Approximation Algorithms for Channel Assignment with Constraints

Cellular networks are generally modeled as node-weighted graphs, where the nodes represent cells and the edges represent the possibility of radio interference. An algorithm for the channel assignment problem must assign as many channels as the weight indicates to every node, such that any two channels assigned to the same node satisfy the co-site constraint, and any two channels assigned to adjacent nodes satisfy the inter-site constraint. We describe several approximation algorithms for channel assignment with arbitrary co-site and inter-site constraints for odd cycles and so-called hexagon graphs that are often used to model cellular networks. The algorithms given for odd cycles are optimal for some values of constraints, and have performance ratio at most 1 + 1=(n ? 1) for all other cases, where n is the length of the cycle. Our main result is an algorithm of performance ratio at most 4=3 + for hexagon graphs with arbitrary co-site and inter-site constraints.