Frequency assignment and multicoloring powers of square and triangular meshes

Abstract

The static frequency assignment problem on cellular networks can be abstracted as a multicoloring problem on a weighted graph, where each vertex of the graph is a base station in the network, and the weight associated with each vertex represents the number of calls to be served at the vertex. The edges of the graph model interference constraints for frequencies assigned to neighboring stations. In this paper, we first propose an algorithm to multicolor any weighted planar graph with at most 11/6-W colors, where W denotes the weighted clique number. Next, we present a polynomial time approximation algorithm which garantees at most 2W colors for multicoloring a power square mesh. Further, we prove that the power triangular mesh is a subgraph of the power square mesh. This means that it is possible to multicolor the power triangular mesh with at most 2 W colors, improving on the known upper bound of 4W. Finally, we show that any power toroidal mesh can be multicolored with strictly less than 4W colors using a distributed algorithm. © Springer-Verlag Berlin Heidelberg 2005.