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A proof of wavelength conversion not improving the lagrangian bound of the static RWA problem

The fact that wavelength conversion hardly improves the performance of static routing and wavelength assignment (RWA) in wavelength division multiplexing (WDM) networks has been observed in many previous studies. However, other than simulation results, until now there was no formal proof of such fact. In this paper, we formally prove that wavelength conversion does not improve the Lagrangian bound of the static RWA problem.