eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2023-11-28
34:1
34:15
10.4230/LIPIcs.ISAAC.2023.34
article
Computing a Subtrajectory Cluster from c-Packed Trajectories
Gudmundsson, Joachim
1
https://orcid.org/0000-0002-6778-7990
Huang, Zijin
1
https://orcid.org/0000-0003-3417-5303
van Renssen, André
1
https://orcid.org/0000-0002-9294-9947
Wong, Sampson
2
https://orcid.org/0000-0003-3803-3804
The University of Sydney, Australia
BARC, University of Copenhagen, Denmark
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol283-isaac2023/LIPIcs.ISAAC.2023.34/LIPIcs.ISAAC.2023.34.pdf
Subtrajectory cluster
c-packed trajectories
Computational geometry