Frequency assignment in mobile and radio networks

We deal with the problem of frequency assignment in mobile and general radio networks, where the signal interferences are modeled using an interference graph G. Our approach uses graph theoretic and optimization techniques. We rst study on-line algorithms for frequency assignment in mobile networks. We prove that the greedy algorithm is-competitive, where is the maximum degree of G. We next employ the \classify and randomly select" paradigm to give a 5-competitive randomized algorithm for the case of planar interference graphs. We also show how the problem of on-line frequency assignment in mobile networks with multiple available frequency channels reduces to the problem of on-line frequency assignment in mobile networks with a single channel. We continue to study radio coloring and radio labeling as combinatorial models for frequency assignment in general radio networks. In both problems, the objective is to minimize the maximum frequency channel used, while the transmittersbeing adjacentin the interferencegraph must be assignedchannels that diier by at least two from each other. In radio coloring, diierent channels must be assigned to transmitters that are at distance two in the interference graph. Additionally, in radio labeling, all the transmitters must be assigned distinct frequency channels. Radio labelling is shown to be equivalent to a generalization of Hamiltonian path, and both problems remain NP-complete, even if they restricted to graphs of diameter two. We nally present algorithms and lower bounds for two on-line variations of radio labeling.