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\(D^2\)-Tree: A New Overlay with Deterministic Bounds

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Abstract

We present a new overlay, called the Deterministic Decentralized tree (\(D^2\)-tree). The \(D^2\)-tree compares favorably to other overlays for the following reasons: (a) it provides matching and better complexities, which are deterministic for the supported operations; (b) the management of nodes (peers) and elements are completely decoupled from each other; and (c) an efficient deterministic load-balancing mechanism is presented for the uniform distribution of elements into nodes, while at the same time probabilistic optimal bounds are provided for the congestion of operations at the nodes. The load-balancing scheme of elements into nodes is deterministic and general enough to be applied to other hierarchical tree-based overlays. This load-balancing mechanism is based on an innovative lazy weight-balancing mechanism, which is interesting in its own right.

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Notes

  1. 1.

    We have chosen this \(\epsilon _{j}\) for simplicity. In fact for any \(\eta >0\), choosing \(\epsilon _{j}=\frac{1}{j^{1+\eta }}\) is sufficient.

  2. 2.

    The alternative of following a height-based approach, resulting in a height (instead of weight) balanced overlay, would render update operations inefficient.

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Acknowledgments

We would like to thank the referees for their valuable comments that improved the presentation of this paper.

Author information

Correspondence to Christos Zaroliagis.

Additional information

Part of this work was done while the last author was visiting the Karlsruhe Institute of Technology.

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Brodal, G.S., Sioutas, S., Tsichlas, K. et al. \(D^2\)-Tree: A New Overlay with Deterministic Bounds. Algorithmica 72, 860–883 (2015). https://doi.org/10.1007/s00453-014-9878-4

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Keywords

  • Overlay
  • Indexing scheme
  • Decentralized system
  • Distributed data structure
  • Load-balancing