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Randomized Lower Bounds for Online Path Coloring

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Randomization and Approximation Techniques in Computer Science (RANDOM 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1518))

Abstract

We study the power of randomization in the design of on-line graph coloring algorithms. No specific network topology for which randomized online algorithms perform substantially better than deterministic algorithms is known until now. We present randomized lower bounds for online coloring of some well studied network topologies.

We show that no randomized algorithm for online coloring of interval graphs achieves a competitive ratio strictly better than the best known deterministic algorithm [KT81].

We also present a first lower bound on the competitive ratio of randomized algorithms for path coloring on tree networks, then answering an open question posed in [BEY98]. We prove an Ω(logδ) lower bound for trees of diameter δ = O(log n) that compares with the known O(δ)-competitive deterministic algorithm for the problem, then still leaving open the question if randomization helps for this specific topology.

This work is partly supported by EU ESPRIT Long Term Research Project ALCOM-IT under contract n 20244, and by Italian Ministry of Scientific Research Project 40% “Algoritmi, Modelli di Calcolo e Strutture Informative”.

This work was partly done while the author was visiting the Max-Planck-Institut für Informatik, Saarbrücken, Germany.

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Author information

Authors and Affiliations

  1. Dipartimento di Informatica e Sistemistica, Università di Roma “La Sapienza”, Via Salaria 113, 00198, Roma, Italy

    Stefano Leonardi & Andrea Vitaletti

Authors
  1. Stefano Leonardi
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  2. Andrea Vitaletti
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Editor information

Editors and Affiliations

  1. International Computer Science Institute, 1947 Center Street, Suite 600, Berkeley, CA, 94704-1198, USA

    Michael Luby

  2. Computer Science Department, University of Geneva, 24, rue Général Dufour, CH-1211, Geneva 4, Switzerland

    José D. P. Rolim

  3. University of Barcelona (UPC), Jordi Girona Salgado 1-3, E-08034, Barcelona, Spain

    Maria Serna

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© 1998 Springer-Verlag Berlin Heidelberg

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Leonardi, S., Vitaletti, A. (1998). Randomized Lower Bounds for Online Path Coloring. In: Luby, M., Rolim, J.D.P., Serna, M. (eds) Randomization and Approximation Techniques in Computer Science. RANDOM 1998. Lecture Notes in Computer Science, vol 1518. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-49543-6_19

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  • DOI: https://doi.org/10.1007/3-540-49543-6_19

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-65142-0

  • Online ISBN: 978-3-540-49543-7

  • eBook Packages: Springer Book Archive

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