A Refined Definition for Groups of Moving Entities and its Computation

Authors Marc van Kreveld, Maarten Löffler, Frank Staals, Lionov Wiratma



PDF
Thumbnail PDF

File

LIPIcs.ISAAC.2016.48.pdf
  • Filesize: 0.52 MB
  • 12 pages

Document Identifiers

Author Details

Marc van Kreveld
Maarten Löffler
Frank Staals
Lionov Wiratma

Cite As Get BibTex

Marc van Kreveld, Maarten Löffler, Frank Staals, and Lionov Wiratma. A Refined Definition for Groups of Moving Entities and its Computation. In 27th International Symposium on Algorithms and Computation (ISAAC 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 64, pp. 48:1-48:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016) https://doi.org/10.4230/LIPIcs.ISAAC.2016.48

Abstract

One of the important tasks in the analysis of spatio-temporal data collected from moving entities is to find a group: a set of entities that travel together for a sufficiently long period of time. Buchin et al. [JoCG, 2015] introduce a formal definition of groups, analyze its mathematical structure, and present efficient algorithms for computing all maximal groups in a given set of trajectories. In this paper, we refine their definition and argue that our proposed definition corresponds better to human intuition in certain cases, particularly in dense environments.

We present algorithms to compute all maximal groups from a set of moving entities according to the new definition. For a set of n moving entities in R^1, specified by linear interpolation in a sequence of tau time stamps, we show that all maximal groups can be computed in O(tau^2 n^4) time. A similar approach applies if the time stamps of entities are not the same, at the cost of a small extra factor of alpha(n) in the running time. In higher dimensions, we can compute all maximal groups in O(tau^2 n^5 log n) time (for any constant number of dimensions).

We also show that one tau factor can be traded for a much higher dependence on n by giving a O(tau n^4 2^n) algorithm for the same problem. Consequently, we give a linear-time algorithm when the number of entities is constant and the input size relates to the number of time stamps of each entity. Finally, we provide a construction to show that it might be difficult to develop an algorithm with polynomial dependence on n and linear dependence on tau.

Subject Classification

Keywords
  • moving entities
  • trajectories
  • grouping
  • computational geometry

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads

References

  1. Marc Benkert, Joachim Gudmundsson, Florian Hübner, and Thomas Wolle. Reporting flock patterns. Computational Geometry, 41(3):111-125, 2008. Google Scholar
  2. Kevin Buchin, Maike Buchin, Marc van Kreveld, Bettina Speckmann, and Frank Staals. Trajectory grouping structure. Journal of Computational Geometry, 6(1):75-98, 2015. Google Scholar
  3. Joachim Gudmundsson, Patrick Laube, and Thomas Wolle. Computational movement analysis. In Handbook of Geographic Information, pages 423-438. Springer, 2012. Google Scholar
  4. Joachim Gudmundsson and Marc van Kreveld. Computing longest duration flocks in trajectory data. In Proc. 14th ACM International Symposium on Advances in Geographic Information Systems, GIS'06, pages 35-42, 2006. Google Scholar
  5. Joachim Gudmundsson, Marc van Kreveld, and Bettina Speckmann. Efficient detection of patterns in 2D trajectories of moving points. GeoInformatica, 11:195-215, 2007. Google Scholar
  6. Yan Huang, Cai Chen, and Pinliang Dong. Modeling herds and their evolvements from trajectory data. In Geographic Information Science, volume 5266 of LNCS, pages 90-105. Springer, 2008. Google Scholar
  7. San Hwang, Ying Liu, Jeng Chiu, and Ee Lim. Mining mobile group patterns: A trajectory-based approach. In Advances in Knowledge Discovery and Data Mining, volume 3518 of LNCS, pages 145-146. Springer, 2005. Google Scholar
  8. Hoyoung Jeung, Man Yiu, Xiaofang Zhou, Christian Jensen, and Heng Shen. Discovery of convoys in trajectory databases. PVLDB, 1:1068-1080, 2008. Google Scholar
  9. Panos Kalnis, Nikos Mamoulis, and Spiridon Bakiras. On discovering moving clusters in spatio-temporal data. In Advances in Spatial and Temporal Databases, volume 3633 of LNCS, pages 364-381. Springer, 2005. Google Scholar
  10. Irina Kostitsyna, Marc van Kreveld, Maarten Löffler, Bettina Speckmann, and Frank Staals. Trajectory grouping structure under geodesic distance. In Proc. 31st International Symposium on Computational Geometry, SoCG 2015, pages 674-688, 2015. Google Scholar
  11. Zhenhui Li, Bolin Ding, Jiawei Han, and Roland Kays. Swarm: Mining relaxed temporal moving object clusters. PVLDB, 3(1):723-734, 2010. Google Scholar
  12. Salman Parsa. A deterministic O(m log m) time algorithm for the Reeb graph. In Proc. 28th Annual Symposium on Computational Geometry, SoCG'12, pages 269-276, 2012. Google Scholar
  13. Micha Sharir and Pankaj K. Agarwal. Davenport-Schinzel Sequences and Their Geometric Applications. Cambridge University Press, 1995. Google Scholar
  14. Arthur van Goethem, Marc van Kreveld, Maarten Löffler, Bettina Speckmann, and Frank Staals. Grouping time-varying data for interactive exploration. In Proc. 32th Annual Symposium on Computational Geometry, SoCG'16, pages 61:1-61:16, 2016. Google Scholar
  15. Yu Zheng and Xiaofang Zhou. Computing with Spatial Trajectories. Springer, 2011. Google Scholar
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail