Static-to-Dynamic Transformation for Metric Indexing Structures

  • Bilegsaikhan Naidan
  • Magnus Lie Hetland
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7404)


In this paper, we study the well-known algorithm of Bentley and Saxe in the context of similarity search in metric spaces. We apply the algorithm to existing static metric index structures, obtaining dynamic ones. We show that the overhead of the Bentley-Saxe method is quite low, and because it facilitates the dynamic use of any state-of-the-art static index method, we can achieve results comparable to, or even surpassing, existing dynamic methods. Another important contribution of our approach is that it is very simple—an important practical consideration. Rather than dealing with the complexities of dynamic tree structures, for example, the core index can be built statically, with full knowledge of its data set.


Leaf Node Static Index Index Structure Construction Cost Range Query 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Bentley, J.L., Saxe, J.B.: Decomposable searching problems I. Static-to-dynamic transformation. Journal of Algorithms 1(4), 301–358 (1980)MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Brin, S.: Near neighbor search in large metric spaces. In: Proceedings of 21th International Conference on Very Large Data Bases, VLDB, pp. 574–584 (1995)Google Scholar
  3. 3.
    Brisaboa, N.R., Pedreira, O., Seco, D., Solar, R., Uribe, R.: Clustering-Based Similarity Search in Metric Spaces with Sparse Spatial Centers. In: Geffert, V., Karhumäki, J., Bertoni, A., Preneel, B., Návrat, P., Bieliková, M. (eds.) SOFSEM 2008. LNCS, vol. 4910, pp. 186–197. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  4. 4.
    Chávez, E., Navarro, G.: A Probabilistic Spell for the Curse of Dimensionality. In: Buchsbaum, A.L., Snoeyink, J. (eds.) ALENEX 2001. LNCS, vol. 2153, pp. 147–160. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  5. 5.
    Figueroa, K., Navarro, G., Chavez, E.: Metric spaces library (2010), (downloaded November 15, 2011)
  6. 6.
    Fu, A.W.-C., Chan, P.M.-S., Cheung, Y.-L., Moon, Y.S.: Dynamic vp-tree indexing for n-nearest neighbor search given pair-wise distances. The VLDB Journal 9(2), 154–173 (2000)CrossRefGoogle Scholar
  7. 7.
    Hetland, M.L.: The Basic Principles of Metric Indexing. In: Coello, C.A.C., Dehuri, S., Ghosh, S. (eds.) Swarm Intelligence for Multi-objective Problems in Data Mining. SCI, vol. 242, pp. 199–232. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  8. 8.
    Navarro, G.: Searching in metric spaces by spatial approximation. The VLDB Journal 11(1), 28–46 (2002)CrossRefGoogle Scholar
  9. 9.
    Navarro, G., Reyes, N.: Dynamic spatial approximation trees. Journal of Experimental Algorithmics, JEA, 12:1.5:1–1.5:68 (2008)Google Scholar
  10. 10.
    Overmars, M., Leeuwen, J.: Two general methods for dynamizing decomposable searching problems. Computing 26, 155–166 (1981)MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    Uribe, R., Navarro, G., Barrientos, R.J., Marín, M.: An Index Data Structure for Searching in Metric Space Databases. In: Alexandrov, V.N., van Albada, G.D., Sloot, P.M.A., Dongarra, J. (eds.) ICCS 2006. LNCS, vol. 3991, pp. 611–617. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  12. 12.
    Yianilos, P.N.: Data structures and algorithms for nearest neighbor search in general metric spaces. In: Proceedings of the Fourth Annual Symposium on Discrete Algorithms, pp. 311–321 (1993)Google Scholar
  13. 13.
    Zezula, P., Amato, G., Dohnal, V., Batko, M.: Similarity Search: The Metric Space Approach. Springer (2006)Google Scholar

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© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Bilegsaikhan Naidan
    • 1
  • Magnus Lie Hetland
    • 1
  1. 1.Department of Computer and Information ScienceNorwegian University of Science and TechnologyTrondheimNorway

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