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A Self-stabilizing General De Bruijn Graph

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Stabilization, Safety, and Security of Distributed Systems (SSS 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10616))

Abstract

Searching for other participants is one of the most important operations in a distributed system. We are interested in topologies in which it is possible to route a packet in a fixed number of hops until it arrives at its destination. Given a constant d, this paper introduces a new self-stabilizing protocol for the q-ary d-dimensional de Bruijn graph (\(q = \root d \of {n}\)) that is able to route any search request in at most d hops w.h.p., while significantly lowering the node degree compared to the clique: We require nodes to have a degree of \(\mathcal O(\root d \of {n})\), which is asymptotically optimal for a fixed diameter d. The protocol keeps the expected amount of edge redirections per node in \(\mathcal O(\root d \of {n})\), when the number of nodes in the system increases by factor \(2^d\). The number of messages that are periodically sent out by nodes is constant.

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Acknowledgements

This work was partially supported by the German Research Foundation (DFG) within the Collaborative Research Center “On-The-Fly Computing” (SFB 901).

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Authors and Affiliations

  1. Paderborn University, Paderborn, Germany

    Michael Feldmann & Christian Scheideler

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  1. Michael Feldmann
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  2. Christian Scheideler
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Correspondence to Michael Feldmann .

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Editors and Affiliations

  1. University of Liverpool, Liverpool, United Kingdom

    Paul Spirakis

  2. Chalmers University of Technology, Gothenburg, Sweden

    Philippas Tsigas

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Feldmann, M., Scheideler, C. (2017). A Self-stabilizing General De Bruijn Graph. In: Spirakis, P., Tsigas, P. (eds) Stabilization, Safety, and Security of Distributed Systems. SSS 2017. Lecture Notes in Computer Science(), vol 10616. Springer, Cham. https://doi.org/10.1007/978-3-319-69084-1_17

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  • DOI: https://doi.org/10.1007/978-3-319-69084-1_17

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-69083-4

  • Online ISBN: 978-3-319-69084-1

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