Elementary landscape decomposition of the frequency assignment problem

The Frequency Assignment Problem (FAP) is an important problem that arises in the design of radio networks, when a channel has to be assigned to each transceiver of the network. This problem is a generalization of the graph coloring problem. In this paper we study a general version of the FAP that can include adjacent frequency constraints. Using concepts from landscapes’ theory, we prove that this general FAP can be expressed as a sum of two elementary landscapes. Further analysis also shows that some subclasses of the problem correspond to a single elementary landscape. This allows us to compute the kind of neighborhood information that is normally associated with elementary landscapes. We also provide a closed form formula for computing the autocorrelation coefficient for the general FAP, which can be useful as an a priori indicator of the performance of a local search method.