Minimizing the span of d-walks to compute optimum frequency assignments

In this paper we deal with the Minimum Span Frequency Assignment Problem (MSFAP), that is the problem of assigning a limited set of radio frequencies to the base stations of a radio network so as the bandwidth occupancy is minimized and the overall interference is not too large. We present a new integer linear formulation for MSFAP in the multidemand case, which is the basis of an exact algorithm to compute both lower and upper bounds for MSFAP. Frequency assignments are represented as walks (sequence of nodes) in a graph. We look for a walk of minimum span, where the span of a walk is defined as the cost of a maximum cost subwalk (subsequence). The new approach is able to find optimum solutions over a large set of classical benchmarks.