eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2020-12-04
9:1
9:15
10.4230/LIPIcs.ISAAC.2020.9
article
Approximating the Packedness of Polygonal Curves
Gudmundsson, Joachim
1
Sha, Yuan
1
Wong, Sampson
1
The University of Sydney, Australia
In 2012 Driemel et al. [Anne Driemel et al., 2012] introduced the concept of c-packed curves as a realistic input model. In the case when c is a constant they gave a near linear time (1+ε)-approximation algorithm for computing the Fréchet distance between two c-packed polygonal curves. Since then a number of papers have used the model.
In this paper we consider the problem of computing the smallest c for which a given polygonal curve in ℝ^d is c-packed. We present two approximation algorithms. The first algorithm is a 2-approximation algorithm and runs in O(dn² log n) time. In the case d = 2 we develop a faster algorithm that returns a (6+ε)-approximation and runs in O((n/ε³)^{4/3} polylog (n/ε))) time.
We also implemented the first algorithm and computed the approximate packedness-value for 16 sets of real-world trajectories. The experiments indicate that the notion of c-packedness is a useful realistic input model for many curves and trajectories.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol181-isaac2020/LIPIcs.ISAAC.2020.9/LIPIcs.ISAAC.2020.9.pdf
Computational geometry
trajectories
realistic input models