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Simple Distributed Spanners in Dense Congest Networks

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SOFSEM 2020: Theory and Practice of Computer Science (SOFSEM 2020)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12011))

Abstract

The problem of computing a sparse spanning subgraph is a well-studied problem in the distributed setting, and a lot of research was done in the direction of computing spanners or solving the more relaxed problem of connectivity. Still, efficiently constructing a linear-size spanner deterministically remains a challenging open problem even in specific topologies.

In this paper we provide several simple spanner constructions of linear size, for various graph families. Our first result shows that the connectivity problem can be solved deterministically using a linear size spanner within constant running time on graphs with bounded neighborhood independence. This is a very wide family of graphs that includes unit-disk graphs, unit-ball graphs, line graphs, claw-free graphs and many others. Moreover, our algorithm works in the \(\mathcal {CONGEST}\) model. It also immediately leads to a constant time deterministic solution for the connectivity problem in the Congested-Clique.

Our second result provides a linear size spanner in the \(\mathcal {CONGEST}\) model for graphs with bounded diversity. This is a subtype of graphs with bounded neighborhood independence that captures various types of networks, such as wireless networks and social networks. Here too our result has constant running time and is deterministic. Moreover, the latter result has an additional desired property of a small stretch.

Research supported by ISF grant 724/15 and Open University of Israel research fund.

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Notes

  1. 1.

    Diversity can be also defined with respect to a clique cover of a given graph. Then, the diversity of a vertex is the number of maximal cliques in the cover that the vertex belongs to. In this paper, however, we do not employ clique covers, and so the diversity is defined as the number of maximal cliques in the input graph.

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Acknowledgments

The authors are grateful to Michael Elkin for fruitful discussions and helpful remarks.

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Authors and Affiliations

  1. The Open University of Israel, Raanana, Israel

    Leonid Barenboim

  2. Ben-Gurion University of The Negev, Beer-Sheva, Israel

    Tzalik Maimon

Authors
  1. Leonid Barenboim
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  2. Tzalik Maimon
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Correspondence to Leonid Barenboim .

Editor information

Editors and Affiliations

  1. University of Macedonia, Thessaloniki, Greece

    Alexander Chatzigeorgiou

  2. University of Bergamo, Bergamo, Italy

    Riccardo Dondi

  3. Cyprus University of Technology, Limassol, Cyprus

    Herodotos Herodotou

  4. Carnegie Mellon University Qatar, Doha, Qatar

    Christos Kapoutsis

  5. Open University of Cyprus, Nicosia, Cyprus

    Yannis Manolopoulos

  6. University of Cyprus, Nicosia, Cyprus

    George A. Papadopoulos

  7. Paris Dauphine University, Paris, France

    Florian Sikora

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Barenboim, L., Maimon, T. (2020). Simple Distributed Spanners in Dense Congest Networks. In: Chatzigeorgiou, A., et al. SOFSEM 2020: Theory and Practice of Computer Science. SOFSEM 2020. Lecture Notes in Computer Science(), vol 12011. Springer, Cham. https://doi.org/10.1007/978-3-030-38919-2_22

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  • DOI: https://doi.org/10.1007/978-3-030-38919-2_22

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-38918-5

  • Online ISBN: 978-3-030-38919-2

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