Global Curve Simplification
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.
Curve simplification
Fréchet distance
Hausdorff distance
Theory of computation~Computational geometry
67:1-67:14
Regular Paper
A full version of the paper is available at http://arxiv.org/abs/1809.10269.
Mees
van de Kerkhof
Mees van de Kerkhof
Utrecht University, The Netherlands
Supported by the Netherlands Organisation for Scientific Research (NWO) under project number 628.011.005.
Irina
Kostitsyna
Irina Kostitsyna
TU Eindhoven, The Netherlands
Maarten
Löffler
Maarten Löffler
Utrecht University, The Netherlands
Partially supported by the Netherlands Organisation for Scientific Research (NWO) under project numbers 614.001.504 and 628.011.005.
Majid
Mirzanezhad
Majid Mirzanezhad
Tulane University, New Orleans, USA
Supported by the National Science Foundation grant CCF-1637576.
Carola
Wenk
Carola Wenk
Tulane University, New Orleans, USA
Supported by the National Science Foundation grant CCF-1637576.
10.4230/LIPIcs.ESA.2019.67
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Mees van de Kerkhof, Irina Kostitsyna, Maarten Löffler, Majid Mirzanezhad, and Carola Wenk
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