Experiments with two heuristic algorithms for the Maximum Algebraic Connectivity Augmentation Problem

In this work we present a heuristic algorithm to solve the Maximum Algebraic Connectivity Augmentation Problem (MACAP). This is an NP-complete problem (proved by Mosk-Aoyama in 2008) and consists in, given a graph, determining the smallest set of edges not belonging to it in such a way that the value of the algebraic connectivity of the augmented graph is maximum. In 2006, Ghosh and Boyd presented a heuristic procedure to solve this problem. This heuristic is an iterative method that selects one edge at a time based on the values of the components of a Fiedler vector of the graph. Our goal is to increase the value of the algebraic connectivity of a given graph by inserting edges based on the eccentricity of vertices. In order to evaluate our algorithm, computational tests comparing it with the Ghosh and Boyd procedure are presented.