# Dual-Neighborhood Tabu Search for Computing Stable Extensions in Abstract Argumentation Frameworks
## 6 Discussion and Analysis
### The Importance of Perturbation Techniques  
This sub-section tests the effect of perturbation techniques on algorithm performance. The algorithm variant that does not implement perturbation techniques is defined as DNTS-NP. We use the same 50 instances as Section 5.2.1. The results in Table 12 show that there is little difference between the performance of the DNTS and DNTS-NP algorithms in most of the instances. However, in some of the higher complexity instances, the DNTS algorithm has a significantly shorter solution time than DNTS-NP. In particular, DNTS-NP is more prone to extremely poor results when dealing with certain instances (e.g., v1000_3, v1000_7, v1000_10, v2000_1, v2000_2), which can have problems with extremely high running times or unsolvability. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & & & **DNTS** & & & **DNTS-NT** & \\ \hline
**Group** & **Instance** & **Best** & **Worst** & **Average** & **Best** & **Worst** & **Average** \\ \hline  & v2000\_1 & 9.17 & 37.30 & 19.15 & 14.01 & 81.66 & 43.66 \\  & v2000\_2 & 20.83 & 39.49 & 28.35 & 5.46 & 141.26 & 43.09 \\  & v2000\_3 & 3.83 & 5.61 & 5.04 & 3.93 & 5.92 & 4.58 \\  & v2000\_4 & 2.97 & 4.14 & 3.80 & 3.53 & 9.02 & 6.32 \\ vertex\_2000 & v2000\_5 & 3.12 & 5.16 & 3.91 & 2.97 & 5.15 & 3.74 \\  & v2000\_6 & 2.21 & 2.41 & 2.30 & 2.16 & 2.26 & 2.21 \\  & v2000\_7 & 2.51 & 2.71 & 2.61 & 2.26 & 2.46 & 2.35 \\  & v2000\_8 & 21.33 & 66.75 & 45.77 & 23.77 & 62.89 & 49.68 \\  & v2000\_9 & 4.90 & 6.53 & 5.82 & 3.83 & 5.31 & 4.63 \\  & v2000\_10 & 2.31 & 2.46 & 2.41 & 2.21 & 3.83 & 2.58 \\ \hline  & v3000\_1 & 4.95 & 6.78 & 5.98 & 5.77 & 6.07 & 5.96 \\  & v3000\_2 & 6.43 & 8.82 & 7.12 & 11.67 & 12.02 & 11.85 \\  & v3000\_3 & 8.21 & 24.28 & 13.56 & 11.31 & 15.63 & 13.28 \\  & v3000\_4 & 9.43 & 14.52 & 11.09 & 17.52 & 31.96 & 21.69 \\ vertex\_3000 & v3000\_5 & 13.75 & 78.64 & 42.33 & 22.45 & 92.95 & 54.65 \\  & v3000\_6 & 6.28 & 11.36 & 8.36 & 12.28 & 18.79 & 15.49 \\  & v3000\_7 & 8.36 & 9.84 & 8.88 & 6.78 & 11.71 & 9.98 \\  & v3000\_8 & 6.53 & 10.65 & 8.85 & 7.50 & 8.77 & 8.03 \\  & v3000\_9 & 12.12 & 16.55 & 14.16 & 9.43 & 14.57 & 11.11 \\  & v3000\_10 & 11.11 & 114.46 & 44.33 & 36.44 & 50.42 & 43.44 \\ \hline  & v4000\_1 & 19.70 & 27.79 & 23.40 & 23.11 & 31.25 & 26.61 \\  & v4000\_2 & 23.87 & 76.72 & 42.90 & 59.28 & 130.74 & 104.79 \\  & v4000\_3 & 35.22 & 169.90 & 77.79 & 45.44 & 119.97 & 80.71 \\  & v4000\_4 & 16.95 & 24.94 & 19.55 & 39.03 & 57.65 & 45.96 \\ vertex\_4000 & v4000\_5 & 19.96 & 30.18 & 24.49 & 43.46 & 49.81 & 46.43 \\  & v4000\_6 & 35.67 & 73.36 & 49.53 & 73.97 & 122.80 & 90.77 \\  & v4000\_7 & 27.84 & 58.36 & 39.37 & 58.71 & 109.27 & 91.50 \\  & v4000\_8 & 24.13 & 34.50 & 30.25 & 45.08 & 55.97 & 50.62 \\  & v4000\_9 & 25.40 & 35.93 & 29.72 & 21.48 & 27.08 & 23.96 \\  & v4000\_10 & 27.08 & 62.94 & 43.40 & 65.53 & 80.03 & 72.62 \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Experimental results on the number of instances correctly solved. We use the same 200 instances as Section 5.2.2. The results in Table 13 indicate that both algorithms are successful in producing solutions when dealing with small instances. When dealing with large instances, the DNTS algorithm is able to solve more instances and shows better performance compared with DNTS-NP.