This paper surveys frequency assignment problems coming up in planning wireless communication services. It particularly focuses on cellular mobile phone systems such as GSM, a technology that revolutionizes communication. Traditional vertex coloring provides a conceptual framework for the mathematical modeling of many frequency planning problems. This basic form, however, needs various extensions to cover technical and organizational side constraints. Among these ramifications are T-coloring and list coloring. To model all the subtleties, the techniques of integer programming have proven to be very useful.
The ability to produce good frequency plans in practice is essential for the quality of mobile phone networks. The present algorithmic solution methods employ variants of some of the traditional coloring heuristics as well as more sophisticated machinery from mathematical programming. This paper will also address this issue.
Finally, this paper discusses several practical frequency assignment problems in detail, states the associated mathematical models, and also points to public electronic libraries of frequency assignment problems from practice. The associated graphs have up to several thousand nodes and range form rather sparse to almost complete.
ZIB-report 00-47, Konrad-Zuse-Zentrum fuer Informationstechnik Berlin (ZIB), December 2000. Published in Discussiones Mathematicae Graph Theory 22 (1), 2002, pp. 51-88