Characterizing optimal topological structures for a class of large distributed data networks

A fundamental graph-theoretic result is presented for characterizing optimal topological structures. An optimal topology is defined as one which maximizes the number of origin-destination pairs that can communicate concurrently, while satisfying practical constraints related to performance, capital investment, and reliability. For a given network topology, the graph-theoretic result gives a bound for the maximum number of origin-destination pairs which can have concurrent communication. This theoretical result is in the form of a simple inequality which relates (among others) the following three parameters: number of concurrently communicating origin-destination pairs, number of network links, and network diameter. The novelty of this result with respect to past research in the area is its strong graph-theoretic foundation. The author aims at developing the mathematical machinery needed to cut to the heart of the topology design problem, as opposed to past approaches which rely heavily on heuristics or rules of thumb