Network design and optimisation based on cost and algebraic connectivity

Network design and optimisation has been one of the major focuses of the research community over the past decades. Connectivity of topologies can be improved by simply adding links; however, this incurs cost for addition of links for increased resilience. Therefore, topological design and optimisation requires developing algorithms so that a designer can select optimum parameters to achieve resilience in the least costly manner. In this paper, we develop a heuristic algorithm that optimises a topology based on algebraic connectivity metric that is defined as the second smallest eigenvalue of the Laplacian matrix. Furthermore, the connectivity of a topology is improved based on the available budget, for which we capture network cost in terms of euclidian distance between two connected nodes. We apply our algorithm on three realistic sets of backbone service provider graphs and compare the utility of our algorithm. The heuristic algorithm we introduce in this paper optimises topologies and is computationally less costly than an exhaustive optimisation.