## 6 Conclusions
\begin{table}
\begin{tabular}{l c c c c c} \hline \hline
**Graph** & 1E1 & 1V1 & 1T1 & **D** & **DLMinTC+ Elapsed** & **FastMinTC+ Elapsed** \\ \hline aves-sparrow-social & 516 & 52 & 1 & \(3.89\times 10^{-1}\) & 0.03 & 0.00 \\ aves-wildbird-network & 11,900 & 202 & 5 & \(1.17\times 10^{-1}\) & 0.12 & 0.05 \\ copresence-InvS13 & 394,247 & 95 & 20,128 & \(4.39\times 10^{-3}\) & 1.82 & 1.07 \\ copresence-InvS15 & 1,283,194 & 219 & 21,535 & \(2.50\times 10^{-3}\) & 5.57 & 3.47 \\ copresence-LH10 & 150,126 & 73 & 12,604 & \(4.53\times 10^{-3}\) & 0.80 & 0.39 \\ copresence-LvSchool & 6,594,492 & 242 & 3123 & \(7.24\times 10^{-2}\) & 22.77 & 15.92 \\ copresence-SFHH & 1,417,485 & 403 & 3148 & \(5.56\times 10^{-3}\) & 4.64 & 3.18 \\ copresence-InST13 & 18,613,039 & 328 & 8937 & \(3.88\times 10^{-2}\) & 75.71 & 43.69 \\ email-dnc & 39,264 & 1892 & 19,382 & \(1.13\times 10^{-6}\) & 0.29 & 0.13 \\ fb-wosn-friends & 1,269,502 & 63,731 & 736,674 & \(8.98\times 10^{-10}\) & 10.86 & 7.19 \\ ia-contacts-dublin & 415,912 & 10,972 & 76,943 & \(8.98\times 10^{-8}\) & 2.87 & 1.12 \\ ia-contacts-hypertext2009 & 20,818 & 113 & 5245 & \(6.27\times 10^{-4}\) & 0.13 & 0.06 \\ i-dnc & 87,627 & 30,398 & 83,942 & \(2.26\times 10^{-9}\) & 2.08 & 1.49 \\ i-dnc & 8,157 & 18,470 & 60,509 & \(5.93\times 10^{-3}\) & 0.77 & 0.32 \\ i-dnc & 8,157 & 1,470 & 6,157 & \(1.42\times 10^{-2}\) & 0.4 & 0.1 \\ i-dnc & 8,157 & 1,470 & 6,157 & \(1.42\times 10^{-2}\) & 0.4 & 0.1 \\ insecta-ant-colomy1 & 111,578 & 18,470 & 60,509 & \(5.93\times 10^{-9}\) & 11.3 & 0.06 \\ insecta-ant-colomy1 & 111,578 & 113 & 40 & \(4.41\times 10^{-1}\) & 1.5 & 6.1 \\ insecta-ant-colomy5 & 241,280 & 160 & 40 & \(4.74\times 10^{-1}\) & 1.8 & 8.5 \\ insecta-ant-colomy5 & 194,317 & 152 & 40 & \(4.23\times 10^{-1}\) & 1.5 & 7.3 \\ mammalian-tortoise-network-by & 1997 & 24 & 51 & \(1.42\times 10^{-1}\) & 0.6 & 0.4 \\ SFHH-conf-sensor & 70,261 & 403 & 3508 & \(2.01\times 10^{-2}\) & 0.6 & 0.4 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Experimental results on real-world publicly available graphs from Dataset3. For each considered graph, we report information on the size of the network and the results in terms of execution time of DLMinTC+ and FastMinTC+. first, to develop a model capable of outperforming traditional heuristic and approximate methods, demonstrating the effectiveness of DL in solving CO problems on dynamic networks; second, to advance the field of temporal knowledge graph analysis by showcasing how DL techniques can capture both temporal and structural nuances, providing robust embeddings that enable meaningful analysis of complex temporal interactions. DLMinTC+ solves the MinTCover problem in a data-driven fashion, combining GraphSAGE for node embedding, Transformer-based temporal encoding to capture sequential dynamics, and a pointer mechanism to determine optimal start and end points for activity intervals. This architecture is designed to model both structural and temporal features of temporal graphs effectively. To train such network, we define a custom loss function to balance covering, minimizing sum-span and granting integrity of the solution. Despite this, since the output of DL models is non-deterministic, to grant that the computed solution is valid, we also provide a novel iterative algorithm to build a valid final timeline, providing theoretical guarantees on the validity and minimality of the solution. We test our methodology on synthetic and real instances. The results of our experiments underscore the stability and generalization ability of the model, particularly on dense, highly connected datasets, where it achieves significant coverage efficiency. While DLMinTC+ incurs slightly higher computational time, this trade-off is offset by the model's enhanced coverage precision, making it a viable approach for applications prioritizing solution accuracy.