# Dual-Neighborhood Tabu Search for Computing Stable Extensions in Abstract Argumentation Frameworks
## 5 Experiment
### Algorithm Comparison
#### 5.2.1 Comparison on Algorithm Efficiency
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**DNTS**} & \multicolumn{3}{c}{**HAYWOOD**} & \multicolumn{3}{c}{**u-toksa**} \\ \hline
**Instance** & **Best** & **Worst** & **Average** & **Best** & **Worst** & **Average** & **Best** & **Worst** & **Average** \\ \hline V2000\_1 & 5.46 & 142.6 & 44.52 & 14 & 14.41 & 14.21 & 26.01 & 27.13 & 26.62 \\ V2000\_2 & 20.62 & 251.33 & 76.89 & 60.09 & 216.14 & 120.46 & 20.57 & 21.18 & 20.83 \\ V2000\_3 & 2.87 & 26.31 & 5.52 & 3.27 & 3.98 & 3.37 & 26.31 & 26.98 & 26.66 \\ V2000\_4 & 2.36 & 20.52 & 6.67 & 8.3 & 9.48 & 8.55 & 20.16 & 20.77 & 20.52 \\ V2000\_5 & 2.92 & 25.86 & 5.79 & 2.87 & 3.38 & 2.98 & 25.75 & 26.47 & 26.07 \\ V2000\_6 & 0.07 & 2.1 & 1.86 & 2 & 2.1 & 2.05 & 0.07 & 0.07 & 0.07 \\ V2000\_7 & 0.12 & 2.51 & 2.06 & 2.15 & 2.21 & 2.18 & 0.12 & 0.12 & 0.12 \\ V2000\_8 & 8.71 & 36.18 & 21.97 & 57.5 & 270.97 & 167.28 & 26.57 & 27.38 & 26.94 \\ V2000\_9 & 2.71 & 9.93 & 3.66 & 3.17 & 3.27 & 3.22 & 9.68 & 9.94 & 9.81 \\ V2000\_10 & 2 & 15.78 & 4.63 & 2.05 & 2.1 & 2.07 & 7.85 & 8 & 7.9 \\ V2000\_11 & 0.07 & 1.95 & 1.64 & 1.75 & 1.8 & 1.8 & 0.07 & 0.07 & 0.07 \\ V2000\_12 & 1.75 & 17.26 & 3.61 & 1.65 & 1.7 & 1.66 & 17.16 & 17.51 & 17.34 \\ V2000\_13 & 2.36 & 20.87 & 4.98 & 2.21 & 2.26 & 2.22 & 20.87 & 21.33 & 21.09 \\ V2000\_14 & 3.07 & 10.65 & 4.35 & 3.78 & 3.99 & 3.85 & 10.65 & 10.85 & 10.74 \\ V2000\_15 & 3.07 & 10.39 & 4.07 & 4.24 & 4.45 & 4.33 & 10.39 & 10.6 & 10.46 \\ V2000\_16 & 1.9 & 6.73 & 2.44 & 1.9 & 1.95 & 1.91 & 6.63 & 6.78 & 6.7 \\ V2000\_17 & 3.22 & 10.9 & 4.61 & 3.48 & 3.63 & 3.57 & 10.75 & 11.01 & 10.86 \\ V2000\_18 & 1.85 & 17.16 & 3.68 & 2.21 & 2.26 & 2.25 & 16.9 & 17.26 & 17.11 \\ V2000\_19 & 2.97 & 33.96 & 15.67 & 7.44 & 7.75 & 7.57 & 20.26 & 20.72 & 20.49 \\ V2000\_20 & 5.56 & 28.76 & 12.26 & 21.07 & 27.89 & 22.11 & 28.75 & 29.17 & 28.9 \\
**Att** & 3.68 & 34.59 & 11.54 & 10.26 & 29.29 & 18.88 & 15.28 & 15.67 & 15.47 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Experimental results for instances of 2000 vertices. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**DNTS**} & \multicolumn{3}{c}{**HAYWOOD**} & \multicolumn{3}{c}{**u-toksa**} \\ \hline
**Instance** & **Best** & **Worst** & **Average** & **Best** & **Worst** & **Average** & **Best** & **Worst** & **Average** \\ \hline V1000\_17 & 2.71 & 28.1 & 12.66 & 13.24 & 41.22 & 30.26 & 17.72 & 18.13 & 17.91 \\ V1000\_18 & 0.32 & 0.99 & 0.43 & 0.27 & 0.27 & 0.27 & 0.04 & 0.04 & 0.04 \\ V1000\_19 & 1.75 & 18.62 & 6.39 & 14.36 & 20.57 & 15.19 & 18.69 & 19.24 & 18.97 \\ V1000\_20 & 0.68 & 2.66 & 1.11 & 0.83 & 0.93 & 0.87 & 18.74 & 19.14 & 18.92 \\
**Att** & 0.59 & 3.7 & 1.53 & 1.87 & 3.66 & 2.82 & 6.5 & 6.68 & 6.59 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: _Cont._Based on the above experimental results, it can be observed that the DNTS algorithm significantly outperforms the HAYWOOD and u-toksia algorithms in terms of the best of the solved instances. However, there is a large difference between its best and worst values, which reveals the lack of stability of the DNTS algorithm. The DNTS algorithm shows more outstanding performance compared with HAYWOOD when dealing with some complex instances that take a long time, which leads to a consistent outperformance