Frequency Assignment Problems

R.A. Murphey, P.M. Pardalos, and M.G.C. Resende

In Handbook of Combinatorial Optimization, D.-Z. Du and P.M. Pardalos, eds., Kluwer Academic Publishers, suppl. vol. A, pp. 295-377, 1999


The ever growing number of wireless communications systems deployed around the globe have made the optimal assignment of a limited radio frequency spectrum a problem of primary importance.  At issue are planning models for permanent spectrum allocation, licensing, regulation, and network design.  Further at issue are on-line algorithms for dynamically assigning frequencies to users within an established network.  Applications include aeronautical mobile, land mobile, maritime mobile, broadcast, land fixed (point-to-point), and satellite systems.  This paper surveys research conducted by theoreticians, engineers, and computer scientists regarding the frequency assignment problem (FAP) in all of its guises.  The paper begins by defining some of the more common types of FAPs.  It continues with a discussion on measures of optimality relating to the use of spectrum, models of interference, and mathematical representations of the many FAPs, both in graph theoretic terms, and as mathematical programs.  Graph theory and, in particular, graph coloring play an important role in the FAP since, in many instances, the FAP is cast in a form which closely resembles a graph coloring. Theoretical results that bound optimal solutions for special FAP structures are presented.  Exact algorithms for general FAPs are explained, and since many FAP instances are computationally hard, much space is devoted to approximate algorithms.  The paper concludes with a review of evaluation methods for FAP algorithms, test problem generators, and a discussion of the underlying engineering issues which should be considered when generating test problems.

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