A Note on Optical Routing on Trees

Bandwidth is a very valuable resource in wavelength division multiplexed optical networks. The problem of nding an optimal assignment of wavelengths to requests is of fundamental importance in bandwidth utilization. We present a polynomial-time algorithm for this problem on xed constant-size topologies. We combine this algorithm with ideas from Raghavan and Upfal 15] to obtain an optimal assignment of wavelengths on constant degree undirected trees. Mihail, Kaklamanis, and Rao 14] posed the following open question: what is the complexity of this problem on directed trees? We show that it is NP-complete both on binary and constant depth directed trees.