Self-stabilizing Balancing Algorithm for Containment-Based Trees

  • Evangelos Bampas
  • Anissa Lamani
  • Franck Petit
  • Mathieu Valero
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8255)

Abstract

Containment-based trees are widely used to build data indexes, range-queryable overlays, publish/subscribe systems both in centralized and distributed contexts. In addition to their versatility, their balanced shape ensures an overall satisfactory performance. Recently, it has been shown that their distributed implementations can be fault-resilient. However, this robustness is achieved at the cost of unbalancing the structure. While the structure remains correct in terms of searchability, its performance can be significantly decreased. In this paper, we propose a distributed self-stabilizing algorithm to balance containment-based trees.

Keywords

self-stabilization balancing algorithms containment-based trees 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Adelson-Velskii, G., Landis, E.M.: An algorithm for the organization of information. Proceedings of the USSR Academy of Sciences 146, 263–266 (1962)MathSciNetGoogle Scholar
  2. 2.
    Bayer, R., McCreight, E.M.: Organization and maintenance of large ordered indices. Acta Inf. 1, 173–189 (1972)CrossRefGoogle Scholar
  3. 3.
    Bein, D., Datta, A.K., Villain, V.: Snap-stabilizing optimal binary search tree. In: Tixeuil, S., Herman, T. (eds.) SSS 2005. LNCS, vol. 3764, pp. 1–17. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  4. 4.
    Bianchi, S., Datta, A.K., Felber, P., Gradinariu, M.: Stabilizing peer-to-peer spatial filters. In: ICDCS, p. 27. IEEE Computer Society (2007)Google Scholar
  5. 5.
    Bui, A., Datta, A.K., Petit, F., Villain, V.: Snap-stabilization and PIF in tree networks. Distributed Computing 20(1), 3–19 (2007)MATHGoogle Scholar
  6. 6.
    Burns, J.E., Gouda, M.G., Miller, R.E.: On relaxing interleaving assumptions. In: Proceedings of the MCC Workshop on Self-Stabilizing Systems, MCC Technical Report No. STP-379-89 (1989)Google Scholar
  7. 7.
    Caron, E., Datta, A.K., Petit, F., Tedeschi, C.: Self-stabilization in tree-structured peer-to-peer service discovery systems. In: SRDS, pp. 207–216. IEEE (2008)Google Scholar
  8. 8.
    Caron, E., Desprez, F., Petit, F., Tedeschi, C.: Snap-stabilizing prefix tree for peer-to-peer systems. Parallel Processing Letters 20(1), 15–30 (2010)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Ciaccia, P., Patella, M., Zezula, P.: M-tree: An efficient access method for similarity search in metric spaces. In: Jarke, M., Carey, M.J., Dittrich, K.R., Lochovsky, F.H., Loucopoulos, P., Jeusfeld, M.A. (eds.) VLDB, pp. 426–435. Morgan Kaufmann (1997)Google Scholar
  10. 10.
    Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to Algorithms, 2nd edn. The MIT Press (2001)Google Scholar
  11. 11.
    Dijkstra, E.W.: Self-stabilizing systems in spite of distributed control. Commun. ACM 17(11), 643–644 (1974)CrossRefMATHGoogle Scholar
  12. 12.
    Dolev, S.: Self-Stabilization. The MIT Press (2000)Google Scholar
  13. 13.
    du Mouza, C., Litwin, W., Rigaux, P.: SD-Rtree: A scalable distributed Rtree. In: Chirkova, R., Dogac, A., Özsu, M.T., Sellis, T.K. (eds.) ICDE, pp. 296–305. IEEE (2007)Google Scholar
  14. 14.
    Guttman, A.: R-trees: A dynamic index structure for spatial searching. In: Yormark, B. (ed.) SIGMOD Conference, pp. 47–57. ACM Press (1984)Google Scholar
  15. 15.
    Herman, T., Masuzawa, T.: Available stabilizing heaps. Inf. Process. Lett. 77(2-4), 115–121 (2001)MathSciNetCrossRefMATHGoogle Scholar
  16. 16.
    Herman, T., Masuzawa, T.: A stabilizing search tree with availability properties. In: ISADS, p. 398. IEEE Computer Society (2001)Google Scholar
  17. 17.
    Izumi, T., Gradinariu Potop-Butucaru, M., Valero, M.: Physical expander in virtual tree overlay. In: Peleg, D. (ed.) DISC 2011. LNCS, vol. 6950, pp. 82–96. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  18. 18.
    Jagadish, H.V., Ooi, B.C., Vu, Q.H., Zhang, R., Zhou, A.: VBI-Tree: A peer-to-peer framework for supporting multi-dimensional indexing schemes. In: Liu, L., Reuter, A., Whang, K.-Y., Zhang, J. (eds.) ICDE, p. 34. IEEE Computer Society (2006)Google Scholar
  19. 19.
    Luccio, F., Pagli, L.: On the height of height-balanced trees. IEEE Trans. Computers 25(1), 87–91 (1976)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2013

Authors and Affiliations

  • Evangelos Bampas
    • 1
  • Anissa Lamani
    • 2
  • Franck Petit
    • 3
  • Mathieu Valero
    • 4
  1. 1.School of Elec. & Comp. Eng.National Technical University of AthensGreece
  2. 2.Graduate School of Information Science and Electrical EngineeringKyushu UniversityJapan
  3. 3.LIP6ParisFrance
  4. 4.Orange LabsIssy-les-MoulineauxFrance

Personalised recommendations