Some simple optimization techniques for self-organized public key management in mobile ad hoc networks

We consider some graph theoretical problems arising from security requirements in some communication networks. Basically one has to associate to each node of a directed graph G=(V,E) a partial subgraph of G. A solution consists hence of a collection of |V| subgraphs, subject to some packing constraints or connectivity requirements. We first describe the usual graph theoretical model and we review a known construction procedure for which we point out some basic properties. We then study in more details the case of complete graphs and show the existence of a solution with a guaranteed quality. Next, we study the performance of the construction procedure and we propose an additional construction. We attempt to characterize the cases in which either construction is preferable. In the last section, a tabu search approach is proposed and tested on a sample of numerical examples.