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Smoothed Analysis of Balancing Networks

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Automata, Languages and Programming (ICALP 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5556))

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Abstract

In a load balancing network each processor has an initial collection of unit-size jobs, tokens, and in each round, pairs of processors connected by balancers split their load as evenly as possible. An excess token (if any) is placed according to some predefined rule. As it turns out, this rule crucially effects the performance of the network. In this work we propose a model that studies this effect. We suggest a model bridging the uniformly-random assignment rule, and the arbitrary one (in the spirit of smoothed-analysis) by starting from an arbitrary assignment of balancer directions, then flipping each assignment with probability α independently. For a large class of balancing networks our result implies that after \(\mathcal O(\log n)\) rounds the discrepancy is whp \(\mathcal O( (1/2-\alpha) \log n + \log \log n)\). This matches and generalizes the known bounds for α= 0 and α= 1/2.

Tobias Friedrich and Thomas Sauerwald were partially supported by postdoctoral fellowships from the German Academic Exchange Service (DAAD).

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Author information

Authors and Affiliations

  1. International Computer Science Institute, Berkeley, CA, USA

    Tobias Friedrich & Thomas Sauerwald

  2. Max-Planck-Institut für Informatik, Saarbrücken, Germany

    Tobias Friedrich

  3. Computer Science Division, University of California, Berkeley, CA, USA

    Dan Vilenchik

Authors
  1. Tobias Friedrich
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  2. Thomas Sauerwald
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  3. Dan Vilenchik
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Freiburg, Georges Köhler Allee 79, 79110, Freiburg, Germany

    Susanne Albers

  2. Department of Computer and Systems Sciences, Sapienza University of Rome, Via Ariosto 25, 00184, Roma, Italy

    Alberto Marchetti-Spaccamela

  3. Tel Aviv University Google R&D Center, School of Computer Science, Tel Aviv University, 69978, Tel Aviv, Israel

    Yossi Matias

  4. University of Patras and CTI, N. Kazantzaki Street 1, 26504, Rion, Patras, Greece

    Sotiris Nikoletseas

  5. RWTH Aachen, Lehrstuhl Informatik 7, Ahornstraße 55, 52056, Aachen, Germany

    Wolfgang Thomas

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© 2009 Springer-Verlag Berlin Heidelberg

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Friedrich, T., Sauerwald, T., Vilenchik, D. (2009). Smoothed Analysis of Balancing Networks. In: Albers, S., Marchetti-Spaccamela, A., Matias, Y., Nikoletseas, S., Thomas, W. (eds) Automata, Languages and Programming. ICALP 2009. Lecture Notes in Computer Science, vol 5556. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02930-1_39

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  • DOI: https://doi.org/10.1007/978-3-642-02930-1_39

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02929-5

  • Online ISBN: 978-3-642-02930-1

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