Radio Labeling with Pre-assigned Frequencies

Hans L. Bodlaender, Haitze J. Broersma, Fedor V. Fomin, Artem Pyatkin, Gerhard Woeginger

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A radio labeling of a graph G is an assignment of pairwise distinct, positive integer labels to the vertices of G such that labels of adjacent vertices differ by at least 2. The radio labeling problem (RL) consists in determining a radio labeling that minimizes the maximum label that is used (the so-called span of the labeling). RL is a well-studied problem, mainly motivated by frequency assignment problems in which transmitters are not allowed to operate on the same frequency channel. We consider the special case where some of the transmitters have preassigned operating frequency channels. This leads to the natural variants p-RL(l) and p-RL(*) of RL with l pre-assigned labels and an arbitrary number of pre-assigned labels, respectively.

We establish a number of combinatorial, algorithmical, and complexitytheoretical results for these variants of radio labeling. In particular, we investigate a simple upper bound on the minimum span, yielding a linear time approximation algorithm with a constant additive error bound for p-RL(*) restricted to graphs with girth ≥ 5. We consider the complexity of p-RL(l) and p-RL(*) for several cases in which RL is known to be polynomially solvable. On the negative side, we prove that p-RL(*) is NP-hard for cographs and for k-colorable graphs where a k-coloring is given (k ≥3). On the positive side, we derive polynomial time algorithms solving p-RL(*) and p-RL(l) for graphs with bounded maximum degree, and for solving p-RL(l) for k-colorable graphs where a k-coloring is given.
Original languageEnglish
Title of host publicationAlgorithms — ESA 2002
Subtitle of host publication10th Annual European Symposium Rome, Italy, September 17–21, 2002 Proceedings
EditorsRalf Möhring, Rajeev Raman
Place of PublicationBerlin
ISBN (Electronic)978-3-540-45749-7
ISBN (Print)978-3-540-44180-9
Publication statusPublished - 2002
Event10th Annual European Symposium on Algorithms, ESA 2002 - Rome, Italy
Duration: 17 Sept 200221 Sept 2002
Conference number: 10

Publication series

NameLecture Notes in Computer Science
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference10th Annual European Symposium on Algorithms, ESA 2002
Abbreviated titleESA


  • METIS-208179


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