Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH scholarly article en Ahmadian, Sara; Liu, Allen; Peng, Binghui; Zadimoghaddam, Morteza https://www.dagstuhl.de/lipics License: Creative Commons Attribution 3.0 Unported license (CC-BY 3.0)
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URN: urn:nbn:de:0030-drops-136186
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Distributed Load Balancing: A New Framework and Improved Guarantees

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Abstract

Inspired by applications on search engines and web servers, we consider a load balancing problem with a general convex objective function. In this problem, we are given a bipartite graph on a set of sources S and a set of workers W and the goal is to distribute the load from each source among its neighboring workers such that the total load of workers are as balanced as possible. We present a new distributed algorithm that works with any symmetric non-decreasing convex function for evaluating the balancedness of the workers' load. Our algorithm computes a nearly optimal allocation of loads in O(log n log² d/ε³) rounds where n is the number of nodes, d is the maximum degree, and ε is the desired precision. If the objective is to minimize the maximum load, we modify the algorithm to obtain a nearly optimal solution in O(log n log d/ε²) rounds. This improves a line of algorithms that require a polynomial number of rounds in n and d and appear to encounter a fundamental barrier that prevents them from obtaining poly-logarithmic runtime [Berenbrink et al., 2005; Berenbrink et al., 2009; Subramanian and Scherson, 1994; Rabani et al., 1998]. In our paper, we introduce a novel primal-dual approach with multiplicative weight updates that allows us to circumvent this barrier. Our algorithm is inspired by [Agrawal et al., 2018] and other distributed algorithms for optimizing linear objectives but introduces several new twists to deal with general convex objectives.

BibTeX - Entry

@InProceedings{ahmadian_et_al:LIPIcs.ITCS.2021.79,
  author =	{Sara Ahmadian and Allen Liu and Binghui Peng and Morteza Zadimoghaddam},
  title =	{{Distributed Load Balancing: A New Framework and Improved Guarantees}},
  booktitle =	{12th Innovations in Theoretical Computer Science Conference (ITCS 2021)},
  pages =	{79:1--79:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-177-1},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{185},
  editor =	{James R. Lee},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/13618},
  URN =		{urn:nbn:de:0030-drops-136186},
  doi =		{10.4230/LIPIcs.ITCS.2021.79},
  annote =	{Keywords: Load balancing, Distributed algorithms}
}

Keywords: Load balancing, Distributed algorithms
Seminar: 12th Innovations in Theoretical Computer Science Conference (ITCS 2021)
Issue date: 2021
Date of publication: 04.02.2021


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