Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH scholarly article en Blin, Lélia; Feuilloley, Laurent; Le Bouder, Gabriel https://www.dagstuhl.de/lipics License: Creative Commons Attribution 4.0 license (CC BY 4.0)
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URN: urn:nbn:de:0030-drops-157997
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Optimal Space Lower Bound for Deterministic Self-Stabilizing Leader Election Algorithms

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Abstract

Given a boolean predicate Π on labeled networks (e.g., proper coloring, leader election, etc.), a self-stabilizing algorithm for Π is a distributed algorithm that can start from any initial configuration of the network (i.e., every node has an arbitrary value assigned to each of its variables), and eventually converge to a configuration satisfying Π. It is known that leader election does not have a deterministic self-stabilizing algorithm using a constant-size register at each node, i.e., for some networks, some of their nodes must have registers whose sizes grow with the size n of the networks. On the other hand, it is also known that leader election can be solved by a deterministic self-stabilizing algorithm using registers of O(log log n) bits per node in any n-node bounded-degree network. We show that this latter space complexity is optimal. Specifically, we prove that every deterministic self-stabilizing algorithm solving leader election must use Ω(log log n)-bit per node registers in some n-node networks. In addition, we show that our lower bounds go beyond leader election, and apply to all problems that cannot be solved by anonymous algorithms.

BibTeX - Entry

@InProceedings{blin_et_al:LIPIcs.OPODIS.2021.24,
  author =	{Blin, L\'{e}lia and Feuilloley, Laurent and Le Bouder, Gabriel},
  title =	{{Optimal Space Lower Bound for Deterministic Self-Stabilizing Leader Election Algorithms}},
  booktitle =	{25th International Conference on Principles of Distributed Systems (OPODIS 2021)},
  pages =	{24:1--24:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-219-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{217},
  editor =	{Bramas, Quentin and Gramoli, Vincent and Milani, Alessia},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2022/15799},
  URN =		{urn:nbn:de:0030-drops-157997},
  doi =		{10.4230/LIPIcs.OPODIS.2021.24},
  annote =	{Keywords: Space lower bound, memory tight bound, self-stabilization, leader election, anonymous, identifiers, state model, ring topology}
}

Keywords: Space lower bound, memory tight bound, self-stabilization, leader election, anonymous, identifiers, state model, ring topology
Seminar: 25th International Conference on Principles of Distributed Systems (OPODIS 2021)
Issue date: 2022
Date of publication: 28.02.2022


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