In a WDM network under multihop architecture, each link is associated with
a set of wavelengths available for channel connections, and in the network,
the number of wavelengths that can be used is limited. Data transmission o
ver one wavelength to another requires wavelength conversion, which causes
a long delay. Given a multicast connection, routing is to construct a tree
for the connection that is rooted from the source and connects all destinat
ions. In this paper, we consider the problem of constructing a routing tree
with a minimal number of wavelengths on the tree. We first prove that this
problem is NP-hard and then propose an approximation algorithm, which prod
uces a routing tree that has not only a small number of wavelengths but als
o a short delay from the source to all destinations. (C) 2000 John Wiley &
Sons, Inc.