Assigning Frequencies in GSM Networks

Mobile communication is a key technology in today’s information age. Despite the ongoing improvements in equipment design, interference remains a limiting factor for the use of radio communication. The author investigates in his PhD thesis how to largely prevent interference in GSM networks by carefully assigning the available frequencies to the installed base stations. The topic is addressed from two directions: first, new algorithms are presented to compute “good” frequency assignments fast; second, a novel approach, based on semidefinite programming, is employed to provide lower bounds for the amount of unavoidable interference. The proposed new methods for automatic frequency planning are compared in terms of running times and effectiveness in computational experiments using instances from practice. For most of the heuristics the running time behavior is suited for interactive planning, and they provide good assignments from a practical point of view. Several of these methods are successfully employed by the German GSM operator E-Plus Mobilfunk GmbH & Co. KG. The best lower bounds on the amount of unavoidable (co-channel) interference are presently obtained from solving semidefinite programs. These programs arise as nonpolyhedral relaxation of a minimum k-partition problem on complete graphs. The success of this approach is underpinned by revealing structural relations between the solution set of the semidefinite program and a polytope associated with an integer linear programming formulation of the minimum k-partition problem. Comparable relations are not known to hold for any polynomial time solvable polyhedral relaxation of the minimum k-partition problem. The application described is among the first of semidefinite programming to large industrial problems in combinatorial optimization.