, Volume 72, Issue 3, pp 860–883 | Cite as

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

  • Gerth Stølting Brodal
  • Spyros Sioutas
  • Kostas Tsichlas
  • Christos ZaroliagisEmail author


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.


Overlay Indexing scheme Decentralized system  Distributed data structure Load-balancing 



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


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Gerth Stølting Brodal
    • 1
  • Spyros Sioutas
    • 2
  • Kostas Tsichlas
    • 3
  • Christos Zaroliagis
    • 4
    • 5
    Email author
  1. 1.MADALGO, Department of Computer ScienceUniversity of AarhusÅarhusDenmark
  2. 2.Department of InformaticsIonian UniversityCorfuGreece
  3. 3.Department of InformaticsAristotle University of ThessalonikiThessaloníkiGreece
  4. 4.Department of Computer Engineering and InformaticsUniversity of PatrasPatrasGreece
  5. 5.Computer Technology Institute & Press “Diophantus”PatrasGreece

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