The VLDB Journal

, Volume 19, Issue 5, pp 715–733 | Cite as

Top-k queries on temporal data

Regular Paper

Abstract

The database community has devoted extensive amount of efforts to indexing and querying temporal data in the past decades. However, insufficient amount of attention has been paid to temporal ranking queries. More precisely, given any time instance t, the query asks for the top-k objects at time t with respect to some score attribute. Some generic indexing structures based on R-trees do support ranking queries on temporal data, but as they are not tailored for such queries, the performance is far from satisfactory. We present the Seb-tree, a simple indexing scheme that supports temporal ranking queries much more efficiently. The Seb-tree answers a top-k query for any time instance t in the optimal number of I/Os in expectation, namely, \({O\left({\rm log}_B\,\frac{N}{B}+\frac{k}{B}\right)}\) I/Os, where N is the size of the data set and B is the disk block size. The index has near-linear size (for constant and reasonable kmax values, where kmax is the maximum value for the possible values of the query parameter k), can be constructed in near-linear time, and also supports insertions and deletions without affecting its query performance guarantee. Most of all, the Seb-tree is especially appealing in practice due to its simplicity as it uses the B-tree as the only building block. Extensive experiments on a number of large data sets, show that the Seb-tree is more than an order of magnitude faster than the R-tree based indexes for temporal ranking queries.

Keywords

Ranking queries Indexing IO efficient algorithms Temporal data Piece-wise linearsegmentation Top-k 

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References

  1. 1.
    Agarwal P.K., Erickson J.: Geometric range searching and its relatives. In: Chazelle, B., Goodman, J.E., Pollack, R. (eds) Advances in discrete and computational geometry, volume 223 of Contemporary Mathematics, pp. 1–56. American Mathematical Society, Providence, RI (1999)Google Scholar
  2. 2.
    Agarwal P.K., Sharir M.: Davenport-Schinzel sequences and their geometric applications. In: Sack, J.-R., Urrutia, J. (eds) Handbook of computational geometry, pp. 1–47. Elsevier Science Publishers, B.V. North-Holland (2000)CrossRefGoogle Scholar
  3. 3.
    Aggarwal, C.C., Agrawal, D.: On nearest neighbor indexing of nonlinear trajectories. In: PODS. (2003)Google Scholar
  4. 4.
    Anagnostopoulos, A., Vlachos, M., Hadjieleftheriou, M., Keogh, E., Yu, P.S.: Global distance-based segmentation of trajectories. In: KDD, (2006)Google Scholar
  5. 5.
    Arge, L., Danner, A., Teh, S.-H.: I/O-efficient point location using persistent B-trees. In: Proceedings of the workshop on algorithm engineering and experimentation, (2003)Google Scholar
  6. 6.
    Arge, L., Procopiuc, O., Vitter, J.S.: Implementing I/O-efficient data structures using TPIE. In: Proceedings of European symposium on algorithms, pp. 88–100, (2002)Google Scholar
  7. 7.
    Becker B., Gschwind S., Ohler T., Seeger B., Widmayer P.: An asymptotically optimal multiversion b-tree. VLDB J. 5(4), 264–275 (1996)CrossRefGoogle Scholar
  8. 8.
    CGAL: Computational geometry algorithms library. http://www.cgal.org
  9. 9.
    Cai, Y., Ng, R. Indexing spatio-temporal trajectories with chebyshev polynomials. In: SIGMOD, (2004)Google Scholar
  10. 10.
    Chan T.M.: Random sampling, halfspace range reporting, and construction of ( ≤ k)-levels in three dimensions. SIAM J. Comput. 30(2), 561–575 (2000)MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Chen, L., Özsu, M.T., Oria, V.: Robust and fast similarity search for moving object trajectories. In: SIGMOD, (2005)Google Scholar
  12. 12.
    Chen, Q., Chen, L., Lian, X., Liu, Y., Yu, J.X.: Indexable PLA for efficient similarity search. In: VLDB, (2007)Google Scholar
  13. 13.
    Clarkson K.L., Shor P.W.: Applications of random sampling in computational geometry, II. Discrete Computational Geometry 4, 387–421 (1989)MATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Ding H., Trajcevski G., Scheuermann P., Wang X., Keogh E.: Querying and mining of time series data: experimental comparison of representations and distance measures. Proc. VLDB Endow. 1(2), 1542–1552 (2008)Google Scholar
  15. 15.
    Fagin, R., Lotem, A.,Naor, M.: Optimal aggregation algorithms for middleware. In: PODS, (2001)Google Scholar
  16. 16.
    Frentzos E., Gratsias K., Pelekis N., Theodoridis Y.: Algorithms for nearest neighbor search on moving object trajectories. Geoinformatica 11(2), 159–193 (2007)CrossRefGoogle Scholar
  17. 17.
    Hadjieleftheriou, M.: The spatialindex library. http://www.research.att.com/~marioh/spatialindex/index.html
  18. 18.
    Hadjieleftheriou, M., Kollios, G., Bakalov, P., Tsotras, V.J.: Complex spatio-temporal pattern queries. In: VLDB, (2005)Google Scholar
  19. 19.
    Hadjieleftheriou M., Kollios G., Tsotras J., Gunopulos D.: Indexing spatiotemporal archives. VLDB J. 15(2), 143–164 (2006)CrossRefGoogle Scholar
  20. 20.
    Hart S., Sharir M.: Nonlinearity of Davenport-Schinzel sequences and of generalized path compression schemes. Combinatorica 6, 151–177 (1986)MATHCrossRefMathSciNetGoogle Scholar
  21. 21.
    Hershberger J.: Finding the upper envelope of n line segments in O(n log n) time. Inform. Process. Lett. 33, 169–174 (1989)MATHCrossRefMathSciNetGoogle Scholar
  22. 22.
    Ilyas I.F., Beskales G., Soliman M.A.: A survey of top-k query processing techniques in relational database systems. ACM Computing Surveys 40(4), 1–58 (2008)CrossRefGoogle Scholar
  23. 23.
    Jensen, C.S., Lin, D., Ooi B.C.: Query and update efficient B+-tree based indexing of moving objects. In: VLDB, (2004)Google Scholar
  24. 24.
    Jensen, C.S., Lomet, D.B.: Transaction timestamping in (temporal) databases. In: VLDB, (2001)Google Scholar
  25. 25.
    Jiang, B., Pei J.: Online interval skyline queries on time series. In: ICDE, (2009)Google Scholar
  26. 26.
    Keogh, E., Xi, X., Wei, L., Ratanamahatana C.: The UCR time series dataset. http://www.cs.ucr.edu/~eamonn/time_series_data/, (2006)
  27. 27.
    Keogh, E.J., Chu, S., Hart, D., Pazzani. M.J.: An online algorithm for segmenting time series. In: ICDM, (2001)Google Scholar
  28. 28.
    Lomet, D., Barga, R., Mokbel, M.F., Shegalov, G., Wang, R., Zhu, Y.: Immortal DB: transaction time support for sql server. In: SIGMOD, (2005)Google Scholar
  29. 29.
    Lomet, D., Li, F.: Improving transaction-time DBMS performance and functionality. In: ICDE, (2009)Google Scholar
  30. 30.
    Mamoulis, N., Cao, H., Kollios, G., Hadjieleftheriou, M., Tao, Y., Cheung, D.W.: Mining, indexing, and querying historical spatiotemporal data. In: KDD, (2004)Google Scholar
  31. 31.
    Mokbel, M.F., Xiong, X., Aref, W.G.: SINA: scalable incremental processing of continuous queries in spatio-temporal databases. In: SIGMOD, (2004)Google Scholar
  32. 32.
    Palpanas, T., Vlachos, M., Keogh, E., Gunopulos, D., Truppel, W.: Online amnesic approximation of streaming time series. In: ICDE, (2004)Google Scholar
  33. 33.
    Pelanis M., Šaltenis S., Jensen C.S.: Indexing the past, present, and anticipated future positions of moving objects. ACM Trans. Database Syst. 31(1), 255–298 (2006)CrossRefGoogle Scholar
  34. 34.
    Pfoser, D., Jensen, C.S., Theodoridis, Y.: Novel approaches in query processing for moving object trajectories. In: VLDB, (2000)Google Scholar
  35. 35.
    Ŝaltenis, S., Jensen, C.S., Leutenegger, S.T., Lopez, M.A.: Indexing the positions of continuously moving objects. In: SIGMOD, (2000)Google Scholar
  36. 36.
    Sherkat R., Rafiei D.: On efficiently searching trajectories and archival data for historical similarities. Proc. VLDB Endow 1(1), 896–908 (2008)Google Scholar
  37. 37.
    Shieh, J.,Keogh, E.: iSAX: indexing and mining terabyte sized time series. In: KDD, (2008)Google Scholar
  38. 38.
    Song, Z., Roussopoulos, N.: SEB-tree: an approach to index continuously moving objects. In: MDM, (2003)Google Scholar
  39. 39.
    Tao, Y., Papadias, D.: MV3R-Tree: a spatio-temporal access method for timestamp and interval queries. In: VLDB, (2001)Google Scholar
  40. 40.
    Tao, Y., Papadias, D.: Time-parameterized queries in spatio-temporal databases. In: SIGMOD, (2002)Google Scholar
  41. 41.
    Yi, B.-K., Faloutsos, C.: Fast time sequence indexing for arbitrary lp norms. In: VLDB, (2000)Google Scholar

Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Computer Science DepartmentFlorida State UniversityTallahasseeUSA
  2. 2.Department of Computer Science and EngineeringHong Kong University of Science and TechnologyHong KongChina

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