Copyright © 2003 Elsevier B.V. All rights reserved.
A fast algorithm for approximating the detour of a polygonal chain*1
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
>0, we compute in time
a pair of points on which the chain makes a detour at least 1/(1+
) times the maximum detour.
Author Keywords: Maximum detour; Dilation; Polygonal chains; Approximation






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