Graph labeling and radio channel assignment

Abstract

The vertex-labeling of graphs with nonnegative integers provides a natural setting in which to study problems of radio channel assignment. Vertices correspond to transmitter locations and their labels to radio channels. As a model for the way in which interference is avoided in real radio systems, each pair of vertices has, depending on their separation, a constraint on the difference between the labels that can be assigned. We consider the question of finding labelings of minimum span, given a graph and a set of constraints. The focus is on the infinite triangular lattice, infinite square lattice, and infinite line lattice, and optimal labelings for up to three levels of constraint are obtained. We highlight how accepted practice can lead to suboptimal channel assignments. © 1998 John Wiley & Sons, Inc. J Graph Theory 29: 263–283, 1998