## The Orientation Model for Frequency Assignment Problems

Please always quote using this URN: urn:nbn:de:0297-zib-5627

- Mobile telecommunication systems establish a large number of communication links with a limited number of available frequencies; reuse of the same or adjacent frequencies on neighboring links causes interference. The task to find an assignment of frequencies to channels with minimal interference is the frequency assignment problem. The frequency assignment problem is usually treated as a graph coloring problem where the number of colors is minimized, but this approach does not model interference minimization correctly. We give in this paper a new integer programming formulation of the frequency assignment problem, the orientation model, and develop a heuristic two-stage method to solve it. The algorithm iteratively solves an outer and an inner optimization problem. The outer problem decides for each pair of communication links which link gets the higher frequency and leads to an acyclic subdigraph problem with additional longest path restrictions. The inner problem to find an optimal assignment respecting an orientation leads to a min-cost flow problem.

Author: | Ralf BorndörferORCiD, Andreas Eisenblätter, Martin Grötschel, Alexander Martin |
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Document Type: | ZIB-Report |

Tag: | Cellular Radio Telephone Systems; Frequency Assignment Problem; Integer Programming; Minimum-Cost Flow Problems |

MSC-Classification: | 90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING / 90Bxx Operations research and management science / 90B10 Network models, deterministic |

90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING / 90Bxx Operations research and management science / 90B80 Discrete location and assignment [See also 90C10] | |

90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING / 90Cxx Mathematical programming [See also 49Mxx, 65Kxx] / 90C10 Integer programming | |

Date of first Publication: | 1998/04/03 |

Series (Serial Number): | ZIB-Report (TR-98-01) |

ZIB-Reportnumber: | TR-98-01 |