## 5 Experimental Results
The results presented in Table 9 reveal that the Malatya Dominating Set Algorithm (MDSA) outperforms other existing algorithms for the BHOSLIB datasets. MDSA achieved the smallest dominating set sizes (2) among all algorithms for these datasets. Additionally, the execution times were significantly shorter (0.761 s) compared to others. Furthermore, these results were performed using a computer with lower hardware capacity than other studies. These results demonstrate that MDSA provides efficient and rapid solutions, especially for large datasets, indicating its adaptability to a wide range of applications and its potential use in solving other NP-hard problems. Table 10 includes a comparison of MDSA with other existing algorithms on large-scale network datasets. The performance metric used is the minimum dominating set (D\({}_{\text{min}}\)) values. MDSA has determined smaller or equal D\({}_{\text{min}}\) values in many datasets compared to other algorithms. However, FastDS has shown the best performance across all benchmarks included in this table. When considering time complexity, MDSA is superior. FastDS consists of two main phases. The first phase, the local search process, has an average time complexity of \(\Theta(n\times logn)\), where \(n\) is node size. The second phase involves the application of inference rules, which has a time complexity of \(\Theta(m)\), where m is edge size. In total, the time complexity of FastDS is expressed as \(\Theta(n\times logn+m)\). For MDSA, Algorithms 1 and 2 operate only among the neighbors for each node, resulting in a total time complexity of \(\Theta(n\times d)\), and it has a simpler and faster growth rate. FastDS, with a time complexity of \(\Theta(n\times logn+m)\), has a more complex growth rate, especially due to the \(n\times logn\) term. This is more evident when looking at the average execution times in Table 9. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Dataset** & **FastMWDS [25]** & **RLS\({}_{\text{0}}\)[17]** & **ScBppw [26]** & **FastDS [27]** & **Our Work** \\ \hline Amazon0302 [46] & 35,616 & 38,735 & 36,199 & **35,593** & 37,806 \\ Amazon0312 [46] & 45,531 & 49,326 & 45,914 & **45,490** & 47,424 \\ Amazon0505 [46] & 47,362 & 51,281 & 47,734 & **47,310** & 49,207 \\ Amazon0601 [146] & 42,319 & 45,952 & 42,717 & **42,289** & 44,274 \\ Cit-HepPh [47] & **3078** & 3192 & 3087 & 3078 & 3223 \\ Cit-HepTh [47] & **2935** & 2985 & 2944 & 2936 & 3023 \\ Email-EuAll [46] & 18,181 & 18,181 & 18,181 & 18,181 & **18,179** \\ p2p-Gnutela04 [47] & **2227** & **2227** & **2227** & **2227** & 2239 \\ p2p-Gnutela24 [47] & **5418** & **5418** & **5418** & **5418** & **5418** \\ p2p-Gnutela25 [47] & **4519** & **4519** & **4519** & **4519** & **4519** \\ p2p-Gnutela30 [47] & **7169** & **7169** & **7169** & **7169** & **7169** \\ p2p-Gnutela31 [47] & **12,582** & **12,593** & **12,582** & **12,582** & **12,582** \\ soc-Shashdot0811 [48] & **14,312** & 14,333 & **14,312** & **14,312** & 14,323 \\ soc-Sdashdot0902 [48] & **15,305** & 15,334 & 15,305 & **15,305** & 15,351 \\ soc-Epinions1 [49] & **15,734** & 15,742 & 15,734 & **15,734** & 15,751 \\ web-BerkStan [48] & 28,434 & 30,119 & 28,615 & **28,432** & 28,972 \\ web-Google [48] & 79,700 & 81,106 & 79,756 & 79,699 & 80,334 \\ web-NudDame [50] & **23,733** & 23,950 & 23,746 & 23,735 & 23,800 \\ web-Stanford [48] & **13,198** & 14,099 & 13,298 & 13,199 & 13,433 \\ Wiki-Vote [3] & **1116** & **1116** & **1116** & **1116** & **1116** \\ cond-mat-2005 [51] & 6508 & 6509 & 6531 & 6508 & **5748** \\ \hline \hline \end{tabular} Note: Bolds are the best results for datasets.  
\end{table} 
Table 10: The comparison results of D\({}_{\text{min}}\) values for big networks. To demonstrate the strengths of the proposed algorithm, another comparison result is presented in Table 11. This comparison example includes the greedy algorithm, the CBC algorithm from [24], and the RLSo algorithm from [17].