An analysis between exact and approximate algorithms for the k-center problem in graphs

Abstract

<span lang="EN-US">This research focuses on the k-center problem and its applications. Different methods for solving this problem are analyzed. The implementations of an exact algorithm and of an approximate algorithm are presented. The source code and the computation complexity of these algorithms are presented and analyzed. The multitasking mode of the operating system is taken into account considering the execution time of the algorithms. The results show that the approximate algorithm finds solutions that are not worse than two times optimal. In some case these solutions are very close to the optimal solutions, but this is true only for graphs with a smaller number of nodes. As the number of nodes in the graph increases (respectively the number of edges increases), the approximate solutions deviate from the optimal ones, but remain acceptable. These results give reason to conclude that for graphs with a small number of nodes the approximate algorithm finds comparable solutions with those founds by the exact algorithm.</span>

A comparative analysis between two heuristic algorithms for the graph vertex coloring problem

“…Distinct aspects of the problem use various techniques [11]- [13], algorithms [14], [15] and approaches [16], [17]. Other algorithms and approaches are used to solve similar problems in graphs [18], [19]. Other in-depth analyses of this problem are presented in [20]- [22].…”

An analysis between different algorithms for the graph vertex coloring problem

“…Different variants use different approaches [19], [20], techniques [21], [22] and algorithms [23], [24]. Similar approaches have been used to solve other problems in graph theory [25]. Detailed reviews of the specifics of the graph vertex coloring problem are discussed in [26], [27].…”