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Approximation Algorithms for Path Coloring in Trees

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Efficient Approximation and Online Algorithms

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3484))

Abstract

The study of the path coloring problem is motivated by the allocation of optical bandwidth to communication requests in all-optical networks that utilize Wavelength Division Multiplexing (WDM). WDM technology establishes communication between pairs of network nodes by establishing transmitter-receiver paths and assigning wavelengths to each path so that no two paths going through the same fiber link use the same wavelength. Optical bandwidth is the number of distinct wavelengths. Since state-of-the-art technology allows for a limited number of wavelengths, the engineering problem to be solved is to establish communication minimizing the total number of wavelengths used. This is known as the wavelength routing problem. In the case where the underlying network is a tree, it is equivalent to the path coloring problem.

We survey recent advances on the path coloring problem in both undirected and bidirected trees. We present hardness results and lower bounds for the general problem covering also the special case of sets of symmetric paths (corresponding to the important case of symmetric communication). We give an overview of the main ideas of deterministic greedy algorithms and point out their limitations. For bidirected trees, we present recent results about the use of randomization for path coloring and outline approximation algorithms that find path colorings by exploiting fractional path colorings. Also, we discuss upper and lower bounds on the performance of on-line algorithms.

This work was partially supported by the European Union under IST FET Project CRESCCO.

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Author information

Authors and Affiliations

  1. Research Academic Computer Technology Institute and Department of Computer Engineering and Informatics, University of Patras, 26500, Rio, Greece

    Ioannis Caragiannis & Christos Kaklamanis

  2. Dipartimento di Informatica ed Applicazioni, Università di Salerno, 84081, Baronissi, Italy

    Giuseppe Persiano

Authors
  1. Ioannis Caragiannis
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  2. Christos Kaklamanis
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  3. Giuseppe Persiano
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Editor information

Editors and Affiliations

  1. IBISC, CNRS FRE 3190, Université d’Evry Val d’Essonne, Boulevard François Mitterand, 91025, Evry Cedex, France

    Evripidis Bampis

  2. Institute for Computer Science, University of Kiel, Olshausenstrasse 40, 24118, Kiel, Germany

    Klaus Jansen

  3. Brown University, 02918, Providence, RI, USA

    Claire Kenyon

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Caragiannis, I., Kaklamanis, C., Persiano, G. (2006). Approximation Algorithms for Path Coloring in Trees. In: Bampis, E., Jansen, K., Kenyon, C. (eds) Efficient Approximation and Online Algorithms. Lecture Notes in Computer Science, vol 3484. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11671541_3

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  • DOI: https://doi.org/10.1007/11671541_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-32212-2

  • Online ISBN: 978-3-540-32213-9

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