## 5 VirtFogSim: Supported Formats of the Rendered Data  
Under the current version of the simulator, both the _VirtFogSim_ and _VirtFogSimGUI_ interfaces (see Appendix A) support four main formats, in order to render the results output by the seven optimization algorithms of Table 4. The functions used to obtain these formats are listed in Table 5 and fully described in the _VirtFogSim_ User Guide (see Section 8). These rendering formats are:  
1. the Tabular format. It is enabled by the _print_solution_ graphic function;
2. the Colored Bar Plot format. It is enabled by the _plot_solution_ graphic function;
3. the Colored Time Plot format. It is enabled by the _plot_FogTracker_ graphic function;
4. the Colored Labeled DAG Map format. It is enabled by the _plot_DAG_ graphic function. \begin{table}
\begin{tabular}{l l} \hline \hline
**Function** & **Asymptotic Computational Complexity** \\ \hline _GeneticTA\_par_ & \(\mathcal{O}\ ((PS\times G_{MAX}\times 8\times I_{MAX})\ /\ (n_{core}))\) \\ _OM\_S_ & \(\mathcal{O}\ (8\times I_{MAX})\) \\ _OF\_S_ & \(\mathcal{O}\ (8\times I_{MAX})\) \\ _OC\_S_ & \(\mathcal{O}\ (8\times I_{MAX})\) \\ _O\_TAS\_par_ & \(\mathcal{O}\ ((PS\times G_{MAX})\ /n_{core})\) \\ _ES\_S_ & \(\mathcal{O}\ \Big{(}\Big{(}3^{(V-2)}\times 8\times G_{MAX}\ \Big{)}\ /n_{core}\Big{)}\) \\ _FogTracker_ & \(\mathcal{O}\ (8\times iteration\_number\times 3)\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: A synoptic overview of the computational complexities of the main functions supported by the VirtFogSim package. Specifically, the _print_solution_ function prints on the MATLAB prompt the result obtained by running the tested strategies under the selected DAG and given input parameters (see Table 10). Its input parameters are: (i) the vector \(\overrightarrow{RS}\) collecting the seven allocated resources; (ii) the vector \(\vec{\mathcal{E}}\) collecting the total computing-plus-networking consumed energy; (iii) the bandwidth \(RB\) of the Fog\(\leftrightarrow\)Cloud two-way backhaul connection; and (iv) a string _strategy_ representing the name of the tested strategy. Then, the function prints the following results in a numerical form:  
1. the Computing/Communication Ratio (_CCR_);
2. the required minimum DAG execution throughput (\(TH_{0}^{MIN}\));
3. the per-core computing frequency at the Mobile device (\(f_{M}\));
4. the per-core computing frequency at the Fog clone (\(f_{F}\));
5. the per-core computing frequency at the Cloud clone (\(f_{C}\));
6. the transport bit rate of the WiFi-based TCP/IP Mobile-to-Fog connection (\(R_{U}\));
7. the transport bit rate of the WiFi-based TCP/IP Fog-to-Mobile connection (\(R_{D}\));
8. the transport bit rate of the 3G/4G Cellular TCP/IP Mobile-to-Cloud connection (\(B_{U}\));
9. the transport bit rate of the 3G/4G Cellular TCP/IP Cloud-to-Mobile connection (\(B_{D}\));
10. the transport rate of the TCP/IP two-way Fog\(\leftrightarrow\)Cloud backhaul connection (\(R_{B}\));
11. the total computing-plus-networking consumed energy (\(\mathcal{E}_{TOT}\));
12. the consumed computing energy (\(\mathcal{E}_{COM}\));
13. the consumed networking energy (\(\mathcal{E}_{NET}\));
14. the percent networking-to-total ratio of the consumed energies: % (\(\mathcal{E}_{NET}\)/\(\mathcal{E}_{TOT}\)). If the input vector \(\overrightarrow{RS}\) is empty, only a reduced set of information is printed. The _plot_solution_ function displays the: (i) utilized computing/bandwidth resources; (ii) task allocation pattern; and (iii) consumed energies, returned by the carried out _VirtFogSim_ run in terms of suitable three-colored bar plots. In addition to the input used by the previous function, the other parameters are: (i) the \((0,1,2)\)-ary allocation vector \(\vec{x}\) to be displayed; and (ii) the number of the _fignumber_ to be displayed. The function renders a figure that is composed of three horizontal subplots.