# 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{2}{c}{**DNTS**} & \multicolumn{4}{c}{**HAYWOOD**} & \multicolumn{4}{c}{**u-toksia**} \\ \hline
**Instance** & **Best** & **Worst** & **Average** & **Best** & **Worst** & **Average** & **Best** & **Worst** & **Average** \\ \hline V4000\_1 & 20.92 & 25.49 & 22.13 & 19.65 & 20.52 & 20.1 & 23.67 & 48.39 & 44.93 \\ V4000\_2 & 23.01 & 93 & 47.8 & 20.16 & 21.28 & 20.59 & 41.63 & 57.65 & 43.79 \\ V4000\_3 & 32.57 & 138.98 & 61.95 & 245.5 & 261.06 & 251.06 & 47.47 & 121.48 & 55.29 \\ V4000\_4 & 17.16 & 24.08 & 20.5 & 17.01 & 17.87 & 17.3 & 18.69 & 38.22 & 36.07 \\ V4000\_5 & 19.75 & 24.89 & 22.63 & 19.04 & 19.96 & 19.51 & 22.14 & 42.39 & 40.01 \\ V4000\_6 & 34.15 & 120.62 & 57.42 & 200.78 & 208.1 & 203.81 & 48.09 & 55.3 & 49.26 \\ V4000\_7 & 28.2 & 83.08 & 46.17 & 76.01 & 80.28 & 77.45 & 30.38 & 48.89 & 46.55 \\ V4000\_8 & 24.79 & 31.56 & 28.24 & 27.33 & 31.1 & 28.29 & 24.02 & 54.65 & 50.96 \\ V4000\_9 & 23.57 & 33.23 & 28.45 & 23.87 & 25.2 & 24.45 & 25.96 & 48.64 & 45.85 \\ V4000\_10 & 30.99 & 65.49 & 37.87 & 33.08 & 34.55 & 33.71 & 46.91 & 52.36 & 50.73 \\ V4000\_11 & 20.77 & 23.67 & 21.65 & 20.06 & 20.87 & 20.47 & 17.72 & 21.33 & 18.21 \\ V4000\_12 & 19.04 & 25.04 & 22.14 & 21.69 & 22.7 & 22 & 23.36 & 44.98 & 42.38 \\ V4000\_13 & 24.13 & 31.25 & 27.19 & 51.95 & 55.05 & 52.85 & 28.15 & 50.43 & 47.57 \\ V4000\_14 & 19.8 & 28.44 & 22.75 & 20.57 & 21.48 & 20.96 & 16.8 & 26.87 & 17.94 \\ V4000\_15 & 19.25 & 25.28 & 22.08 & 22.75 & 23.72 & 23.15 & 17.41 & 21.18 & 17.88 \\ V4000\_16 & 28.65 & 79.62 & 51.66 & 155.61 & 162.32 & 158.73 & 50.27 & 82.52 & 53.94 \\ V4000\_17 & 21.99 & 26.92 & 24.41 & 26.92 & 28.35 & 27.42 & 25.5 & 47.27 & 44.49 \\ V4000\_18 & 36.59 & 86.28 & 52.3 & 71.53 & 75.25 & 73.03 & 48.54 & 82.01 & 52.37 \\ V4000\_19 & 28.55 & 46.51 & 33.91 & 34.61 & 36.33 & 35.14 & 32.06 & 55.41 & 52.46 \\ V4000\_20 & 36.84 & 67.62 & 49.89 & 287.14 & 299.6 & 291.57 & 48.49 & 68.33 & 50.89 \\
**Att** & 25.54 & 54.05 & 35.06 & 69.76 & 73.28 & 71.08 & 31.86 & 53.42 & 43.08 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Experimental results for instances of 4000 vertices. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**DNTS**} & \multicolumn{4}{c}{**HAYWOOD**} & \multicolumn{4}{c}{**u-toksia**} \\ \hline
**Instance** & **Best** & **Worst** & **Average** & **Best** & **Worst** & **Average** & **Best** & **Worst** & **Average** \\ \hline V3000\_1 & 5 & 7.19 & 5.8 & 4.85 & 5.05 & 4.96 & 22.7 & 23.16 & 22.87 \\ V3000\_2 & 6.17 & 7.85 & 6.66 & 6.27 & 6.43 & 6.36 & 10.95 & 11.21 & 11.13 \\ V3000\_3 & 8.51 & 13.35 & 11.33 & 7.7 & 8.11 & 7.92 & 34.3 & 35.32 & 35.05 \\ V3000\_4 & 8.05 & 11.16 & 10.46 & 10.04 & 10.65 & 10.44 & 14.21 & 14.57 & 14.41 \\ V3000\_5 & 12.89 & 31.71 & 21.28 & 23.16 & 24.18 & 23.77 & 33.94 & 34.76 & 34.35 \\ V3000\_6 & 6.38 & 8.61 & 7.37 & 9.63 & 10.14 & 9.92 & 28.45 & 29.89 & 28.93 \\ V3000\_7 & 7.29 & 11.51 & 9.45 & 6.93 & 7.29 & 7.17 & 27.28 & 27.89 & 27.58 \\ V3000\_8 & 7.09 & 11.21 & 8.73 & 18.53 & 19.04 & 18.73 & 28.25 & 28.91 & 28.6 \\ V3000\_9 & 11.01 & 16.09 & 13.27 & 22.45 & 23.21 & 22.92 & 15.33 & 15.63 & 15.5 \\ V3000\_10 & 12.58 & 44.47 & 22.96 & 63.5 & 68.07 & 66.21 & 33.84 & 34.55 & 34.09 \\ V3000\_11 & 5.61 & 5.97 & 5.73 & 5.56 & 5.72 & 5.61 & 8.87 & 9.17 & 9.06 \\ V3000\_12 & 5.46 & 5.77 & 5.6 & 5.26 & 5.36 & 5.33 & 22.55 & 23.01 & 22.81 \\ V3000\_13 & 9.83 & 13.34 & 11.44 & 10.8 & 11.21 & 10.98 & 35.42 & 36.34 & 36.01 \\ V3000\_14 & 12.28 & 31.25 & 18.69 & 11.87 & 12.22 & 12.1 & 38.06 & 38.88 & 38.41 \\ V3000\_15 & 9.43 & 13.8 & 1 of the DNTS algorithm over HAYWOOD and u-toksa in terms of the overall average time (att). Therefore, the DNTS algorithm can be considered as an effective optimization of the HAYWOOD algorithm in terms of improving the upper bound of the performance of the solved instances.