## 5 Experimental Evaluation
### Experimental Results
The results show the large amount of memory required by the DL-based solution to produce results, against the limited amount of memory required by the baseline heuristic. tion in sum-span of 13.4% compared to FastMinTC+, with some cases reaching a reduction around 50% and others with reductions limited to around 2-3%. This clearly depends on the size and complexity of the network analyzed and on the behavior of FastMinTC+ too. Indeed, if we better analyze Figure 4, we can see that the highest improvement is obtained in cases of graphs with smaller densities, which in general correspond to cases of graphs with a larger number of timestamps. This means that the proposed approach is better at scaling with larger instances with complex temporal structures. The variability in sum-span reduction is also reflected in the execution time, with an increase of around 50% on average. This is because the baseline heuristic processes simpler graphs more efficiently, whereas the DL-based approach incurs additional computational overhead even for less complex structures. Thus, overall, DLMinTC+ demonstrates superior performance in terms of sum-span compared to FastMinTC+ on all graphs. Specifically, in the analysis of 25 real-world instances, DLMinTC+ achieves a better sum-span in all cases. Notably, DLMinTC+ not only outperforms FastMinTC+ on all instances but, comparing results presented in [11], also the Inner and 2 Phases algorithms on all instances. Note that the improvements achieved can be translated into tangible benefits in various real-life scenarios. As an example, consider the case of telecommunication networks. In temporal graphs representing communication events, a reduction in the sum-span by 10% means a significant reduction in the time and resources needed to monitor and maintain network activity logs. For large networks with millions of interactions, this can reduce storage requirements by gigabytes, ensuring faster query responses and lower costs. In the case of transportation scheduling, instead, a 10% improvement in the coverage size of dynamic transportation networks (e.g., bus or train schedules), translates to fewer overlapping intervals when monitoring vehicle activity. This could result in optimized resource allocation (e.g., fewer active vehicles needed during certain time intervals) and improved passenger wait times. The results also confirm the performance in terms of execution time and of memory consumption of the FastMinTC+, which always achieves a lower execution time and a lower memory consumption compared to DLMinTC+, even though the order of magnitude of the execution time is comparable and memory consumption is still limited, making it a suitable solution in real-world scenarios. Figure 4: This graph illustrates the percentage reduction in sum-span and percentage increment in the execution time of DLMinTC+ compared to FastMinTC+ for a variety of graph densities on the real-world DIMACS instances. Overall, the proposed approach produces better results in cases of less dense graphs, which in general correspond to cases with a larger number of timestamps. This proves the ability of the proposed approach to scale to larger instances with respect to the baseline heuristic.