On bounds for the wavelength assignment problem on optical ring networks

This research note presents two new bounds for the oo-line wavelength assignment problem in optical ring networks that use wavelength division multiplexing. In this context, we consider a well-known bound 28, 35] that, to our knowledge, remains the only published bound for a ring topology and for which examples exist that show tightness. In this note, we show the bound can be improved in two ways: (1) by considering an additional parameter (the number of network nodes), we provide a sharper bound than the existing bound, and (2) we extend a classic result in 35] that was proved for the special case of k = 3 (no k connections cover the ring) to the general case of arbitrary k.

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