K2-Treaps: Range Top-k Queries in Compact Space

  • Nieves R. Brisaboa
  • Guillermo de Bernardo
  • Roberto Konow
  • Gonzalo Navarro
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8799)

Abstract

Efficient processing of top-k queries on multidimensional grids is a common requirement in information retrieval and data mining, for example in OLAP cubes. We introduce a data structure, the K2-treap, that represents grids in compact form and supports efficient prioritized range queries. We compare the K2-treap with state-of-the-art solutions on synthetic and real-world datasets, showing that it uses 30% of the space of competing solutions while solving queries up to 10 times faster.

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References

  1. 1.
    Afshani, P., Arge, L., Larsen, K.G.: Higher-dimensional orthogonal range reporting and rectangle stabbing in the pointer machine model. In: Proc. SCG, pp. 323–332 (2012)Google Scholar
  2. 2.
    Bentley, J.L.: Multidimensional binary search trees used for associative searching. Comm. ACM 18(9), 509–517 (1975)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    de Bernardo, G., Álvarez-García, S., Brisaboa, N.R., Navarro, G., Pedreira, O.: Compact querieable representations of raster data. In: Kurland, O., Lewenstein, M., Porat, E. (eds.) SPIRE 2013. LNCS, vol. 8214, pp. 96–108. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  4. 4.
    Brisaboa, N., Ladra, S., Navarro, G.: DACs: Bringing direct access to variable-length codes. Inf. Proc. Manag. 49(1), 392–404 (2013)CrossRefGoogle Scholar
  5. 5.
    Brisaboa, N., Ladra, S., Navarro, G.: Compact representation of web graphs with extended functionality. Inf. Sys. 39(1), 152–174 (2014)CrossRefGoogle Scholar
  6. 6.
    Chazelle, B.: Lower bounds for orthogonal range searching I: The reporting case. J. ACM 37(2), 200–212 (1990)MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Claude, F., Navarro, G.: Practical rank/select queries over arbitrary sequences. In: Amir, A., Turpin, A., Moffat, A. (eds.) SPIRE 2008. LNCS, vol. 5280, pp. 176–187. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  8. 8.
    Fischer, J., Heun, V.: Space-efficient preprocessing schemes for range minimum queries on static arrays. SIAM J. Comp. 40(2), 465–492 (2011)MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Golin, M., Iacono, J., Krizanc, D., Raman, R., Rao, S.S.: Encoding 2D range maximum queries. In: Asano, T., Nakano, S.-i., Okamoto, Y., Watanabe, O. (eds.) ISAAC 2011. LNCS, vol. 7074, pp. 180–189. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  10. 10.
    Grossi, R., Gupta, A., Vitter, J.: High-order entropy-compressed text indexes. In: Proc. 14th SODA, pp. 841–850 (2003)Google Scholar
  11. 11.
    Konow, R., Navarro, G., Clarke, C., López-Ortíz, A.: Faster and smaller inverted indices with treaps. In: Proc. 36th SIGIR, pp. 193–202 (2013)Google Scholar
  12. 12.
    Mäkinen, V., Navarro, G.: Position-restricted substring searching. In: Correa, J.R., Hevia, A., Kiwi, M. (eds.) LATIN 2006. LNCS, vol. 3887, pp. 703–714. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  13. 13.
    Martínez, C., Roura, S.: Randomized binary search trees. J. ACM 45(2), 288–323 (1997)CrossRefGoogle Scholar
  14. 14.
    McCreight, E.M.: Priority search trees. SIAM J. Comp. 14(2), 257–276 (1985)MathSciNetCrossRefMATHGoogle Scholar
  15. 15.
    Munro, J.I.: Tables. In: Chandru, V., Vinay, V. (eds.) FSTTCS 1996. LNCS, vol. 1180, pp. 37–42. Springer, Heidelberg (1996)CrossRefGoogle Scholar
  16. 16.
    Navarro, G., Nekrich, Y.: Top-k document retrieval in optimal time and linear space. In: Proc. 23rd SODA, pp. 1066–1078 (2012)Google Scholar
  17. 17.
    Navarro, G., Nekrich, Y., Russo, L.: Space-efficient data-analysis queries on grids. Theor. Comp. Sci. 482, 60–72 (2013)MathSciNetCrossRefMATHGoogle Scholar
  18. 18.
    Seidel, R., Aragon, C.: Randomized search trees. Algorithmica 16(4/5), 464–497 (1996)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Nieves R. Brisaboa
    • 1
  • Guillermo de Bernardo
    • 1
  • Roberto Konow
    • 2
    • 3
  • Gonzalo Navarro
    • 2
  1. 1.Databases Lab.Univ. of A. CoruñaSpain
  2. 2.Dept. of Computer ScienceUniv. of ChileChile
  3. 3.Escuela de Informática y TelecomunicacionesUniv. Diego PortalesChile

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