Detecting Regular Visit Patterns

  • Bojan Djordjevic
  • Joachim Gudmundsson
  • Anh Pham
  • Thomas Wolle
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5193)


We are given a trajectory \(\mathcal{T}\) and an area \(\mathcal{A}\). \(\mathcal{T}\) might intersect \(\mathcal{A}\) several times, and our aim is to detect whether \(\mathcal{T}\) visits \(\mathcal{A}\) with some regularity, e.g. what is the longest time span that a GPS-GSM equipped elephant visited a specific lake on a daily (weekly or yearly) basis, where the elephant has to visit the lake most of the days (weeks or years), but not necessarily on every day (week or year).

During the modelling of such applications, we encounter an elementary problem on bitstrings, that we call LDS (LongestDenseSubstring). The bits of the bitstring correspond to a sequence of regular time points, in which a bit is set to 1 iff the trajectory \(\mathcal{T}\) intersects the area \(\mathcal{A}\) at the corresponding time point. For the LDS problem, we are given a string s as input and want to output a longest substring of s, such that the ratio of 1’s in the substring is at least a certain threshold.

In our model, LDS is a core problem for many applications that aim at detecting regularity of \(\mathcal{T}\) intersecting \(\mathcal{A}\). We propose an optimal algorithm to solve LDS, and also for related problems that are closer to applications, we provide efficient algorithms for detecting regularity.


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  1. 1.
    Wildlife tracking projects with GPS GSM collars (2006),
  2. 2.
    Agarwal, P., Erickson, J.: Geometric range searching and its relatives (1999)Google Scholar
  3. 3.
    Al-Naymat, G., Chawla, S., Gudmundsson, J.: Dimensionality reduction for long duration and complex spatio-temporal queries. In: Proceedings of the 22nd ACM Symposium on Applied Computing, pp. 393–397. ACM, New York (2007)Google Scholar
  4. 4.
    Andersson, M., Gudmundsson, J., Laube, P., Wolle, T.: Reporting leaders and followers among trajectories of moving point objects. GeoInformatica (2007)Google Scholar
  5. 5.
    Benkert, M., Gudmundsson, J., Hübner, F., Wolle, T.: Reporting flock patterns. Computational Geometry—Theory and Applications (2007)Google Scholar
  6. 6.
    Frank, A.U.: Socio-Economic Units: Their Life and Motion. In: Frank, A.U., Raper, J., Cheylan, J.P. (eds.) Life and motion of socio-economic units. GISDATA, vol. 8, pp. 21–34. Taylor & Francis, London (2001)Google Scholar
  7. 7.
    Gudmundsson, J., Laube, P., Wolle, T.: Encyclopedia of GIS, chapter Movement Patterns in Spatio-temporal Data, pp. 726–732. Springer, Heidelberg (2008)Google Scholar
  8. 8.
    Gudmundsson, J., van Kreveld, M.: Computing longest duration flocks in trajectory data. In: Proceedings of the 14th ACM Symposium on Advances in GIS, pp. 35–42 (2006)Google Scholar
  9. 9.
    Gudmundsson, J., van Kreveld, M., Speckmann, B.: Efficient detection of motion patterns in spatio-temporal sets. GeoInformatica 11(2), 195–215 (2007)CrossRefGoogle Scholar
  10. 10.
    Güting, R.H., Schneider, M.: Moving Objects Databases. Morgan Kaufmann Publishers, San Francisco (2005)Google Scholar
  11. 11.
    Lee, J.-G., Han, J., Whang, K.-Y.: Trajectory clustering: a partition-and-group framework. In: SIGMOD 2007: Proceedings of the 2007 ACM SIGMOD international conference on Management of data, pp. 593–604. ACM Press, New York (2007)CrossRefGoogle Scholar
  12. 12.
    Mamoulis, N., Cao, H., Kollios, G., Hadjieleftheriou, M., Tao, Y., Cheung, D.: Mining, indexing, and querying historical spatiotemporal data. In: Proceedings of the 10th ACM SIGKDD International Conference On Knowledge Discovery and Data Mining, pp. 236–245. ACM, New York (2004)CrossRefGoogle Scholar
  13. 13.
    Vlachos, M., Kollios, G., Gunopulos, D.: Discovering similar multidimensional trajectories. In: Proceedings of the 18th International Conference on Data Engineering (ICDE 2002), pp. 673–684 (2002)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Bojan Djordjevic
    • 1
    • 2
  • Joachim Gudmundsson
    • 2
  • Anh Pham
    • 1
    • 2
  • Thomas Wolle
    • 2
  1. 1.School of Information TechnologiesUniversity of SydneyAustralia
  2. 2.NICTASydneyAustralia

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