Near-Linear Time Approximation Algorithms for Curve Simplification

Authors:
Pankaj K. Agarwal;Sariel Har-Peled;Nabil H. Mustafa;Yusu Wang
Affiliations:
-;-;-;-
Venue:
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Year:
2002

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Abstract

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