On the geometric dilation of closed curves, graphs, and point sets☆
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Some results of this article were presented at the 21st European Workshop on Computational Geometry (EWCG '05) [A. Dumitrescu, A. Grüne, G. Rote, Improved lower bound on the geometric dilation of point sets, in: Abstracts 21st European Workshop Comput. Geom., Technische Universiteit Eindhoven, 2005, pp. 37–40], others at the 9th Workshop on Algorithms and Data Structures (WADS '05) [A. Dumitrescu, A. Ebbers-Baumann, A. Grüne, R. Klein, G. Rote, On geometric dilation and halving chords, in: Proc. 9th Workshop on Algorithms and Data Structures (WADS 2005), Lecture Notes Comput. Sci., vol. 3608, Springer, Berlin, August 2005, pp. 244–255].
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Ansgar Grüne was partially supported by a DAAD PhD-grant.
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Rolf Klein was partially supported by DFG-grant KL 655/14-1.