Open Access

Andreas Eisenblätter

• Mobile cellular communcication is a key technology in today's information age. Despite the continuing improvements in equipment design, interference is and will remain a limiting factor for the use of radio communication. This Ph. D. thesis investigates how to prevent interference to the largest possible extent when assigning the available frequencies to the base stations of a GSM cellular network. The topic is addressed from two directions: first, new algorithms are presented to compute "good" frequency assignments fast; second, a novel approach, based on semidef inite programming, is employed to provide lower bounds for the amount of unavoidable interference. The new methods proposed for automatic frequency planning are compared in terms of running times and effectiveness in computational experiments, where the planning instances are taken from practice. For most of the heuristics the running time behavior is adequate for inter active planning; at the same time, they provide reasonable assignments from a practical point of view (compared to the currently best known, but substantially slower planning methods). In fact, several of these methods are successfully applied by the German GSM network operator E-Plus. The currently best lower bounds on the amount of unavoidable (co-channel) interference are obtained from solving semidefinite programs These programs arise as nonpolyhedral relaxation of a minimum /c-parti tion problem on complete graphs. The success of this approach is made plausible by revealing structural relations between the feasible set of the semidefinite program and a polytope associated with an integer linear programming formulation of the minimum ^-partition problem. Comparable relations are not known to hold for any polynomial time solvable polyhedral relaxation of the minimum ^-partition problem. The appli cation described is one of the first of semidefinite programming for large industrial problems in combinatorial optimization.