A fast algorithm for approximating the detour of a polygonal chain

Authors:
Annette Ebbers-Baumann;Rolf Klein;Elmar Langetepe;Andrzej Lingas
Affiliations:
Universität Bonn, Institut für Informatik I, D-53117 Bonn, Germany;Universität Bonn, Institut für Informatik I, D-53117 Bonn, Germany;Universität Bonn, Institut für Informatik I, D-53117 Bonn, Germany;Department of Computer Science, Lund University, 22100 Lund, Sweden
Venue:
Computational Geometry: Theory and Applications
Year:
2004

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Abstract

Let C be a simple 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 ε 0, we compute in time O(1/ε n log n) a pair of points on which the chain makes a detour at least 1/(1 + ε) times the maximum detour.