## 5 Experimental Evaluation
### Experimental Results
\begin{table}
\begin{tabular}{l c c c c c c} \hline \hline
**Graph** & 1E1 & 1V1 & 1T1 & **D** & **DLMinTC+ \(S(\mathcal{T})\)** & **FastMinTC+ \(S(\mathcal{T})\)** \\ \hline aves-sparrow-social & 516 & 52 & 1 & \(3.89\times 10^{-1}\) & \(1.00\times 10^{1}\) & \(1.00\times 10^{1}\) \\ aves-wildbird-network & 11,900 & 202 & 5 & \(1.17\times 10^{-1}\) & \(4.66\times 10^{2}\) & \(4.78\times 10^{2}\) \\ copresence-InVS13 & 394,247 & 95 & 20,128 & \(4.39\times 10^{-3}\) & \(1.42\times 10^{6}\) & \(1.49\times 10^{6}\) \\ copresence-InVS15 & 1,283,194 & 219 & 21,535 & \(2.50\times 10^{-3}\) & \(3.49\times 10^{6}\) & \(3.64\times 10^{6}\) \\ copresence-LH10 & 150,126 & 73 & 12,604 & \(4.53\times 10^{-3}\) & \(3.72\times 10^{5}\) & \(3.87\times 10^{5}\) \\ copresence-LyonSchool & 6,594,492 & 242 & 3123 & \(7.24\times 10^{-2}\) & \(6.61\times 10^{5}\) & \(6.64\times 10^{5}\) \\ copresence-SFHH & 1,417,485 & 403 & 3148 & \(5.56\times 10^{-3}\) & \(8.76\times 10^{5}\) & \(8.92\times 10^{5}\) \\ copresence-Thiers13 & 18,613,039 & 328 & 8937 & \(3.88\times 10^{-2}\) & \(2.42\times 10^{6}\) & \(2.45\times 10^{6}\) \\ email-dnc & 39,264 & 1892 & 19,382 & \(1.13\times 10^{-6}\) & \(3.96\times 10^{5}\) & \(5.84\times 10^{5}\) \\ fb-wons-fpcn & 1,269,502 & 63,731 & 736,674 & \(8.49\times 10^{-10}\) & \(8.77\times 10^{8}\) & \(9.83\times 10^{8}\) \\ ia-contacts-dublin & 415,912 & 10,972 & 76943 & \(8.98\times 10^{-8}\) & \(7.83\times 10^{5}\) & \(9.60\times 10^{5}\) \\ ia-contacts-hypertext2009 & 20,818 & 113 & 5245 & \(6.27\times 10^{-4}\) & \(3.43\times 10^{5}\) & \(3.93\times 10^{5}\) \\ ia-digg-reply & 87,627 & 30,398 & 83,942 & \(2.26\times 10^{-9}\) & \(8.41\times 10^{7}\) & \(1.76\times 10^{8}\) \\ ia-hospital-ward-proximity & 32,424 & 75 & 9452 & \(1.24\times 10^{-3}\) & \(3.02\times 10^{5}\) & \(3.18\times 10^{5}\) \\ ia-primary-school-proximity & 125,773 & 242 & 3099 & \(1.39\times 10^{-3}\) & \(5.97\times 10^{5}\) & \(6.30\times 10^{5}\) \\ ia-prosper-loans & 3,394,979 & 89,269 & 1258 & \(6.77\times 10^{-7}\) & \(7.39\times 10^{5}\) & \(1.00\times 10^{6}\) \\ ia-retweet-pol & 61,157 & 18,470 & 60,500 & \(5.93\times 10^{-9}\) & \(9.43\times 10^{6}\) & \(1.21\times 10^{7}\) \\ insecta-ant-colony1 & 111,578 & 113 & 40 & \(4.41\times 10^{-1}\) & \(3.23\times 10^{3}\) & \(3.25\times 10^{3}\) \\ insecta-ant-colony3 & 241,280 & 160 & 40 & \(4.74\times 10^{-1}\) & \(4.76\times 10^{3}\) & \(4.77\times 10^{3}\) \\ insecta-ant-colony5 & 194,317 & 152 & 40 & \(4.23\times 10^{-1}\) & \(4.13\times 10^{3}\) & \(4.14\times 10^{3}\) \\ mammalia-raccoon-proximity & 1997 & 24 & 51 & \(1.42\times 10^{-1}\) & \(7.43\times 10^{2}\) & \(7.61\times 10^{2}\) \\ rec-amz-Baby & 915,446 & 596,316 & 4868 & \(1.06\times 10^{-9}\) & \(1.39\times 10^{6}\) & \(2.91\times 10^{6}\) \\ reptilia-tortoise-network-bsv & 554 & 136 & 3 & \(2.01\times 10^{-2}\) & \(5.00\times 10^{1}\) & \(9.60\times 10^{1}\) \\ reptilia-tortoise-network-fi & 1713 & 787 & 8 & \(6.92\times 10^{-4}\) & \(2.70\times 10^{2}\) & \(3.12\times 10^{2}\) \\ SFHH-conf-sensor & 70,261 & 403 & 3508 & \(2.47\times 10^{-4}\) & \(7.07\times 10^{5}\) & \(8.27\times 10^{5}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Experimentalresults 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 the sum-span \(S(\mathcal{T})\) of DLMinTC+ and FastMinTC+. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Instances** & **Algorithm** & \
\begin{tabular}{c} **Avg RAM Usage** \\ **on Dataset1** \\ \end{tabular} &
\begin{tabular}{c} **Avg RAM Usage** \\ **on Dataset1** \\ \end{tabular} \\ \hline Small & FastMinTC+ & 0.2 MB & 0.6 MB \\ Instances & DLMinTC+ & 0.4 GB & 1.8 GB \\ \hline Medium & FastMinTC+ & 10.3 MB & 25.8 MB \\ Instances & DLMinTC+ & 1.2 GB & 3.1 GB \\ \hline Hard & FastMinTC+ & 24.2 MB & 44.7 MB \\ Instances & DLMinTC+ & 3.1 GB & 7.2 GB \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Experimentalresults on Dataset1 and Dataset2 in terms of RAM consumption.