research-article

Topology recognition with advice

Authors:

Emanuele G. Fusco,

Rossella PetreschiAuthors Info & Claims

Information and Computation, Volume 247, Issue C

Pages 254 - 265

https://doi.org/10.1016/j.ic.2016.01.005

Published: 01 April 2016 Publication History

Abstract

In topology recognition, each node of an anonymous network has to deterministically produce an isomorphic copy of the underlying graph, with all ports correctly marked. This task is usually unfeasible without any a priori information. Such information can be provided to nodes as advice. An oracle knowing the network can give a (possibly different) string of bits to each node, and all nodes must reconstruct the network using this advice, after a given number of rounds of communication. During each round each node can exchange arbitrary messages with all its neighbors and perform arbitrary local computations. The time of completing topology recognition is the number of rounds it takes, and the size of advice is the maximum length of a string given to nodes.We investigate tradeoffs between the time in which topology recognition is accomplished and the minimum size of advice that has to be given to nodes. We provide upper and lower bounds on the minimum size of advice that is sufficient to perform topology recognition in a given time, in the class of all graphs of size n and diameter D α n, for any constant α < 1 . In most cases, our bounds are asymptotically tight.

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Cited By

Balliu ABrandt SKuhn FNowicki KOlivetti DRotenberg ESuomela JKuznetsov PGelles ROlivetti D(2024)Brief Announcement: Local Advice and Local DecompressionProceedings of the 43rd ACM Symposium on Principles of Distributed Computing10.1145/3662158.3662805(117-120)Online publication date: 17-Jun-2024
https://dl.acm.org/doi/10.1145/3662158.3662805
Gańczorz AJurdziński TLewko MPelc A(2023)Deterministic size discovery and topology recognition in radio networks with short labelsInformation and Computation10.1016/j.ic.2023.105010292:COnline publication date: 1-Jun-2023
https://dl.acm.org/doi/10.1016/j.ic.2023.105010
Dhar AGorain BMondal KPatra SSingh R(2023)Edge exploration of anonymous graph by mobile agent with external helpComputing10.1007/s00607-022-01136-8105:2(483-506)Online publication date: 1-Feb-2023
https://dl.acm.org/doi/10.1007/s00607-022-01136-8
Show More Cited By

Index Terms

Topology recognition with advice
1. Mathematics of computing
  1. Discrete mathematics
    1. Graph theory
      1. Graph algorithms
      2. Network flows
2. Theory of computation
  1. Design and analysis of algorithms
    1. Graph algorithms analysis
      1. Network flows

Index terms have been assigned to the content through auto-classification.

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cover image Information and Computation

Information and Computation Volume 247, Issue C

April 2016

314 pages

ISSN:0890-5401

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Copyright © Elsevier Inc.

Publisher

Academic Press, Inc.

United States

Publication History

Published: 01 April 2016

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Cited By

Balliu ABrandt SKuhn FNowicki KOlivetti DRotenberg ESuomela JKuznetsov PGelles ROlivetti D(2024)Brief Announcement: Local Advice and Local DecompressionProceedings of the 43rd ACM Symposium on Principles of Distributed Computing10.1145/3662158.3662805(117-120)Online publication date: 17-Jun-2024
https://dl.acm.org/doi/10.1145/3662158.3662805
Gańczorz AJurdziński TLewko MPelc A(2023)Deterministic size discovery and topology recognition in radio networks with short labelsInformation and Computation10.1016/j.ic.2023.105010292:COnline publication date: 1-Jun-2023
https://dl.acm.org/doi/10.1016/j.ic.2023.105010
Dhar AGorain BMondal KPatra SSingh R(2023)Edge exploration of anonymous graph by mobile agent with external helpComputing10.1007/s00607-022-01136-8105:2(483-506)Online publication date: 1-Feb-2023
https://dl.acm.org/doi/10.1007/s00607-022-01136-8
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: 1-Dec-2023
https://dl.acm.org/doi/10.1007/s00446-023-00451-3
Gańczorz AJurdziński TLewko MPelc AAgrawal KAzar Y(2021)Deterministic Size Discovery and Topology Recognition in Radio Networks with Short LabelsProceedings of the 33rd ACM Symposium on Parallelism in Algorithms and Architectures10.1145/3409964.3461821(432-434)Online publication date: 6-Jul-2021
https://dl.acm.org/doi/10.1145/3409964.3461821
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
Ellen FGorain BMiller APelc AScheideler CBerenbrink P(2019)Constant-Length Labeling Schemes for Deterministic Radio BroadcastThe 31st ACM Symposium on Parallelism in Algorithms and Architectures10.1145/3323165.3323194(171-178)Online publication date: 17-Jun-2019
https://dl.acm.org/doi/10.1145/3323165.3323194
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
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Gorain BPelc A(2018)Deterministic Graph Exploration with AdviceACM Transactions on Algorithms10.1145/328082315:1(1-17)Online publication date: 16-Nov-2018
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Gorain BPelc A(2018)Finding the Size of a Radio Network with Short LabelsProceedings of the 19th International Conference on Distributed Computing and Networking10.1145/3154273.3154298(1-10)Online publication date: 4-Jan-2018
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