Modeling and Optimizing for NP-hard Problems in Graph Theory

This PhD thesis introduces optimization methods for graph problems classified as NP-hard. These are problems for which no deterministic algorithm is capable of solving them in polynomial time. More specifically, three graph problems were addressed, and for each, different optimization methods were used. These methods include standard methods, metaheuristics, and heuristics. In all cases, the performance of these methods was compared with those proposed in the literature, considering factors such as execution time and the quality of the solutions achieved. This comparative analysis aims to demonstrate the effectiveness of the proposed optimization methods

An efficient g-centroid location algorithm for cographs

In 1998, Pandu Rangan et al. proved that locating the g-centroid for an arbitrary graph is ��-hard by reducing the problem of finding the maximum clique size of a graph to the g-centroid location problem. They have also given an efficient polynomial time algorithm for locating the g-centroid for maximal outerplanar graphs, Ptolemaic graphs, and split graphs. In this paper, we present an O(nm) time algorithm for locating the g-centroid for cographs, where n is the number of vertices and m is the number of edges of the graph. 1