Channel Assignment in Honeycomb Networks

The honeycomb grid is a network topology based on the hexagonal plane tessellation, which is convenient to model the regular placement on the plane of the base stations of wireless networks. For an efficient use of the radio spectrum in such networks, channels have to be assigned to the base stations so as to avoid interferences. Such a problem can be modeled as a suitable coloring problem. Precisely, given an integer t and a honeycomb grid G=(V,E), an L(1^t )-coloring of G is a function f from the vertex set V to a set of nonnegative integers such that |f(u) − f(v)| ≥ 1, if the distance between the vertices u and v is at most t. This paper presents efficient algorithms for finding optimal L(1^t )-colorings of honeycomb grids