## Article  
### MDSA: A Dynamic and Greedy Approach to Solve the Minimum Dominating Set Problem  
[PERSON],*(c) and [PERSON](c)  
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The algorithms developed to solve the MDS problem provide highly effective solutions to the main problems such as optimizing resource allocation and reducing costs in complex network structures where a complex network is a network with non-trivial topological features that do not occur in lattice or simple graphs; on the contrary, they occur in social networks [2; 3; 4], wireless networks [5], sensor networks [6], transportation [7], biology [8], etc. The work performed in [9] to improve routing efficiency in wireless networks can give an idea about the real-life application of the MDS problem. In addition, the methodologies proposed to solve MDS can be effective in various contexts including Hopfield networks, maximum clique identification, and maximum independent set isolation [10]. The application domain of MDS is quite wide and there is a scarcity of efficient algorithms to solve the MDS problem for these application domains [11; 12; 13; 14]. Since the MDS problem is NP-hard and it is generally not practical to find an exact solution in large-scale graphs, methods aiming to obtain results close to the optimal solution have been proposed in the literature. These methods are classified as approximation algorithms, heuristic and metaheuristic algorithms that provide fast solutions, parameterized algorithms with features arranged according to the characteristics of the problem, and integer linear programming that can be applied to certain situations [15; 16; 17; 18; 19]. The application of greedy approaches in these methods can offer significant advantages in the context of simplicity, speed, and reduced computational load. This makes them useful in quickly obtaining appropriate solutions when faced with very large or complex examples [5]. The method applied to the MDS problem is expected to be fast and therefore have low algorithm complexity, especially when considering large graphs. The studies proposed in the literature focus on time complexity and obtain better measurements than the traditional exhaustive \(\Omega(2^{n})\) method for graphs with n nodes. An algorithm that reduces the time complexity to \(O(1.81^{n})\) is presented in [20]. A greedy search algorithm finds the optimal or nearly optimal solution with \(O(n^{3})\) time complexity [2]. In another study, the time complexity of the algorithm is reported as \(O\big{(}n^{2}lgn\big{)}\)[21]. A special spanning tree, the Kmax tree, is introduced using basic cut sets with \(O\big{(}n^{2}+\mathrm{m}\big{)}\) complexity and then a series of steps are executed [22]. This study aims to contribute to the literature by proposing a new approach using the Malatya centrality values for the MDS problem with complexity \(\Theta(n\times d)\). The Malatya centrality algorithm was first presented in [23] and it is updated and improved by our work. The Malatya centrality algorithm is used to compute centrality values of each node in the first and second phases.