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Energy Efficient Naming in Beeping Networks

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Ad-Hoc, Mobile, and Wireless Networks (ADHOC-NOW 2019)

Part of the book series: Lecture Notes in Computer Science ((LNCCN,volume 11803))

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Abstract

A single-hop beeping network is a distributed communication model in which each station can communicate with all other but only by \(1-bit\) messages called beeps. In this paper, we focus on resolving two fundamental distributed computing issues: the naming and the counting on this model. Especially, we are interested in optimizing energy complexity and running time for those issues. Our contribution is to have design randomized algorithms with an optimal running time of \(O(n \log n)\) and optimal \(O(\log n)\) energy complexity whether for the naming or the counting for a single-hop beeping network of n stations.

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Notes

  1. 1.

    The underlying graph of the network is a complete graph.

  2. 2.

    An event \(\varepsilon _n\) occurs with high probability if \(\mathbb {P}[\varepsilon _n]\ge 1-\frac{1}{n^c}\) for any constant \(c>0\).

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Author information

Authors and Affiliations

  1. Université de Paris, IRIF, CNRS, 75013, Paris, France

    Ny Aina Andriambolamalala & Vlady Ravelomanana

Authors
  1. Ny Aina Andriambolamalala
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  2. Vlady Ravelomanana
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Corresponding authors

Correspondence to Ny Aina Andriambolamalala or Vlady Ravelomanana .

Editor information

Editors and Affiliations

  1. Luxembourg Institute of Science and Technology, Belvaux, Luxembourg

    Maria Rita Palattella

  2. CNR-IEIIT, Turin, Italy

    Stefano Scanzio

  3. Koc Üniversitesi Mühendislik, Istanbul, Turkey

    Sinem Coleri Ergen

Appendices

Appendix 1: Worst Case for \(\mathrm {STL}\)

Here, we show a simulation of the execution of Algorithm 1 on the worst case for \(\mathrm {STL}\) in a complete binary Tree to count the number of waking time of this node.

figure d

Legends: hexagons represent the \(\mathrm {STL}\) waking steps of the node, squares are the \(\mathrm {STN}\) waking steps and circles represent the other waking steps. The numbers inside these shapes represent the season where the node wakes up. Numbers without any shape represent the sleeping steps of the node. Dotted lines represents the transition between two steps \(t_i, t_{i+1}\) on any season where the node starts to sleeps or remains sleeping. And solid lines the transition between two steps \(t_i, t_{i+1}\) on any season where the node wakes up or remains awake.

Appendix 2: Worst Case for \(\mathrm {STN}\)

In this section, we show a simulation of the execution of Algorithm 1 on the worst case for \(\mathrm {STN}\) in a complete binary Tree to count the number of waking time of this node.

figure e

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Andriambolamalala, N.A., Ravelomanana, V. (2019). Energy Efficient Naming in Beeping Networks. In: Palattella, M., Scanzio, S., Coleri Ergen, S. (eds) Ad-Hoc, Mobile, and Wireless Networks. ADHOC-NOW 2019. Lecture Notes in Computer Science(), vol 11803. Springer, Cham. https://doi.org/10.1007/978-3-030-31831-4_25

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  • DOI: https://doi.org/10.1007/978-3-030-31831-4_25

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  • Print ISBN: 978-3-030-31830-7

  • Online ISBN: 978-3-030-31831-4

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