eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2019-09-06
67:1
67:14
10.4230/LIPIcs.ESA.2019.67
article
Global Curve Simplification
van de Kerkhof, Mees
1
Kostitsyna, Irina
2
Löffler, Maarten
1
Mirzanezhad, Majid
3
Wenk, Carola
3
Utrecht University, The Netherlands
TU Eindhoven, The Netherlands
Tulane University, New Orleans, USA
Due to its many applications, curve simplification is a long-studied problem in computational geometry and adjacent disciplines, such as graphics, geographical information science, etc. Given a polygonal curve P with n vertices, the goal is to find another polygonal curve P' with a smaller number of vertices such that P' is sufficiently similar to P. Quality guarantees of a simplification are usually given in a local sense, bounding the distance between a shortcut and its corresponding section of the curve. In this work we aim to provide a systematic overview of curve simplification problems under global distance measures that bound the distance between P and P'. We consider six different curve distance measures: three variants of the Hausdorff distance and three variants of the Fréchet distance. And we study different restrictions on the choice of vertices for P'. We provide polynomial-time algorithms for some variants of the global curve simplification problem, and show NP-hardness for other variants. Through this systematic study we observe, for the first time, some surprising patterns, and suggest directions for future research in this important area.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol144-esa2019/LIPIcs.ESA.2019.67/LIPIcs.ESA.2019.67.pdf
Curve simplification
Fréchet distance
Hausdorff distance