Trajectory grouping structure under geodesic distance

I. Kostitsyna, M.J. van Kreveld, M. Löffler, B. Speckmann, F. Staals

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

9 Citations (Scopus)


In recent years trajectory data has become one of the main types of geographic data, and hence algorithmic tools to handle large quantities of trajectories are essential. A single trajectory is typically represented as a sequence of time-stamped points in the plane. In a collection of trajectories one wants to detect maximal groups of moving entities and their behaviour (merges and splits) over time. This information can be summarized in the trajectory grouping structure. Significantly extending the work of Buchin et al. [WADS 2013] into a realistic setting, we show that the trajectory grouping structure can be computed efficiently also if obstacles are present and the distance between the entities is measured by geodesic distance. We bound the number of critical events: times at which the distance between two subsets of moving entities is exactly ", where " is the threshold distance that determines whether two entities are close enough to be in one group. In case the n entities move in a simple polygon along trajectories with τ vertices each we give an O(τn2) upper bound, which is tight in the worst case. In case of well-spaced obstacles we give an O(τ (n2 + mλ4(n))) upper bound, where m is the total complexity of the obstacles, and λs(n) denotes the maximum length of a Davenport-Schinzel sequence of n symbols of order s. In case of general obstacles we give an O(τ min{n2 + m3λ4(n), n2m2}) upper bound. Furthermore, for all cases we provide efficient algorithms to compute the critical events, which in turn leads to efficient algorithms to compute the trajectory grouping structure.

Original languageEnglish
Title of host publicationProc. 31st International Symposium on Computational Geometry (SoCG)
Place of Publications.l.
PublisherSchloss Dagstuhl - Leibniz-Zentrum für Informatik
Number of pages15
ISBN (Electronic)9783939897835
Publication statusPublished - 1 Jun 2015
Event31st International Symposium on Computational Geometry (SoCG 2015) - Eindhoven, Netherlands
Duration: 22 Jun 201525 Jun 2015
Conference number: 31


Workshop31st International Symposium on Computational Geometry (SoCG 2015)
Abbreviated titleSoCG 2015
Internet address


  • Computational geometry
  • Grouping
  • Moving entities
  • Trajectories


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