On bounds for the wavelength assignment problem on optical ring networks

This research note presents two new bounds for the off‐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 $k$ .