Optimal virtual topologies for one-to-many communication in WDM paths and rings

In this paper we examine the problem of constructing optimal virtual topologies for one-to-many communication in optical networks employing wavelength-division multiplexing. A virtual topology is a collection of optical lightpaths embedded in a physical topology. A packet sent from the source node travels over one or more lightpaths en route to its destination. Within a lightpath, transmission is entirely optical. At the terminus of a lightpath the data is converted into the electronic domain where it may be retransmitted on another lightpath toward its destination. Since the conversion of the packet from the optical to the electronic domain introduces delays and uses limited physical resources, one important objective is to find virtual topologies which minimize either the maximum or average number of lightpaths used from the source to all destination nodes. Although this problem is NP-complete in general, we show that minimizing the maximum or average number of lightpaths in path and ring topologies can be solved optimally by efficient algorithms.