Some graph partitioning problems and algorithms related to routing in large computer networks

The problem of partitioning a large computer network into clusters in order to reduce the amount of network resources consumed by the routing algorithm is addressed. The clustering problem is formulated as a general graph partitioning problem. It is shown that the problem of partitioning a graph into a minimum number of clusters with unit weight vertices and a given weight bound on the cluster size is NP-complete if each cluster is required to be internally connected. It is also shown that if a diameter bound is imposed on the cluster instead of the weight bound, then the problem is NP-complete, even when cluster connectivity is not required. An optimum partitioning algorithm is presented for the latter problem when the graph is a tree. An optimum partitioning algorithm is presented for another problem in which each cluster is required to contain exactly one of a set of specified vertices called cluster heads