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Computational Geometry
Volume 27, Issue 2, February 2004, Pages 123-134
 
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doi:10.1016/S0925-7721(03)00046-4    How to Cite or Link Using DOI (Opens New Window)
Copyright © 2003 Elsevier B.V. All rights reserved.

A fast algorithm for approximating the detour of a polygonal chain*1

Annette Ebbers-Baumanna, Rolf Kleina, Elmar LangetepeCorresponding Author Contact Information, E-mail The Corresponding Author, a and Andrzej Lingasb

a Universität Bonn, Institut für Informatik I, D-53117, Bonn, Germany b Department of Computer Science, Lund University, 22100, Lund, Sweden

Received 22 July 2001; 
accepted 15 February 2003;
Communicated by S. Suri 
Available online 10 September 2003.

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Abstract

Let C be a simple1 polygonal chain of n edges in the plane, and let p and q be two arbitrary points on C. The detour of C on (p,q) is defined to be the length of the subchain of C that connects p with q, divided by the Euclidean distance between p and q. Given an var epsilon>0, we compute in time Image a pair of points on which the chain makes a detour at least 1/(1+var epsilon) times the maximum detour.

Author Keywords: Maximum detour; Dilation; Polygonal chains; Approximation


Computational Geometry
Volume 27, Issue 2, February 2004, Pages 123-134
 
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