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Top-k queries on temporal data

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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 k max values, where k max 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.

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References

  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. 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)

    Chapter  Google Scholar 

  3. Aggarwal, C.C., Agrawal, D.: On nearest neighbor indexing of nonlinear trajectories. In: PODS. (2003)

  4. Anagnostopoulos, A., Vlachos, M., Hadjieleftheriou, M., Keogh, E., Yu, P.S.: Global distance-based segmentation of trajectories. In: KDD, (2006)

  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)

  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)

  7. Becker B., Gschwind S., Ohler T., Seeger B., Widmayer P.: An asymptotically optimal multiversion b-tree. VLDB J. 5(4), 264–275 (1996)

    Article  Google Scholar 

  8. CGAL: Computational geometry algorithms library. http://www.cgal.org

  9. Cai, Y., Ng, R. Indexing spatio-temporal trajectories with chebyshev polynomials. In: SIGMOD, (2004)

  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)

    Article  MATH  MathSciNet  Google Scholar 

  11. Chen, L., Özsu, M.T., Oria, V.: Robust and fast similarity search for moving object trajectories. In: SIGMOD, (2005)

  12. Chen, Q., Chen, L., Lian, X., Liu, Y., Yu, J.X.: Indexable PLA for efficient similarity search. In: VLDB, (2007)

  13. Clarkson K.L., Shor P.W.: Applications of random sampling in computational geometry, II. Discrete Computational Geometry 4, 387–421 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  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. Fagin, R., Lotem, A.,Naor, M.: Optimal aggregation algorithms for middleware. In: PODS, (2001)

  16. Frentzos E., Gratsias K., Pelekis N., Theodoridis Y.: Algorithms for nearest neighbor search on moving object trajectories. Geoinformatica 11(2), 159–193 (2007)

    Article  Google Scholar 

  17. Hadjieleftheriou, M.: The spatialindex library. http://www.research.att.com/~marioh/spatialindex/index.html

  18. Hadjieleftheriou, M., Kollios, G., Bakalov, P., Tsotras, V.J.: Complex spatio-temporal pattern queries. In: VLDB, (2005)

  19. Hadjieleftheriou M., Kollios G., Tsotras J., Gunopulos D.: Indexing spatiotemporal archives. VLDB J. 15(2), 143–164 (2006)

    Article  Google Scholar 

  20. Hart S., Sharir M.: Nonlinearity of Davenport-Schinzel sequences and of generalized path compression schemes. Combinatorica 6, 151–177 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  21. Hershberger J.: Finding the upper envelope of n line segments in O(n log n) time. Inform. Process. Lett. 33, 169–174 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  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)

    Article  Google Scholar 

  23. Jensen, C.S., Lin, D., Ooi B.C.: Query and update efficient B+-tree based indexing of moving objects. In: VLDB, (2004)

  24. Jensen, C.S., Lomet, D.B.: Transaction timestamping in (temporal) databases. In: VLDB, (2001)

  25. Jiang, B., Pei J.: Online interval skyline queries on time series. In: ICDE, (2009)

  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. Keogh, E.J., Chu, S., Hart, D., Pazzani. M.J.: An online algorithm for segmenting time series. In: ICDM, (2001)

  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)

  29. Lomet, D., Li, F.: Improving transaction-time DBMS performance and functionality. In: ICDE, (2009)

  30. Mamoulis, N., Cao, H., Kollios, G., Hadjieleftheriou, M., Tao, Y., Cheung, D.W.: Mining, indexing, and querying historical spatiotemporal data. In: KDD, (2004)

  31. Mokbel, M.F., Xiong, X., Aref, W.G.: SINA: scalable incremental processing of continuous queries in spatio-temporal databases. In: SIGMOD, (2004)

  32. Palpanas, T., Vlachos, M., Keogh, E., Gunopulos, D., Truppel, W.: Online amnesic approximation of streaming time series. In: ICDE, (2004)

  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)

    Article  Google Scholar 

  34. Pfoser, D., Jensen, C.S., Theodoridis, Y.: Novel approaches in query processing for moving object trajectories. In: VLDB, (2000)

  35. Ŝaltenis, S., Jensen, C.S., Leutenegger, S.T., Lopez, M.A.: Indexing the positions of continuously moving objects. In: SIGMOD, (2000)

  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. Shieh, J.,Keogh, E.: iSAX: indexing and mining terabyte sized time series. In: KDD, (2008)

  38. Song, Z., Roussopoulos, N.: SEB-tree: an approach to index continuously moving objects. In: MDM, (2003)

  39. Tao, Y., Papadias, D.: MV3R-Tree: a spatio-temporal access method for timestamp and interval queries. In: VLDB, (2001)

  40. Tao, Y., Papadias, D.: Time-parameterized queries in spatio-temporal databases. In: SIGMOD, (2002)

  41. Yi, B.-K., Faloutsos, C.: Fast time sequence indexing for arbitrary lp norms. In: VLDB, (2000)

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Authors and Affiliations

  1. Computer Science Department, Florida State University, Tallahassee, FL, USA

    Feifei Li & Wangchao Le

  2. Department of Computer Science and Engineering, Hong Kong University of Science and Technology, Hong Kong, China

    Ke Yi

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  1. Feifei Li
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  2. Ke Yi
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  3. Wangchao Le
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Correspondence to Feifei Li.

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Li, F., Yi, K. & Le, W. Top-k queries on temporal data. The VLDB Journal 19, 715–733 (2010). https://doi.org/10.1007/s00778-010-0186-6

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  • DOI: https://doi.org/10.1007/s00778-010-0186-6

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