## 4 Experiments and Results
### Experiments and Analysis
#### 4.2.1 Comparison of Load Balancing  
We performed the load balancing evaluation on both real data set CSLOGS10 and synthetic data set D50. For CSLOGS10, the number of nodes is set to 1-5; for D50, the number is set to 1-8.  
Table 1 shows the amount of subtrees and computing time in different groups of CSLOGS10 in Reduce 2 while the total number of nodes are 3, 4, 5 and the support threshold is 0.01. The subtree amounts in each group divided by PCFMIS1 and PCFMIS3 are shown in Table 1. For PCFMIS1, when the number of nodes is 3, the amount of subtrees in the most loaded group (\(Gnum\) = 3) is 3.66 times that of the least loaded group (\(Gnum\) = 1); when the number of nodes is 4 and 5, the ratio is 4.54 and 6.96. For PCFMIS3, when the number of nodes is 3, the amount of subtrees in the most loaded group (\(Gnum\) = 1) is 1.32 times that of the least loaded group (\(Gnum\) = 2); when the number of nodes is 4 and 5, the ratio is 1.30 and 1.31. For the computing time, when the number of nodes is 3 in PCFMIS1, the longest computing time (\(Gnum\) = 3) is 3.31 times that of the shortest computing time (\(Gnum\) = 1). The corresponding amount ratio and time ratio are shown in Table 2. The closer the ratio is to 1, the better the effect of the load balancing. The same load balancing test is done on D50 (the support threshold is 0.01) which is shown in Table 3, and the corresponding amount ratio and time ratio are shown in Table 4. The experiments indicate that the efficient division of edges in the original data set affects the load of the slave nodes. The proposed EDS can achieve load balancing.  
Figure 4: System configuration diagram.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Number of Nodes**} & \multirow{2}{*}{_Gnum_} & \multicolumn{2}{c}{**PCFMIS1**} & \multicolumn{2}{c}{**PCFMIS3**} \\ \cline{3-6}  & & **Amount** & **Time (s)** & **Amount** & **Time (s)** \\ \hline \multirow{3}{*}{3} & 1 & 96,386 & 82.36 & 134,526 & 118.63 \\  & 2 & 113,695 & 113.67 & 101,637 & 113.6 \\  & 3 & 155,692 & 136.98 & 116,985 & 123.64 \\  & 4 & 277,258 & 187.63 & 114,329 & 117.25 \\ \hline \multirow{3}{*}{6} & 1 & 75,264 & 52.69 & 96,452 & 86.66 \\  & 2 & 65,897 & 53.76 & 93,658 & 84.32 \\ \cline{1-1}  & 3 & 193,648 & 122.25 & 107,612 & 83.59 \\ \cline{1-1}  & 4 & 85,638 & 85.96 & 84,369 & 83.12 \\ \cline{1-1}  & 5 & 84,567 & 93.21 & 83,695 & 83.72 \\ \cline{1-1}  & 6 & 156,942 & 110.67 & 92,418 & 84.87 \\ \hline \multirow{3}{*}{8} & 1 & 87,526 & 67.77 & 54,960 & 63.89 \\  & 2 & 40,236 & 45.63 & 76,147 & 62.14 \\ \cline{1-1}  & 3 & 73,658 & 62.37 & 58,426 & 63.45 \\ \cline{1-1}  & 4 & 54,269 & 43.73 & 66,545 & 64.77 \\ \cline{1-1}  & 5 & 86,352 & 58.23 & 65,471 & 62.95 \\ \cline{1-1}  & 6 & 125,621 & 87.12 & 64,774 & 64.01 \\ \cline{1-1}  & 7 & 97,634 & 81.69 & 70,425 & 63.52 \\ \cline{1-1}  & 8 & 177,563 & 93.28 & 69,998 & 62.59 \\ \hline \hline \end{tabular}
\end{table}
Table 1: The amount of subtrees and computing time in different _Gnum_ groups of CSLOGS10.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Number of Nodes**} & \multirow{2}{*}{_Gnum_} & \multicolumn{2}{c}{**PCFMIS1**} & \multicolumn{2}{c}{**PCFMIS3**} \\ \cline{3-6}  & & **Amount** & **Time (s)** & **Amount** & **Time (s)** \\ \hline
3 & 3.66 & 3.31 & 1.32 & 1.06 \\ \hline
4 & 4.54 & 3.02 & 1.3 & 1.17 \\ \hline
5 & 6.96 & 3.1 & 1.31 & 1.08 \\ \hline \hline \end{tabular}
\end{table}
Table 2: The amount ratio and time ratio in different _Gnum_ groups of CSLOGS10.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Number of Nodes**} & \multirow{2}{*}{_Gnum_} & \multicolumn{2}{c}{**PCFMIS1**} & \multicolumn{2}{c}{**PCFMIS3**} \\ \cline{3-6}  & & **Amount** & **Time (s)** & **Amount** & **Time (s)** \\ \hline \multirow{3}{*}{4} & 1 & 96,386 & 82.36 & 134,526 & 118.63 \\  & 2 & 113,695 & 113.67 & 101,637 & 113.6 \\  & 3 & 155,692 & 136.98 & 116,9