L(p, q) labeling of d-dimensional grids

In this paper, we address the problem of λ labelings, that was introduced in the context of frequency assignment for telecommunication networks. In this model, stations within a given radius r must use frequencies that differ at least by a value p, while stations that are within a larger radius r > r must use frequencies that differ by at least another value q. The aim is to minimize the span of frequencies used in the network. This can be modeled by a graph coloring problem, called the L(p, q) labeling, where one wants to label vertices of the graph G modeling the network by integers in the range [0; M], in such a way that (1) neighbors in G are assigned colors differing by at least p and (2) vertices at distance 2 in G are assigned colors differing by at least q, while minimizing the value of M. M is then called the λ number of G, and is denoted by λp q (G). In this paper, we study the L(p, q) labeling for a specific class of networks, namely the d-dimensional grid Gd = G...

• Type: Journal
• Year: 2007
• Where: DM
• Authors: Guillaume Fertin, André Raspaud
• Keywords: DM 2007, Frequencies, Frequency Assignment, Graph Coloring Problem