article

Knowledge, level of symmetry, and time of leader election

Authors:

Emanuele G. Fusco,

Andrzej PelcAuthors Info & Claims

Distributed Computing, Volume 28, Issue 4

Pages 221 - 232

https://doi.org/10.1007/s00446-014-0237-0

Published: 01 August 2015 Publication History

Abstract

We study the time needed for deterministic leader election in the $$\mathcal{LOCAL}$$LOCAL model, where in every round a node can exchange any messages with its neighbors and perform any local computations. The topology of the network is unknown and nodes are unlabeled, but ports at each node have arbitrary fixed labelings which, together with the topology of the network, can create asymmetries to be exploited in leader election. We consider two versions of the leader election problem: strong LE in which exactly one leader has to be elected, if this is possible, while all nodes must terminate declaring that leader election is impossible otherwise, and weak LE, which differs from strong LE in that no requirement on the behavior of nodes is imposed, if leader election is impossible. We show that the time of leader election depends on three parameters of the network: its diameter $$D$$D, its size $$n$$n, and its level of symmetry$$\lambda $$, which, when leader election is feasible, is the smallest depth at which some node has a unique view of the network. It also depends on the knowledge by the nodes, or lack of it, of parameters $$D$$D and $$n$$n.

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Cited By

Gorain B Miller APelc A(2023)Four shades of deterministic leader election in anonymous networksDistributed Computing10.1007/s00446-023-00451-336:4(419-449)Online publication date: 31-May-2023
https://dl.acm.org/doi/10.1007/s00446-023-00451-3
Gilbert SRobinson PSourav S(2022)Leader Election in Well-Connected GraphsAlgorithmica10.1007/s00453-022-01068-x85:4(1029-1066)Online publication date: 24-Nov-2022
https://dl.acm.org/doi/10.1007/s00453-022-01068-x
Gorain BMiller APelc AAgrawal KAzar Y(2021)Four Shades of Deterministic Leader Election in Anonymous NetworksProceedings of the 33rd ACM Symposium on Parallelism in Algorithms and Architectures10.1145/3409964.3461794(265-274)Online publication date: 6-Jul-2021
https://dl.acm.org/doi/10.1145/3409964.3461794
Show More Cited By

Knowledge, level of symmetry, and time of leader election
1. Mathematics of computing
  1. Discrete mathematics
    1. Graph theory
2. Theory of computation
  1. Design and analysis of algorithms
    1. Graph algorithms analysis

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cover image Distributed Computing

Distributed Computing Volume 28, Issue 4

August 2015

75 pages

ISSN:0178-2770

Issue’s Table of Contents

Copyright © Copyright © 2015 Springer-Verlag Berlin Heidelberg.

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Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 01 August 2015

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Cited By

Gorain B Miller APelc A(2023)Four shades of deterministic leader election in anonymous networksDistributed Computing10.1007/s00446-023-00451-336:4(419-449)Online publication date: 31-May-2023
https://dl.acm.org/doi/10.1007/s00446-023-00451-3
Gilbert SRobinson PSourav S(2022)Leader Election in Well-Connected GraphsAlgorithmica10.1007/s00453-022-01068-x85:4(1029-1066)Online publication date: 24-Nov-2022
https://dl.acm.org/doi/10.1007/s00453-022-01068-x
Gorain BMiller APelc AAgrawal KAzar Y(2021)Four Shades of Deterministic Leader Election in Anonymous NetworksProceedings of the 33rd ACM Symposium on Parallelism in Algorithms and Architectures10.1145/3409964.3461794(265-274)Online publication date: 6-Jul-2021
https://dl.acm.org/doi/10.1145/3409964.3461794
Casteigts AMétivier YRobson JZemmari A(2019)Deterministic Leader Election Takes $$\Theta (D + \log n)$$?(D+logn) Bit RoundsAlgorithmica10.1007/s00453-018-0517-381:5(1901-1920)Online publication date: 1-May-2019
https://dl.acm.org/doi/10.1007/s00453-018-0517-3
Dieudonné YPelc A(2019)Impact of Knowledge on Election Time in Anonymous NetworksAlgorithmica10.1007/s00453-018-0444-381:1(238-288)Online publication date: 1-Jan-2019
https://dl.acm.org/doi/10.1007/s00453-018-0444-3
Dieudonné YPelc AScheideler CHajiaghayi M(2017)Impact of Knowledge on Election Time in Anonymous NetworksProceedings of the 29th ACM Symposium on Parallelism in Algorithms and Architectures10.1145/3087556.3087563(207-215)Online publication date: 24-Jul-2017
https://dl.acm.org/doi/10.1145/3087556.3087563
Glacet CMiller APelc A(2017)Time vs. Information Tradeoffs for Leader Election in Anonymous TreesACM Transactions on Algorithms10.1145/303987013:3(1-41)Online publication date: 6-Mar-2017
https://dl.acm.org/doi/10.1145/3039870

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