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**Frequency assignment in mobile and radio networks.**
*(English)*
Zbl 0929.68005

Mavronicolas, Marios (ed.) et al., Networks in distributed computing. DIMACS workshop, Rutgers Univ., New Brunswick, NJ, USA, October 27–29, 1997. Providence, RI: AMS. DIMACS, Ser. Discrete Math. Theor. Comput. Sci. 45, 73-90 (1999).

Summary: We deal with the problem of frequency assignment in mobile and general networks, where the signal interferences are modeled using an interference graph \(G\). Our approach uses graph theoretic and optimization techniques. We first study on-line algorithms for frequency assignment in mobile networks. We prove that the greedy algorithm is \(\Delta\)-competitive, where \(\Delta\) 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 transmitters being adjacent in the interference graph must be assigned channels that differ by at least two from each other. In radio coloring, different 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 \({\mathcal N}P\)-complete, even if they restricted to graphs of diameter two. We finally present algorithms and lower bounds for two on-line variations of radio labeling.

For the entire collection see [Zbl 0907.00026].

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 transmitters being adjacent in the interference graph must be assigned channels that differ by at least two from each other. In radio coloring, different 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 \({\mathcal N}P\)-complete, even if they restricted to graphs of diameter two. We finally present algorithms and lower bounds for two on-line variations of radio labeling.

For the entire collection see [Zbl 0907.00026].

### MSC:

68M10 | Network design and communication in computer systems |