License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ICALP.2017.139
URN: urn:nbn:de:0030-drops-74839
URL: https://drops.dagstuhl.de/opus/volltexte/2017/7483/
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Cai, Leran ; Sauerwald, Thomas

Randomized Load Balancing on Networks with Stochastic Inputs

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LIPIcs-ICALP-2017-139.pdf (0.6 MB)

Abstract

Iterative load balancing algorithms for indivisible tokens have been studied intensively in the past. Complementing previous worst-case analyses, we study an average-case scenario where the load inputs are drawn from a fixed probability distribution. For cycles, tori, hypercubes and expanders, we obtain almost matching upper and lower bounds on the discrepancy, the difference between the maximum and the minimum load. Our bounds hold for a variety of probability distributions including the uniform and binomial distribution but also distributions with unbounded range such as the Poisson and geometric distribution. For graphs with slow convergence like cycles and tori, our results demonstrate a substantial difference between the convergence in the worst- and average-case. An important ingredient in our analysis is a new upper bound on the t-step transition probability of a general Markov chain, which is derived by invoking the evolving set process.

BibTeX - Entry

@InProceedings{cai_et_al:LIPIcs:2017:7483,
  author =	{Leran Cai and Thomas Sauerwald},
  title =	{{Randomized Load Balancing on Networks with Stochastic Inputs}},
  booktitle =	{44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)},
  pages =	{139:1--139:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-041-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{80},
  editor =	{Ioannis Chatzigiannakis and Piotr Indyk and Fabian Kuhn and Anca Muscholl},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2017/7483},
  URN =		{urn:nbn:de:0030-drops-74839},
  doi =		{10.4230/LIPIcs.ICALP.2017.139},
  annote =	{Keywords: random walks, randomized algorithms, parallel computing}
}

Keywords: random walks, randomized algorithms, parallel computing
Collection: 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)
Issue Date: 2017
Date of publication: 07.07.2017

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