Discrete Applied Mathematics 129 (2003) 155 – 169
www.elsevier.com/locate/dam
An enumerative algorithm for the frequency
assignment problem
Carlo Mannino
∗
, Antonio Sassano
Dipartimento di Informatica e Sistemistica, Universit
Â
a di Roma La Sapienza, Via Buonarroti 12, 00185
Roma, Italy
Abstract
We present an algorithm to solve the frequency assignment problem for mobile cellular systems
and radio and television broadcasting. Frequencies must be assigned to transmitters in order to
meet interference requirements so that the overall signal=noise ratio is satisfactory. The basic
scheme is an exact enumerative method provided with ÿxing criteria to reduce the size of
the instances. Larger instances are solved by applying the algorithm to suitable subinstances,
eventually extending the solutions found. We were able to solve large real-life instances arising
in radio broadcasting and mobile cellular systems. Computational results outperform previous
results reported in the literature.
? 2002 Elsevier Science B.V. All rights reserved.
Keywords: Telecommunication systems; Frequency assignment
1. Introduction
The radio spectrum is a limited resource; moreover, the demand for frequencies has
grown very fast in the last decades. Thus, it is crucial to develop eective ways of
managing this scarce resource. The frequency assignment problem (FAP) is the problem
of eciently assigning a limited number of radio frequencies to the transmitters of a
network in such a way that interference requirements are satisÿed. This sort of problems
arise in telecommunication systems, such as mobile telephone and radio and television
broadcasting. Let T be the set of transmitters and let A
i
⊆{1;:::;k} be the set of
available frequencies of transmitter i, for all i ∈ T . A
i
is called the frequency domain
of transmitter i.Afrequency assignment is a vector x ∈ Z
|T |
+
, such that x
i
∈ A
i
, for
i =1;:::;|T|. Distance requirements due to pairwise interference are represented by a
∗
Corresponding author.
E-mailaddresses: mannino@dis.uniroma1.it (C. Mannino), sassano@dis.uniroma1.it (A. Sassano).
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