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Algorithmica

, Volume 42, Issue 3–4, pp 203–219 | Cite as

Near-Linear Time Approximation Algorithms for Curve Simplification

  • Pankaj K. AgarwalEmail author
  • Sariel Har-PeledEmail author
  • Nabil H. MustafaEmail author
  • Yusu WangEmail author
Article

Abstract

We consider the problem of approximating a polygonal curve P under a given error criterion by another polygonal curve P’ whose vertices are a subset of the vertices of P. The goal is to minimize the number of vertices of P’ while ensuring that the error between P’ and P is below a certain threshold. We consider two different error measures: Hausdorff and Frechet. For both error criteria, we present near-linear time approximation algorithms that, given a parameter ε > 0, compute a simplified polygonal curve P’ whose error is less than ε and size at most the size of an optimal simplified polygonal curve with error ε/2. We consider monotone curves in ℝ2 in the case of the Hausdorff error measure under the uniform distance metric and arbitrary curves in any dimension for the Frechet error measure under Lp metrics. We present experimental results demonstrating that our algorithms are simple and fast, and produce close to optimal simplifications in practice.

Computational geometry Curve simplification Approximation algorithms 

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Copyright information

© Springer 2005

Authors and Affiliations

  1. 1.Department of Computer Science, Duke University, Box 90129, Durham, NC 27708-0129USA
  2. 2.Department of Computer Science, DCL 2111, University of Illinois, 1304 West Springfield Ave., Urbana, IL 61801USA

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