The VLDB Journal

, Volume 19, Issue 5, pp 687–714 | Cite as

Efficient k-nearest neighbor search on moving object trajectories

Regular Paper

Abstract

With the growing number of mobile applications, data analysis on large sets of historical moving objects trajectories becomes increasingly important. Nearest neighbor search is a fundamental problem in spatial and spatio-temporal databases. In this paper, we consider the following problem: Given a set of moving object trajectories D and a query trajectory mq, find the k nearest neighbors to mq within D for any instant of time within the lifetime of mq. We assume D is indexed in a 3D-R-tree and employ a filter-and-refine strategy. The filter step traverses the index and creates a stream of so-called units (linear pieces of a trajectory) as a superset of the units required to build the result of the query. The refinement step processes an ordered stream of units and determines the pieces of units forming the precise result. To support the filter step, for each node p of the index, in preprocessing a time-dependent coverage function Cp(t) is computed which is the number of trajectories represented in p present at time t. Within the filter step, sophisticated data structures are used to keep track of the aggregated coverages of the nodes seen so far in the index traversal to enable pruning. Moreover, the R-tree index is built in a special way to obtain coverage functions that are effective for pruning. As a result, one obtains a highly efficient kNN algorithm for moving data and query points that outperforms the two competing algorithms by a wide margin. Implementations of the new algorithms and of the competing techniques are made available as well. Algorithms can be used in a system context including, for example, visualization and animation of results. Experiments of the paper can be easily checked or repeated, and new experiments be performed.

Keywords

Continuous nearest neighbor Moving object Filter-and-refine 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
  2. 2.
  3. 3.
  4. 4.
    Scripts to execute the experiments of this paper. http://dna.fernuni-hagen.de/papers/KNN/knn-experiment-script.zip
  5. 5.
    Secondo. A Database System for Moving Objects. http://dna.fernuni-hagen.de/Secondo.html/Secondo-mod.pdf
  6. 6.
  7. 7.
  8. 8.
  9. 9.
    Benetis R., Jensen C.S., Karciauskas G., Saltenis S.: Nearest and reverse nearest neighbor queries for moving objects. VLDB J. 15(3), 229–249 (2006)CrossRefGoogle Scholar
  10. 10.
    Bentley J.L., Ottmann T.: Algorithms for reporting and counting geometric intersections. IEEE Trans. Comput. 28(9), 643–647 (1979)MATHCrossRefGoogle Scholar
  11. 11.
    Berchtold, S., Böhm, C., Kriegel, H.P.: Improving the query performance of high-dimensional index structures by bulk load operations. In: EDBT, pp. 216–230 (1998)Google Scholar
  12. 12.
    Bercken, J., Seeger, B., Widmayer, P.: A generic approach to bulk loading multidimensional index structures. In: VLDB, pp. 406–415 (1997)Google Scholar
  13. 13.
    Cao H., Wolfson O., Trajcevski G.: Spatio-temporal data reduction with deterministic error bounds. VLDB J. 15(3), 211–228 (2006)CrossRefGoogle Scholar
  14. 14.
    Chakka, V.P., Everspaugh, A., Patel. J.M.: Indexing large trajectory data sets with SETI. In: CIDR (2003)Google Scholar
  15. 15.
    de Berg M., Cheong O., van Kreveld M., Overmars M.: Computational Geometry: Algorithms and Applications. 3rd edn. Springer, Heidelberg (2008)MATHGoogle Scholar
  16. 16.
    Düntgen C., Behr T., Güting R.H.: BerlinMOD: a benchmark for moving object databases. VLDB J. 18(6), 1335–1368 (2009)CrossRefGoogle Scholar
  17. 17.
    Forlizzi, L., Güting, R.H., Nardelli, E., Schneider, M.: A data model and data structures for moving objects databases. In: SIGMOD, pp. 319–330 (2000)Google Scholar
  18. 18.
    Frentzos, E.: Personal communicationGoogle Scholar
  19. 19.
    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
  20. 20.
    Frentzos, E., Gratsias, K., Theodoridis, Y.: Index-based most similar trajectory search. In: ICDE, pp. 816–825. IEEE (2007)Google Scholar
  21. 21.
    Gao, Y., Li, C., Chen, G., Li, Q., Chen, C.: Efficient algorithms for historical continuous k NN query processing over moving object trajectories. In: APWeb/WAIM, pp. 188–199 (2007)Google Scholar
  22. 22.
    Gao Y.J., Li C., Chen G.C., Chen L., Jiang X.T., Chen C.: Efficient k-nearest neighbor search algorithms for historical moving object trajectories. J. Comput. Sci. Technol. 22(2), 232–244 (2007)CrossRefMathSciNetGoogle Scholar
  23. 23.
    Giannotti, F., Pedreschi, D. (eds): Mobility, Data Mining and Privacy—Geographic Knowledge Discovery. Springer, Heidelberg (2008)Google Scholar
  24. 24.
    Gudmundsson, J., van Kreveld, M.J.: Computing longest duration flocks in trajectory data. In: de By R.A., Nittel, S. (eds.) GIS, pp. 35–42. ACM (2006)Google Scholar
  25. 25.
    Güting R.H., Böhlen M.H., Erwig M., Jensen C.S., Lorentzos N.A., Schneider M., Vazirgiannis M.: A foundation for representing and querying moving objects. ACM TODS 25(1), 1–42 (2000)CrossRefGoogle Scholar
  26. 26.
    Güting R.H., Schneider M.: Moving Objects Databases. Elsevier, Amsterdam (2005)Google Scholar
  27. 27.
    Hjaltason G.R., Samet H.: Distance browsing in spatial databases. ACM Trans. Database Syst. 24(2), 265–318 (1999)CrossRefGoogle Scholar
  28. 28.
    Huang Y.-K., Chen C.-C., Lee C.: Continous k-nearest neighbor query for moving objects with uncertain velocity. Geoinformatica 13(1), 1–25 (2007)MATHCrossRefMathSciNetGoogle Scholar
  29. 29.
    Iwerks, G.S., Samet, H., Smith, K.P.: Continuous k-nearest neighbor queries for continuously moving points with updates. In: VLDB, pp. 512–523 (2003)Google Scholar
  30. 30.
    Jensen, C.S., Schneider, M., Seeger, B., Tsotras, V.J., (eds): Advances in Spatial and Temporal Databases, 7th International Symposium, SSTD 2001, Redondo Beach, CA, USA, July 12–15, 2001, Proceedings, volume 2121 (2001)Google Scholar
  31. 31.
    Jeung, H., Yiu, M.L., Zhou, X., Jensen, C.S., Shen, H.T.: Discovery of convoys in trajectory databases. In: VLDB (2008)Google Scholar
  32. 32.
    Jürgens, M., Lenz, H.-J.: The ra*-tree: an improved r-tree with materialized data for supporting range queries on olap-data. In: DEXA Workshop, pp. 186–191 (1998)Google Scholar
  33. 33.
    Kellaris, G., Pelekis, N., Theodoridis, Y.: Trajectory compression under network constraints. In: Mamoulis, N., Seidl, T., Pedersen, T.B., Torp, K., Assent, I. (eds.) SSTD, pp. 392–398 (2009)Google Scholar
  34. 34.
    Lazaridis, I., Mehrotra, S.: Progressive approximate aggregate queries with a multi-resolution tree structure. In: SIGMOD Conference, pp. 401–412 (2001)Google Scholar
  35. 35.
    Mokbel M.F., Ghanem T.M., Aref W.G.: Spatio-temporal access methods. IEEE Data Eng. Bull. 26(2), 40–49 (2003)Google Scholar
  36. 36.
    Morton, G.M.: A Computer Oriented Geodetic Data Base and a New Technique in File Sequencing. Technical report, IBM Ltd. Ottawa (1966)Google Scholar
  37. 37.
    Mouratidis, K., Hadjieleftheriou, M., Papadias, D.: Conceptual partitioning: an efficient method for continuous nearest neighbor monitoring. In: SIGMOD, pp. 634–645 (2005)Google Scholar
  38. 38.
    Papadias, D., Kalnis, P., Zhang, J., Tao, Y.: Efficient olap operations in spatial data warehouses. In: Jensen et al. [30], pp. 443–459Google Scholar
  39. 39.
    Pfoser, D., Jensen, C.S., Theodoridis, Y.: Novel approaches in query processing for moving object trajectories. In: VLDB, pp. 395–406 (2000)Google Scholar
  40. 40.
    Raptopoulou K., Papadopoulos A., Manolopoulos Y.: Fast nearest-neighbor query processing in moving-object databases. GeoInformatica 7(2), 113–137 (2003)CrossRefGoogle Scholar
  41. 41.
    Rasetic, S., Sander, J., Elding, J., Nascimento, M.A.: A trajectory splitting model for efficient spatio-temporal indexing. In: VLDB (2005)Google Scholar
  42. 42.
    Roussopoulos, N., Kelly, S., Vincent, F.: Nearest neighbor queries. In: SIGMOD (1995)Google Scholar
  43. 43.
    Sistla, A.P., Wolfson, O., Chamberlain, S., Dao, S.: Modeling and querying moving objects. In: Gray, W.A., Larson, P.-Å. (eds.) Proceedings of the Thirteenth International Conference on Data Engineering, April 7–11, 1997 Birmingham UK, pp. 422–432. IEEE Computer Society (1997). ISBN 0-8186-7807-0. DBLP, http://dblp.uni-trier.de
  44. 44.
    Song, Z., Roussopoulos, N.: K-nearest neighbor search for moving query point. In: Jensen et al. [30], pp. 79–96Google Scholar
  45. 45.
    Tao, Y., Papadias, D.: Time-parameterized queries in spatio- temporal databases. In: SIGMOD, pp. 334–345 (2002)Google Scholar
  46. 46.
    Tao Y., Papadias D.: Historical spatio-temporal aggregation. ACM Trans. Inf. Syst. 23(1), 61–102 (2005)CrossRefGoogle Scholar
  47. 47.
    Tao, Y., Papadias, D., Shen, Q.: Continuous nearest neighbor search. In: VLDB, pp. 287–298 (2002)Google Scholar
  48. 48.
    Wolfson, O., Xu, B., Chamberlain, S., Jiang, L.: Moving objects databases: Issues and solutions. In: SSDBM, pp. 111–122 (1998)Google Scholar
  49. 49.
    Xiong, X., Mokbel, M.F., Aref, W.G.: Sea-cnn: scalable processing of continuous k-nearest neighbor queries in spatio-temporal databases. In: ICDE, pp. 643–654 (2005)Google Scholar
  50. 50.
    Yu, X., Pu, K.Q., Koudas, N.: Monitoring k-nearest neighbor queries over moving objects. In: ICDE, pp. 631–642 (2005)Google Scholar

Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  • Ralf Hartmut Güting
    • 1
  • Thomas Behr
    • 1
  • Jianqiu Xu
    • 1
  1. 1.Faculty of Mathematics and Computer ScienceUniversity of HagenHagenGermany

Personalised recommendations