Advertisement

Algorithmica

, 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 Zaroliagis
Article

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.

Keywords

Overlay Indexing scheme Decentralized system  Distributed data structure Load-balancing 

Notes

Acknowledgments

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

References

  1. 1.
    Abraham, I., Awerbuch, B., Azar, Y., Bartal, Y., Malkhi, D., Pavlov, E.: A generic scheme for building overlay networks in adversarial scenarios. In: Proceedings of the 17th IPDPS, 40 (2003)Google Scholar
  2. 2.
    Arge, L., Eppstein, D., Goodrich, M.T.: Skip-Webs: efficient distributed data structures for multidimensional data sets. In: Proeedings of the 24th PODC, 69–76 (2005)Google Scholar
  3. 3.
    Arge, L., Vitter, J.: Optimal external memory interval management. SIAM J. Comput. 32(6), 1488–1508 (2003)MATHMathSciNetCrossRefGoogle Scholar
  4. 4.
    Aspnes, J., Kirsch, J., Krishnamurthy, A.: Load-balancing and locality in range-queriable data structures. In: Proceeding of the 23rd PODC, 115–124 (2004)Google Scholar
  5. 5.
    Aspnes, J., Shah, G.: Skip graphs. In: Proceedings of the 14th SODA, 384–393 (2003)Google Scholar
  6. 6.
    Awerbuch, B., Scheideler, C.: Consistent and compact data management in distributed storage systems. In: Proceedings of the 16th SPAA, 44–53 (2004)Google Scholar
  7. 7.
    Brodal, G., Sioutas, S., Tsichlas, K., Zaroliagis, C.: \(D^2\)-Tree: A New Overlay with Deterministic Bounds. In: Algorithms and Computation—ISAAC 2010, Lecture Notes in Computer Science, vol. 6507, Part II, Springer, pp. 1–12 (2010)Google Scholar
  8. 8.
    Li, Dongsheng, Cao, Jiannong: Efficient range query processing in peer-to-peer systems. IEEE Tran. Knowl. Data Eng. 21(1), 78–91 (2009)CrossRefGoogle Scholar
  9. 9.
    Gasenan, P., Bawa, M., Garcia-Molina, H.: Online balancing of range-partitioned data with applications to peer-to-peer systems. In: Proceedings of the 13th VLDB, 444–455 (2004)Google Scholar
  10. 10.
    Goodrich, M.T., Nelson, M.J., Sun, J.Z.: The rainbow skip graph: a fault-tolerant constant-degree distributed data structure. In: Proceedings of the 17th SODA, 384–393 (2006)Google Scholar
  11. 11.
    Gupta, A., Agrawal, D., El Abbadi, A.: Approximate range selection queries in peer-to-peer systems. In: Proceedings of the 1st CIDR (2003)Google Scholar
  12. 12.
    Harvey, N., Munro, J.I.: Deterministic SkipNet. In: Proceedings of the 22nd PODC, 152–153 (2003)Google Scholar
  13. 13.
    Jagadish, H.V., Ooi, B.C., Vu, Q. H.: BATON: a balanced tree structure for peer-to-peer networks, In: Proceedings of the 31st VLDB, 661–672 (2005)Google Scholar
  14. 14.
    Jagadish, H.V., Ooi, B.C., Tan, K.L., Vu, Q.H., Zhang, R.: Speeding up search in P2P networks with a multi-way tree structure. In: Proceedings ACM International Conference on Management of Data (SIGMOD), pp. 1–12, Chicago, IL (2006)Google Scholar
  15. 15.
    Karger, D., Kaashoek, F., Stoica, I., Morris, R., Balakrishnan, H.: Chord: A scalable peer-to-peer lookup service for internet applications. In: Proceedings of the SIGCOMM, 149–160 (2001)Google Scholar
  16. 16.
    Manku, G.S., Bawa, M., Raghavan, P.: Symphony: distributed hashing in a small world. In: 4th USENIX Symposium on Internet Technologies and Systems (2003)Google Scholar
  17. 17.
    Manku, G.S., Naor, M., Wieder, U.: Know thy neighbor’s neighbor: the power of lookahead in randomized P2P networks. In: Proceedings of the 36th STOC, 54–63 (2004)Google Scholar
  18. 18.
    Pugh, W.: Skip lists: a probabilistic alternative to balanced trees. Commun. ACM 33(6), 668–676 (1990)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Rowstron, A., Druschel, P.: Pastry: a scalable. Decentralized Object Location, and Routing for Large-Scale Peer-to-Peer Systems, In: Middleware, LNCS 2218, 329–350 (2001)Google Scholar
  20. 20.
    Ratnasamy, S., Francis, P., Handley, M., Karp, R., Shenker, S.: A scalable content addressable network. In: Proceedings ACM Conference on Applications, Technologies, Architectures, and Protocols for Computer Communication (SIGCOMM), pp. 161–172, San Diego, CA (2001)Google Scholar
  21. 21.
    Sahin, O.D., Gupta, A., Agrawal, D., El Abbadi, A.: A peer-to-peer framework for caching range queries. In: Proceedings of the 20th ICDE, 165 (2004)Google Scholar
  22. 22.
    Scheideler, C., Schmid, S.: A distributed and oblivious Heap. In: Proceedings of the 36th ICALP, 571–582 (2009)Google Scholar
  23. 23.
    Zatloukal, K.C., Harvey, N.J.A.: Family trees: an ordered dictionary with optimal congestion, locality, degree and search time. In: Proceedings of the 15th SODA, 301–310 (2004)Google Scholar
  24. 24.
    Zhang, Y., Liu, L., Li, D., Liu, F., Lu, X.: DHT-based range query processing for web service discovery. In: Proceedings of the 2009 IEEE ICWS, 477–484 (2009)Google Scholar
  25. 25.
    Zhao, B.Y., Huang, L., Stribling, J., Rhea, S.C., Joseph, A.D., Kubiatowicz, J.D.: Tapestry: a resilient global-scale overlay for service deployment. IEEE J. Sel. Areas Commun. 22(1), 41–53 (2004)CrossRefGoogle Scholar

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
  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

Personalised recommendations