## 5 Results  
### Optimal Selection of Technology Set  
We assessed our algorithm carrying out numerical calculations using the above mentioned topologies. The first experiment we conducted aims to evaluate the ability of the clique method in finding the optimum value, for the problem of selecting the technology set. In agreement with the network topologies in Figure 6, we used in our calculations a set of \(N=15\) different technologies and a total of \(M=15\) different possible SRNG events and \(L=15\) communication protocols. We randomly generated the risk matrix \(\mathbf{X}\) sampling zeros and ones from independent and identically distributed (iid) Bernoulli random variables with probability \(p=0.3\) for a \"1.\" Fixing this probability to such value we controlled that the average number of SRNG events, per technology, is 4.5, a value that is consistent with those found in [25, 26]. Similarly, the communication protocol matrix \(\mathbf{Y}\) was randomly generated from independent and identically distributed Bernoulli random variables with probability \(p=0.5\) for a \"1.\" This likelihood also allows us to control that, on average, we will have communicating protocols between pairs of technologies.  
In brief, we state that the method proposed in Section 4.3.1 was able to reach the optimum value: three technologies that do not share risks and can communicate with each other. In addition, we carried out experiments to compute the optimal number of selected technologies while increasing the number  
Figure 6: Networks topologies used for placement methods evaluation.  
of available technologies, SRNG events, and communication protocols. In particular, we sampled \(\mathbf{X}\) from iid Bernoulli random variables with probability \(q=0.1\), \(0.2\), and \(0.3\) for all the technologies, while the number of available technologies, SRNG events, and communication protocols varied from \(15\) to \(25\). Figure 7 shows the results for the optimal number of selected technologies. We comment that when the range of available technologies is between \(15\) and \(25\), the proposed algorithm selects, for deploying onto the network topologies, between: (i) \(2\) and \(5\) when \(p=0.3\); (ii) \(4\) and \(7\) when \(p=0.2\); and (iii) \(6\) and \(11\) when \(p=0.1\). Remarkably, we note that as the likelihood of the SRNG events increases the optimal number of technologies decreases. This result is counterintuitive because we expect that as the diversity increases so it does the resilience. However, the single SRNG event constraints stated in the optimization problem impose additional restrictions, which, in turn, forces the tradeoff between diversity and number of SRNG events, to reduce the number of technologies in the optimal set.  
Since we sampled \(\mathbf{X}\), for all the technologies, from iid Bernoulli random variables with the same \(p\) value, this means that all the SRNG events associated with the available technologies are statistically homogeneous. To introduce some heterogeneity, we randomly sample \(p\), for each available technology, from a uniform discrete distribution in the range [0.15,0.5]. This sampled value is next used to sample the rows in the risk matrices from iid Bernoulli random variables. In this experiment, we fixed the number of available technologies, SRNG events, and communication protocols to \(15\). We generated \(1000\) risk matrices, computed the distribution for the number of selected technologies, and plotted the result in Figure 8. From the histogram, we can observe that the most likely number of selected technologies is again three.