An improved algorithm to determine lower bounds for the fixed spectrum frequency assignment problem

Frequencies have to be assigned to transmitters whenever a radio network is established or modified. This is ideally done in a way which minimises interference in the network. Lower bounds are necessary to establish the effectiveness of the heuristic algorithms used for this task and to assess the quality of the assignments obtained. In the fixed spectrum frequency assignment problem the available frequencies are known in advance. The constraints are often binary constraints, specifying the necessary frequency separation between given pairs of transmitters. There may be penalties (or weights) associated with the violation of each constraint; it is then either necessary to minimise the number of constraints violated or, increasingly often, to minimise the sum of the weights associated with violated constraints. A technique for generating lower bounds for these quantities is presented. This is an evolution of a technique which has recently appeared in the literature. It produces better quality bounds, is in general significantly faster and allows larger problems to be handled.