Placement of wavelength converters for minimal wavelength usage in WDM networks

An important goal of the design of WDM (wavelength division multiplexing) networks is to use less wavelengths to serve more communication needs. According to the wavelength conflict rule, we know that the number of wavelengths required in a WDM network is at least equal to the maximal number of channels over a fiber (called maximal link load) in the network. By placing wavelength converters at some nodes in the network, the number of wavelengths needed can be made equal to the maximal link load. In this paper we study the problem of placing the minimal number of converters in a network to achieve that the number of wavelengths in use is equal to the maximal link load. For duplex communication channels, we prove that an optimal solution can be obtained in polynomial-time. For unidirectional communication channels, which was proved to be NP-complete, we develop a set of lemmas which lead to an efficient approximation algorithm whose approximation ratio is two.