A Doubly Cyclic Channel Assignment Problem

Abstract A standard model for radio channel assignment involves a set V of sites, the set {0,1,2,…} of channels, and a constraint matrix (w(u, v)) specifying minimum channel separations. An assignment f:V→{0,1,2,…} is feasible if the distance ∣f(u) − f(v)∣⩾w(u, v) for each pair of sites u and v. The aim is to find the least k such that there is a feasible assignment using only the k channels 0, 1, …, k − 1, and to find a corresponding optimal assignment. We consider here a related problem involving also two cycles. There is a given cyclic order τ on the sites, and feasible assignments f must also satisfy f(τv) ⩾ f(v) for all except one site v. Further, the channels are taken to be evenly spaced around a circle, so that if the k channels 0, 1, …, k − 1 are available then the distance between channels i and j is the minimum of ¦i − j¦ and k − ¦i − j¦ . We show how to find a corresponding optimal channel assignment in O (¦V¦ 3 ) steps.