Multicasting and broadcasting in undirected WDM networks

This paper addresses the problem of multicasting and broadcasting in undirected wavelength-division multiplexing (WDM) networks. Given an undirected network G=(VE) with a source nodes and a set of destination nodes D, /spl Lambda/ is the set of wavelength that can be used in the network. Associated with every edge e, there is a set of available wavelengths on it. The multicast problem is to find a tree rooted at s including all nodes in D such that the cost of the tree is minimum in terms of the cost of wavelength conversion at nodes and the cost of using wavelength on edges. This paper proves that the multicast problem is NP-complete and can not be approximated within a constant factor, unless P=NP. Then we construct an auxiliary graph for the original WDM networks and reduce the multicast problem to a group Steiner tree problem on the auxiliary graph. Employing the known algorithm for the group Steiner tree problem, we derive an algorithm for the problem, which delivers a solution within O(log/sup 2/ (nk)loglog(nk)logp) times the optimum.