# Multilayer Backbones for Internet of Battlefield Things +
## 4 Performance Evaluation
### Experimental Evaluation
#### 4.1.4 Impact of Layer's Size Increase  
Here we consider the impact of layer's size increase on the competitors' performance; we evaluate the _per layer_ size of the \(CDS\) for medium skewness, and depict the results in Figure 14. A first, generic observation is that the cardinality of CDS increases with increasing layer size. This is easily explained by the fact that the as the size of each layer increases, so does the need for more nodes to act as connectors, and consequently we get a larger CDS. Looking at the performance of the competitors, we note that an increase in the size of each subsequent layer by 30% or less results in having \(CCDS\) to outperform \(FAST\)-\(CMDSM\) with a margin from 11% up to 16%. The basic reason behind that is the dense topology, with the consequence that many redundant paths remain within the vicinity of \(CCDS\) (i.e., 2-hop), and therefore the pruning process eliminates many redundant dominators. On the contrary, an increase in the size of each subsequent layer by 50% or more results in having the centralized \(FAST\)-\(CMDSM\) outperform \(CCDS\) from 18% up to 21%. This is expected, since the large difference in the cardinality of the layers implies a large number of interlayer links, and therefore the calculation of the redundant paths by the pruning process requires a broader/global view of the topology, which is only available to the centralized \(FAST\)-\(CMDSM\) algorithm and not the distributed \(CCDS\) algorithm. As a last comment to this experiment, we see that the versions without pruning of the algorithms select almost all nodes as dominators; in particular the performance of the pruning mechanism for \(CCDS\) and \(FAST\)-\(CMDSM\) regarding the \(CDS\) size reduction is up to 80% and 83%, respectively.  
Conducting the experiment by changing the set of variables in the interconnectivity generator to \(0.1-0.1-0.1-0.1\) (almost uniform distribution), we observe that \(CCDS\) is the champion algorithm, because of the dense topologies formed, as it is shown in Figure 15. In this case, \(CCDS\) achieves 82% reduction in the total \(CDS\) size, while \(FAST\)-\(CMDSM\) achieves 80%. The last experiment in this section is conducted by setting the respective interconnectivity generator parameters to: \(0.9-0.9-0.9-0.9\) and the results are presented in Figure 16. In this case, we have a barely arbitrarily-formed distribution (high skewness). We see that while increasing the number of nodes, set in every layer, the \(CCDS\) algorithm remains our best option, as it is justified above. In this case, \(CCDS\) achieves 76% reduction in the total \(CDS\) size, while \(FAST\)-\(CMDSM\) achieves 75%.  
Figure 13: Impact of number of layers (CDS size aggregated over all layers).  
Figure 14: Impact of increasing layer cardinality (Medium skewness).  
Figure 15: Impact of increasing layer cardinality (Low skewness).  
Comparing the experiments, done, by changing the values in variables of skewness, we conclude that having a more uniform distribution (Low Skewness) is the best scenario, in which, our algorithms achieves their highest efficiency. This happens because this type of distribution, normalizes well the degree of every node in every layer, which means less nodes are important for the coverage of the network and this results in smaller \(CDS\) size. On the other hand, when we have high skewness, nodes are arbitrarily connected which means, more nodes in total \(DS\) are needed in order to cover the whole network properly. Furthermore, in every case, \(CCDS\) is the more efficient algorithm to use, bearing in mind that in every section, it provides better reduction from \(FAST\)-\(CMDSM\), except for the one in which we examine low skewness and our variables are set to 0.5 in which \(FAST\)-\(CMDSM\) outperforms \(CCDS\) (3% variance).