On the optimal placement of wavelength converters in WDM networks

An important goal of the design of wavelength division multiplexing (WDM) 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 the 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 a simple approximation algorithm whose theoretically guaranteed performance ratio is at most two.