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European Symposium on Algorithms

ESA 2002: Algorithms — ESA 2002 pp 736–747Cite as

Frequency Channel Assignment on Planar Networks

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2461))

Abstract

For integers p ≥ q, a L(p, q)-labeling of a network G is an integer labeling of the nodes of G such that adjacent nodes receive integers which differ by at least p, and nodes at distance two receive labels which differ by at least q. The minimum number of labels required in such labeling is λ p q (G). This arises in the context of frequency channel assignment in mobile and wireless networks and often G is planar. We show that if G is planar then \( \lambda _q^p (G) \leqslant \tfrac{5} {3}(2q - 1)\Delta + 12p + 144q - 78 \). We also provide an O(n 2) time algorithm to find such a labeling. This provides a \( (\tfrac{5} {3} + o(1)) \)-approximation algorithm for the interesting case of q = 1, improving the best previous approximation ratio of 2.

A full version of this paper is available with title “A Bound on the Chromatic Number of the Square of a Planar Graph” at http://www.cs.toronto.edu/~mreza/research.html

Supported by NSERC, a Sloan Research Fellowship, and a Premier’s Research Excellence Award.

Supported by Research Assistantship, Department of computer science, and University open fellowship, University of Toronto.

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of Toronto, 10 King’s College Rd., M5S 3G4, Toronto, Canada

    Michael Molloy & Mohammad R. Salavatipour

Authors
  1. Michael Molloy
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  2. Mohammad R. Salavatipour
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Editor information

Editors and Affiliations

  1. Fakultät II: Mathematik und Naturwissenschaften, Technische Universität Berlin, Strasse des 17. Juni 136, 10623, Berlin, Germany

    Rolf Möhring

  2. Department of Mathematics and Computer Science, University of Leicester, University Road, LE1 7RH, Leicester, UK

    Rajeev Raman

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© 2002 Springer-Verlag Berlin Heidelberg

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Molloy, M., Salavatipour, M.R. (2002). Frequency Channel Assignment on Planar Networks. In: Möhring, R., Raman, R. (eds) Algorithms — ESA 2002. ESA 2002. Lecture Notes in Computer Science, vol 2461. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45749-6_64

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  • DOI: https://doi.org/10.1007/3-540-45749-6_64

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-44180-9

  • Online ISBN: 978-3-540-45749-7

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