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ART\(^+\): A Fault-Tolerant Decentralized Tree Structure with Ultimate Sub-logarithmic Efficiency

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Algorithmic Aspects of Cloud Computing (ALGOCLOUD 2015)

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Abstract

In this paper, we focus on large-scale, decentralized environments. Our aim is to develop an architecture that can support range queries and scale in terms of number of nodes as well as of data items stored. The solutions proposed in literature are inadequate for our purposes, since their classic logarithmic complexity is too expensive even for single queries. In this work, we contribute the ART\(^+\) (Autonomous Range Tree) structure, which outperforms the most popular decentralized structures, since it achieves sub-logarithmic complexity. ART\(^+\) achieves an \(O(\log _b^2{\log {N}})\) communication cost for query and update operations, where b is a double-exponentially power of 2 and N is the total number of nodes. Moreover, ART\(^+\) is a fully dynamic and fault-tolerant structure, which supports the join/leave node operations in \(O(\log {\log {N}})\) expected w.h.p number of hops and performs load-balancing in \(O(\log {\log {N}})\) amortized cost. The theoretical performance is verified through experiments.

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Notes

  1. 1.

    Autonomous Range Tree.

  2. 2.

    Dynamic Deterministic Decentralized Tree.

  3. 3.

    Maximum fanout of the hierarchical structure on top of the ring.

  4. 4.

    https://github.com/sourlaef/d3-tree-sim.

  5. 5.

    LRT: Level Range Tree.

  6. 6.

    LSI: Left Spine Index.

  7. 7.

    CI: Collection Index.

  8. 8.

    http://code.google.com/p/d-p2p-sim/.

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Acknowledgments

This research has been co-financed by the European Union (European Social Fund - ESF) and Greek national funds through the Operational Program “Education and Lifelong Learning” of the National Strategic Reference Framework (NSRF) – Research Funding Programs Thales & Heracletus II, Investing in knowledge society through the European Social Fund.

Author information

Authors and Affiliations

  1. Department of Informatics, Ionian University, 49100, Corfu, Greece

    Spyros Sioutas

  2. Department of Computer Engineering and Informatics, University of Patras, 26500, Patras, Greece

    Efrosini Sourla & Christos Zaroliagis

  3. Department of Informatics, Aristotle University of Thessaloniki, 54124, Thessaloniki, Greece

    Kostas Tsichlas

  4. Computer Technology Institute & Press “Diophantus”, N. Kazantzaki Str., Patras University Campus, 26504, Patras, Greece

    Christos Zaroliagis

Authors
  1. Spyros Sioutas
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  2. Efrosini Sourla
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  3. Kostas Tsichlas
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  4. Christos Zaroliagis
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Corresponding author

Correspondence to Efrosini Sourla .

Editor information

Editors and Affiliations

  1. Dept of Informatics, Ionian Univ, Kerkyra, Greece

    Ioannis Karydis

  2. Ionian University, Corfu, Greece

    Spyros Sioutas

  3. University of Glasgow, Glasgow, United Kingdom

    Peter Triantafillou

  4. Ionian University, Kerkyra, Greece

    Dimitrios Tsoumakos

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Sioutas, S., Sourla, E., Tsichlas, K., Zaroliagis, C. (2016). ART\(^+\): A Fault-Tolerant Decentralized Tree Structure with Ultimate Sub-logarithmic Efficiency. In: Karydis, I., Sioutas, S., Triantafillou, P., Tsoumakos, D. (eds) Algorithmic Aspects of Cloud Computing. ALGOCLOUD 2015. Lecture Notes in Computer Science(), vol 9511. Springer, Cham. https://doi.org/10.1007/978-3-319-29919-8_10

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  • DOI: https://doi.org/10.1007/978-3-319-29919-8_10

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-29918-1

  • Online ISBN: 978-3-319-29919-8

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