# Influence Maximization with Priority in Online Social Networks
## 5 Experiments
### Experimental Results
As the whole, IGS's running time gives the most stable results and usually runs around the 0.1-s mark. The time of IGS is fast and stable because of parallel programming and this algorithm costs most of time to find out \(S1\) while the loop to calculate \(S2\) usually stops at 1-2 rounds. The TRR sampling technique also helps to quickly identify which seeds will affect to the priority \(U\). Memory Usage.The Table 3 illustrates the memory consumption of IGS and state-of-the-art methods including DSSA, BCT, OPIM \(-\)\(C\) and Degree. The smallest numbers are highlighted in bold while the largest ones are in red. The output shows that IGS outperforms the others, especially on small databases with tens of thousands of nodes and from tens to hundreds of thousands of edges such as netHEPT, ENRON, and netPHY. IGS also consumes sharply less memory than OPIM \(-\)\(C\) and Degree when testing with larger databases such as DBLP and RETWEET. When IGS spends only more than 130 MB and more than 200 MB, OPIM \(-\)\(C\) and Degree spend about four times higher with DBLP and RETWEET, respectively. Besides, DSSA also results less expensive memory usage in all cases. BCT is less stable than IGS and DSSA because it works as DSSA does on ENRON, netPHY, DBLPB and RETWEET but suddenly costs the most memory in NetHEPT. \begin{table}
\begin{tabular}{l l l l l l l l} \hline \hline  & & & \multicolumn{6}{c}{**Dataset**} \\ \cline{2-7}  & **T** & & **NetHept** & **Enron** & **netPHY** & **DBLP** & **RETWEET** \\ \hline \multirow{8}{*}{IGS} & \multirow{2}{*}{100} & \(\sigma(S)\) & 5666.16 & 14,267.40 & 1865.92 & 54,033.50 & 17,307.70 \\  & & \(\sigma_{U}(S)\) & **1482.04** & **1075.77** & **1192.84** & **1271.62** & **511.08** \\ \cline{1-1} \cline{2-7}  & \multirow{2}{*}{200} & \(\sigma(S)\) & 5581.34 & 14,162.20 & 1805.26 & 53,553.90 & 18,581.50 \\  & & \(\sigma_{U}(S)\) & **1478.93** & **1079.74** & **1175.32** & **1267.52** & **491.35** \\ \cline{1-1} \cline{2-7}  & \multirow{2}{*}{300} & \(\sigma(S)\) & 5645.40 & 14,284.80 & 1773.33 & 53,240.50 & 19,459.10 \\  & & \(\sigma_{U}(S)\) & **1476.08** & **1074.30** & **1153.32** & **1264.79** & **492.39** \\ \cline{1-1} \cline{2-7}  & \multirow{2}{*}{400} & \(\sigma(S)\) & 5640.21 & 14,196.50 & 1688.53 & 52,918.80 & 18,832.20 \\  & & \(\sigma(S)\) & **1468.48** & **1075.68** & **1125.69** & **1260.31** & **490.46** \\ \cline{1-1} \cline{2-7}  & \multirow{2}{*}{500} & \(\sigma(S)\) & 5039.45 & 14,245.50 & 1593.66 & 52,130.90 & 228,801.00 \\  & & \(\sigma_{U}(S)\) & **1238.54** & **1079.28** & **1104.20** & **1252.70** & **994.40** \\ \hline \multirow{2}{*}{**DSSA**} & \multirow{2}{*}{\(\sigma(S)\)} & 4098.63 & 9960.35 & 3230.27 & 58,197.7 & 38,253.7 \\  & & \(\sigma_{U}(S)\) & _1093.7_ & _857.608_ & _174.479_ & _474.635_ & _168.087_ \\ \hline \multirow{2}{*}{**BCT**} & \(\sigma(S)\) & 11,088.10 & 19,901.70 & 6675.95 & 117,197.00 & _77,316.90_ \\  & & \(\sigma_{U}(S)\) & _1280.54_ & _1701.60_ & _386.49_ & _474.635_ & _159.77_ \\ \hline \multirow{2}{*}{**OPIM-C**} & \(\sigma(S)\) & 3779.09 & 19,326.3 & 6262.5 & 112,334 & 72,026.1 \\  & & \(\sigma_{U}(S)\) & _600.93_ & _894.18_ & _194.04_ & _459.801_ & _173.41_ \\ \hline \multirow{2}{*}{**Degree**} & \(\sigma(S)\) & 3824.44 & 19,349.10 & 6345.86 & 114,249 & 73,936 \\  & & \(\sigma_{U}(S)\) & _292.82_ & _779.84_ & _164_ & _260.94_ & 22.77 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparisons about \(\sigma(S)\) and \(\sigma_{U}(S)\) between IGS and _the others_ with k = 500, U size = 1 K and \(T=100\to 500\). TRR sampling technique focuses on finding the seeds that influence the priority \(U\) first then Algorithm 3 explores another seeds to push on the seed set. Hence the algorithm 3 saves memory to run loop more than the others because of must not check whether a seed node influences to \(U\) set or not. Moreover, the condition of \(\frac{F_{1}(S_{2},R_{2},\delta)}{F_{1}(S_{2},R_{2},\delta)}\geq 1-(1-\frac{1}{k})^{ t}-\epsilon\) helps \(S_{2}\) generated soon without waiting for the stop condition of the repeat.