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On Range and Edge Capacity in the Congested Clique

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SOFSEM 2018: Theory and Practice of Computer Science (SOFSEM 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10706))

Abstract

The congested clique is a synchronous, message-passing model of distributed computing in which each computational unit (node) in each round can send message of \(O(\log n)\) bits to each other node of the network, where n is the number of nodes.

Following recent progress in design of algorithms for graph connectivity and minimum spanning tree (MST) in the congested clique, we study these problems in limited variants of the congested clique. We show that MST can be computed deterministically and connected components can be computed by a randomized algorithm with optimal edge capacity \(\varTheta (\log n)\), while preserving the best known round complexity [6, 13]. Moreover, our algorithms work in the rcast model with range \(r=2\), the weakest model of the congested clique above the broadcast variant (\(r=1\)) in the hierarchy with respect to the range [2].

This work was supported by the Polish National Science Centre grant DEC-2012/07/B/ST6/01534.

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Notes

  1. 1.

    The authors of [15] allow for different capacities of various edges in a round; this assumption makes their measure and results incomparable to ours.

  2. 2.

    Random edges are necessary in order to deal with components with degree \(>x^5\), because sketches do not help much to find their neighbors.

References

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Authors and Affiliations

  1. Institute of Computer Science, University of Wroclaw, Wroclaw, Poland

    Tomasz Jurdziński & Krzysztof Nowicki

Authors
  1. Tomasz Jurdziński
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  2. Krzysztof Nowicki
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Corresponding author

Correspondence to Tomasz Jurdziński .

Editor information

Editors and Affiliations

  1. Vienna University of Technology , Vienna, Austria

    A Min Tjoa

  2. ISAE-ENSMA, Chasseneuil-du-Poitou, France

    Ladjel Bellatreche

  3. Vienna University of Technology, Vienna, Austria

    Stefan Biffl

  4. Utrecht University, Utrecht, The Netherlands

    Jan van Leeuwen

  5. Academy of Sciences, Prague, Czech Republic

    Jiří Wiedermann

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Jurdziński, T., Nowicki, K. (2018). On Range and Edge Capacity in the Congested Clique. In: Tjoa, A., Bellatreche, L., Biffl, S., van Leeuwen, J., Wiedermann, J. (eds) SOFSEM 2018: Theory and Practice of Computer Science. SOFSEM 2018. Lecture Notes in Computer Science(), vol 10706. Edizioni della Normale, Cham. https://doi.org/10.1007/978-3-319-73117-9_22

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  • DOI: https://doi.org/10.1007/978-3-319-73117-9_22

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  • Publisher Name: Edizioni della Normale, Cham

  • Print ISBN: 978-3-319-73116-2

  • Online ISBN: 978-3-319-73117-9

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