# Multilayer Backbones for Internet of Battlefield Things +
## 4 Performance Evaluation  
**Competing Algorithms. ** We compare the proposed algorithms, namely \(CCDS\) and \(FAST\)-\(CMDSM\), but in order to explain the usefulness of their pruning procedures, we develop and include in our comparison their annotated with an asterisk version of them, namely \(CCDS\)1 and \(FAST\)-\(CMDSM\)2; these versions are simply the same algorithms but without activating the pruning procedure. Solely for illustrative purposes we include the experimentation, and \(FAST\)-\(MDSM\) algorithm which constructs minimum but _unconnced_\(DS\); we proved in [5] that any (unconnected) \(DS\) of size \(\|DS\|\) can be turned into a \(CDS\) by adding \(2\times\|DS\|\) additional nodes in the \(DS\) in the worst case. Table 1 summarizes the competing algorithms. Footnote 1: \(\Delta\) is the maximum node degree; 2 Number of transmitted messages per node; 3 Not applicable due to its centralized nature. Footnote 2: \(\Delta\) is the maximum node degree; 4 Number of transmitted messages per node; 5 Not applicable due to its centralized nature. **Simulation testbed. ** Due to the lack of available, real military networks, and the inability (The requirement of modern battlefields is to able to operate ad hoc networks consisting of an order of magnitude more nodes; for instance a battalion would need a thousand nodes. e.g., [[https://www.darpa.mil/news-events/2013-04-30](https://www.darpa.mil/news-events/2013-04-30)]([https://www.darpa.mil/news-events/2013-04-30](https://www.darpa.mil/news-events/2013-04-30)) (accessed on 15 May 2022)). of wireless testbeds and emulation environments for ad hoc networks to deal with several hundreds of nodes, we developed a generator for multilayer networks in MATLAB. The details of our generator can be found in [6; 23], and here we present its basic features. The construction of a multilayer network is driven by the average node degree, by the nodes' number per layer (i.e., the so-called layer size), and the number of layers. The interconnection of the layers is driven by: (a) the number of a node's links towards nodes in different layers, and (b) the distribution of the interconnections to the nodes within a particular layer. We apply the _Zipfian_ distribution to our connectivity generator. Skewness is managed by parameter \(s\in(0,1)\). We make use of four distinct _Zipfian_ distributions, one per parameter of interest:  
* \(s_{\textit{degree}}\): to generate the frequency of appearance of highly interconnected nodes,
* \(s_{\textit{layer}}\): to choose how frequently a specific layer is selected,
* \(s_{\textit{node}}\): to choose how frequently a specific node is selected in a specific layer. * \(s_{\textit{weight}}\): to choose how uniformly the energy is distributed in the nodes. We call these parameters as the _topology skewness_, and represent it as a sequence of four floats, meaning that \(s_{\textit{degree}}=0.5\), \(s_{\textit{layer}}=0.5\), \(s_{\textit{node}}=0.5\) and \(s_{\textit{weight}}=0.5\) (which are the default settings we used to create the datasets). \begin{table}
\begin{tabular}{c c c c c} \hline  & **CDS** & **Pruning** & \multicolumn{2}{c}{**Complexities**} \\
**Competitor** & **Calculation** & **Heuristic** & **CPU**1 ** & **Comm**2 ** \\ \hline \(CCDS\) & Distributed & ✓ & \(\Delta^{3}\) & / & 7 \\ \(CCDS\)1  & **Distributed** & - & \(\Delta^{3}\) & / & 7 \\ \(FAST\)-\(CMDSM\) & Centralized & ✓ & _exp_ & / & \(c\) \\ \(FAST\)-\(CMDSM\)2  & **Centralized** & - & _exp_ & / & \(c\) \\ \hline \end{tabular}
\end{table} 
Table 1: Competitor characteristics. **Performance measures. ** The competitors are compared in terms of the cardinality of the \(CDS\); apparently an algorithm is more efficient than another, if it generates a \(CDS\) having smaller cardinality [16]. Moreover, an algorithm that establishes a (per node) relay set with larger residual energy is naturally considered to be more efficient in terms of energy than another algorithm whose per node relay set has less residual energy. **Datasets.