Channel assignment with large demands

We introduce a general static model for radio channel assignment, the ‘feasible assignments model’, in which to investigate the effects of changes in demand. For a fixed instance of this model where only the demands can vary, we consider the span of spectrum needed for a feasible assignment of channels to transmitters, and compare this span with a collection of lower bounds, in the limit when demands at the transmitters get large. We introduce a relevant measure which generalises the imperfection ratio of a graph and give alternative descriptions. We show that for a fixed instance of the feasible assignments model where only the demands can vary, on input of the demands we can find the span in polynomial time. For the special case when the feasible assignments can be described by means of a complete graph together with co-site and adjacent constraints, we give a formula for the span. This yields clique-based lower bounds for the span in general problems.