Wavelength assignment and generalized interval graph coloring

  • Authors:

  • Peter Winkler;Lisa Zhang

  • Affiliations:

  • Bell Labs, Murray Hill, NJ;Bell Labs, Murray Hill, NJ

  • Venue:
  • SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
  • Year:
  • 2003

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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 on the same fiber require distinct wavelengths. Suppose μ wavelengths are available in the system and each fiber can carry all μ wavelengths. We define ℓ(e), the load on link e, to be the smallest integer such that ℓ(e)μ is at least the number of demands passing through e. Hence, ℓ(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 ℓ(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 ℓ(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 ℓ(e) fibers. In fact, we show that it is NP-complete 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.