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Global Curve Simplification

Authors Mees van de Kerkhof, Irina Kostitsyna, Maarten Löffler, Majid Mirzanezhad, Carola Wenk

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Author Details

Mees van de Kerkhof
  • Utrecht University, The Netherlands
Irina Kostitsyna
  • TU Eindhoven, The Netherlands
Maarten Löffler
  • Utrecht University, The Netherlands
Majid Mirzanezhad
  • Tulane University, New Orleans, USA
Carola Wenk
  • Tulane University, New Orleans, USA

Funding

  • van de Kerkhof, Mees: Supported by the Netherlands Organisation for Scientific Research (NWO) under project number 628.011.005.
  • Löffler, Maarten: Partially supported by the Netherlands Organisation for Scientific Research (NWO) under project numbers 614.001.504 and 628.011.005.
  • Mirzanezhad, Majid: Supported by the National Science Foundation grant CCF-1637576.
  • Wenk, Carola: Supported by the National Science Foundation grant CCF-1637576.

Cite AsGet BibTex

Mees van de Kerkhof, Irina Kostitsyna, Maarten Löffler, Majid Mirzanezhad, and Carola Wenk. Global Curve Simplification. In 27th Annual European Symposium on Algorithms (ESA 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 144, pp. 67:1-67:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
https://doi.org/10.4230/LIPIcs.ESA.2019.67

Abstract

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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Computational geometry
Keywords
  • Curve simplification
  • Fréchet distance
  • Hausdorff distance

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