An exact algorithm for the channel assignment problem

A channel assignment problem is a triple (V,E,w) where V is a vertex set, E is an edge set and w is a function assigning edges positive integer weights. An assignment c of integers between 1 and K to the vertices is proper if |c(u)-c(v)|⩾w(uv) for each uv∈E; the smallest K for which there is a proper assignment is called the span. The input problem is set to be l-bounded if the values of w do not exceed l. We present an algorithm running in time O(n(l+2)n) which outputs the span for l-bounded channel assignment problems with n vertices. An algorithm running in time O(nl(l+2)n) for computing the number of different proper assignments of span at most K is further presented.