Abstract
We consider the problem of minimizing the number of wavelength interchangers in the design of wide-sense nonblocking cross-connects for wavelength division multiplexed (WDM) optical networks. The problem is modeled as a graph theoretic problem that we call dynamic edge coloring. In dynamic edge coloring the nodes of a graph are fixed but edges appear and disappear, and must be colored at the time of appearance without assigning the same color to adjacent edges. For wide-sense nonblocking WDM cross-connects with k input and k output fibers, it is straightforward to show that 2k-1 wavelength interchangers are always sufficient. We show that there is a constant c > 0 such that if there are at least ck 2 wavelengths then 2k-1 wavelength interchangers are also necessary. This improves previous exponential bounds. When there are only 2 or 3 wavelengths available, we show that far fewer than 2k-1 wavelength interchangers are needed. However we also prove that for any ε > 0 and k > 1/2ε, if the number of wavelengths is at least 1/ε2 then 2(1-ε)k wavelength interchangers are needed
Partially supported by NSERC.
Supported by a Lucent GRPW Fellowship.
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Haxell, P., Rasala, A., Wilfong, G., Winkler, P. (2002). Wide-Sense Nonblocking WDM Cross-Connects. In: Möhring, R., Raman, R. (eds) Algorithms — ESA 2002. ESA 2002. Lecture Notes in Computer Science, vol 2461. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45749-6_48
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DOI: https://doi.org/10.1007/3-540-45749-6_48
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