Wavelength assignment and generalized interval graph coloring

Abstract In this paper we study wavelength assignment on an optical linesystem without wavelength conversion. Consider a set of undirected demands along the line. Each demand is carried on a wavelength and any two overlapping demands require distinct wavelengths. Suppose _ wavelengths are available in the system. We define `(e), the load on link e, to be the smallest integer such that `(e) _ is at least the number of demands passing through e. Hence, `(e) is the minimum number of fibers required on e in order to support all demands. We present a polynomial-time wavelength assignment algorithm that guarantees each wavelength appears at most `(e) times on each link e. (This generalizes the well-known fact that interval graphs are perfect.) In the presence of MOADMs (mesh optical add/drop multiplexers), devices that multiplex distinct wavelengths from different fibers into a new fiber, we only need to deploy `(e) fibers per link. On the other hand, if each demand has to stay on a single fiber, as is the case without MOADMs, we show that some links may require more than `(e) fibers. In fact, we show that it is NPcomplete to decide if a set of demands can be carried on a given set of fibers, or if there exists a set of fibers with a given total length that can carry all the demands