A complete characterization of the path layout construction problem for ATM networks with given hop count and load

Abstract

We investigate the time complexity of deciding the existence of layouts of virtual paths in high-speed networks, that enable a connection from one vertex to all others and have maximum hop count h and maximum edge load l, for a stretch factor of one. We prove that the problem of determining the existence of such layouts is NP-complete for every given values of h and I, except for the cases h = 2,l = 1 and h = 1, any l, for which we give polynomial-time layout constructions.