Frequency allocation and linear programming

The present paper deals with optimal fixed channel assignment for large real-world cellular radio networks. Examples are taken from data of the D2-network, operated by Mannesmann Mobilfunk (MMO) in Germany. Because of the huge size of the problems an exact optimal solution is presently out of reach. We present a heuristic iterative approach which performs extremely well, and significantly outperforms channel designs presently used by network operators. The basic ingredients of our approach are: (1) fast and well established simple heuristics as initial assignments; (2) splitting the whole problem into smaller subproblems which can be optimized efficiently by solving a binary linear program (BLP), and repeating this process iteratively; (3) past-processing the resulting near-optimal design to avoid undesirable properties. A lot of detailed problems must be solved, such as a powerful preprocessing of constraints for the BLPs, and a careful selection of the subproblems in (2). In summary, a very flexible tool is derived, also capable of taking into account external constraints from practical requirements.