On-Line Multicasting in All-Optical Networks

We consider the routing for a special type of communication requests, called a multicast, consisting of a fixed source and a multiset of destinations in a wavelength division multiplexing all optical network. We prove a min-max equality that the minimum number of wavelengths necessary for routing a multicast is equal to the maximum of the average number of paths that share a link in a cut of the network. Based on the min-max equality above, we propose an on-line algorithm for routing a multicast, and show that the competitive ratio of our algorithm is equal to the ratio of the degree of the source to the link connectivity of the network. We also show that 4/3 is a lower bound for the competitive ratio of an on-line algorithm for routing a multicast.