Wavelength Routing on DirectedFiber Trees ?

We address the issue of eeciently assigning wavelengths to communication requests in wavelength division multiplexing (WDM) optical networks. We consider directed tree and tree of rings topologies. These are topologies of concrete practical relevance for which undirected underlying graph models have been studied by Raghavan and Upfal 6]. Directed models were rst studied by Mihail et al 4]. For trees, we give a polynomial time routing algorithm that, for requests of maximum load L per directed ber link, uses at most 7=4L wavelengths. This improves the bound of Mihail et al.. As a corollary we also give an algorithm for trees of rings that uses 7=2L wavelengths.