Multicast virtual topologies in WDM paths and rings with splitting loss

This paper addresses the problem of constructing optimal virtual topologies for multicast communication in optical networks employing wavelength-division multiplexing (WDM). For concreteness, we use the average hop distance as the metric of optimality. WDM networks supporting multicast communication typically employ multicast-capable switches which permit a path entering a switch on an incoming wavelength to be replicated or "split" optically to one or more output links. This splitting incurs a power loss which is frequently neglected in existing heuristics and algorithms. In this paper we show that the problem of finding optimal virtual topologies with splitting loss constraints can be solved in polynomial time in directed paths and rings, although the problem is NP-complete for general topologies.