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Computing a Subtrajectory Cluster from c-Packed Trajectories

Authors Joachim Gudmundsson , Zijin Huang , André van Renssen , Sampson Wong

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ACM Subject Classification
  • Theory of computation → Computational geometry
Keywords
  • Subtrajectory cluster
  • c-packed trajectories
  • Computational geometry

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Abstract

We present a near-linear time approximation algorithm for the subtrajectory cluster problem of c-packed trajectories. Given a trajectory T of complexity n, an approximation factor ε, and a desired distance d, the problem involves finding m subtrajectories of T such that their pair-wise Fréchet distance is at most (1 + ε)d. At least one subtrajectory must be of length l or longer. A trajectory T is c-packed if the intersection of T and any ball B with radius r is at most c⋅r in length.
Previous results by Gudmundsson and Wong [Gudmundsson and Wong, 2022] established an Ω(n³) lower bound unless the Strong Exponential Time Hypothesis fails, and they presented an O(n³ log² n) time algorithm. We circumvent this conditional lower bound by studying subtrajectory cluster on c-packed trajectories, resulting in an algorithm with an O((c² n/ε²)log(c/ε)log(n/ε)) time complexity.

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Joachim Gudmundsson, Zijin Huang, André van Renssen, and Sampson Wong. Computing a Subtrajectory Cluster from c-Packed Trajectories. In 34th International Symposium on Algorithms and Computation (ISAAC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 283, pp. 34:1-34:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023) https://doi.org/10.4230/LIPIcs.ISAAC.2023.34

Author Details

Joachim Gudmundsson
  • The University of Sydney, Australia
Zijin Huang
  • The University of Sydney, Australia
André van Renssen
  • The University of Sydney, Australia
Sampson Wong
  • BARC, University of Copenhagen, Denmark

Funding

  • Gudmundsson, Joachim: Funded by the Australian Government through the Australian Research Council DP180102870.

Acknowledgements

The authors thank Kevin Buchin for the insightful discussion on the important Lemma 13. The authors thank the anonymous reviewers for their helpful feedback.

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