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Analysis of the Harmonic Algorithm for Three Servers

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STACS 2003 (STACS 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2607))

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Abstract

Harmonic is a randomized algorithm for the k-server problem that, at each step, given a request point r, chooses the server to be moved to r with probability inversely proportional to the distance to r. For general k, it is known that the competitive ratio of Harmonic is at least 1/2k(k + 1), while the best upper bound on this ratio is exponential in k. It has been conjectured that Harmonic is 1/2k(k + 1)-competitive for all k. This conjecture has been proven in a number of special cases, including k = 2 and for the so-called lazy adversary.

In this paper we provide further evidence for this conjecture, by proving that Harmonic is 6-competitive for k = 3. Our approach is based on the random walk techniques and their relationship to the electrical network theory. We propose a new potential function Φ and reduce the proof of the validity of Φ to several inequalities involving hitting costs. Then we show that these inequalities hold for k = 3.

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of California, 92521, Riverside, CA

    Marek Chrobak

  2. Mathematical Inst., AS CR, Žitná 25, CZ-11567, Praha 1, Czech Republic

    Jiří Sgall

Authors
  1. Marek Chrobak
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  2. Jiří Sgall
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Editor information

Editors and Affiliations

  1. Institut für Informatik, Freie Universität Berlin, Takusstr. 9, 14195, Berlin, Germany

    Helmut Alt

  2. LIRMM, 161, Rue Ada, 34392, Montpellier Cedex 5, France

    Michel Habib

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© 2003 Springer-Verlag Berlin Heidelberg

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Chrobak, M., Sgall, J. (2003). Analysis of the Harmonic Algorithm for Three Servers. In: Alt, H., Habib, M. (eds) STACS 2003. STACS 2003. Lecture Notes in Computer Science, vol 2607. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36494-3_23

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  • DOI: https://doi.org/10.1007/3-540-36494-3_23

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-00623-7

  • Online ISBN: 978-3-540-36494-8

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