance, we see that in busly topologies (diameter \(\leq\) 5) \(CCDS\) presents up to 18% smaller \(CDS\) compared to \(FAST\)-\(CMDSM\). This gain is attributed to the employment of the \(clPCI\) by \(CCDS\) and which helps in getting a better pruning. On the other hand, in busly topologies an unfortunate erase from the \(CDS\) of a strategically located \(DS\) node will probably result in keeping a lot of (practically \"useless\") \(DS\) nodes just to ensure connectivity. When diameter \(=\) 8 or diameter \(=\) 12 the competitors have similar performance (less than 10% variance). As expected, in long and skinny topologies (diameter \(=\) 17) \(FAST\)-\(CMDSM\) outperforms \(CCDS\) by 16%, due to its centralized nature. Examining the pruning-free versions of the competitors, we see that both of them practically exhibit the worst-case behaviour, i.e., almost all nodes are selected as \(DS\) nodes; the performance of the pruning mechanism for \(CCDS\) and \(FAST\)-\(CMDSM\) regarding the \(CDS\) size reduction is up to 83% and 79%, respectively.  
In case of low skewness as it is illustrated in Figure 7, we can also say that when diameter \(\leq\) 5, \(CCDS\) algorithm outperforms FAST-CMDSM and when diameter \(=\) 8 or diameter \(=\) 12, both proposed algorithms have similar performance (less than 10% variance). Finally, we see that for diameter \(=\) 17, \(FAST\)-\(CMDSM\) has a better performance than \(CCDS\), due to the benefits of its centralized form, in long paths. So, in this case, \(CDS\) reduction is up to 85% for \(CCDS\) and 81% for \(FAST\)-\(CMDSM\).  
Finally, when the interconnectivity generator parameters are \(0.9-0.9-0.9-0.9\) (high skewness), as it is depicted in Figure 8, we observe a general increase in \(CDS\) size, due to the fact that the degrees of the nodes have a great variance in this case and as a result, more nodes needed to join the \(DS\). When diameter \(=\) 3, \(CCDS\) has better performance than the other proposed algorithm, due to the fact that we have smaller paths to check and as a result the distributed algorithm can discover easier the redundant paths (2-hop coverage). When diameter \(=\) 5, or diameter \(=\) 8, \(FAST\)-\(CMDSM\) starts to have a better performance,  
Figure 5: Impact of topology density (CDS size aggregated over all layers).  
as it creates \(CDS\) with smaller size. This is expected, since the centralized control of this algorithm contributes efficiently in finding the redundant paths. The longer the diameter is, the better performance \(FAST\)-\(CMDSM\) has as it is shown in Figure 8. To sum up, in this case, \(CCDS\) can achieve up to 81% reduction in the size of total \(CDS\), while \(FAST\)-\(CMDSM\) can achieve 79%. As a summary, we provide Figure 9 to show average performance of the competitors.  
Figure 6: Impact of network diameter (Medium skewness).  
Figure 7: Impact of network diameter (Low skewness).