Most Finite Point Sets in the Plane have Dilation $$>1$$ > 1-Reference-Cited by-同舟云学术

Most Finite Point Sets in the Plane have Dilation $$>1$$ > 1

Published:2014-12-17 Issue:1 Volume:53 Page:80-106
ISSN:0179-5376
Container-title:Discrete & Computational Geometry
language:en
Short-container-title:Discrete Comput Geom

Author:

Klein Rolf,Kutz Martin,Penninger Rainer

Publisher

Springer Science and Business Media LLC

Subject

Computational Theory and Mathematics,Discrete Mathematics and Combinatorics,Geometry and Topology,Theoretical Computer Science

Link

http://link.springer.com/content/pdf/10.1007/s00454-014-9651-0.pdf

Reference18 articles.

1. Agarwal, P.K., Klein, R., Knauer, C., Langerman, S., Morin, P., Sharir, M., Soss, M.A.: Computing the detour and spanning ratio of paths, trees, and cycles in 2D and 3D. Discrete Comput. Geom. 39(1–3), 17–37 (2008)

2. Aronov, B., de Berg, M., Cheong, O., Gudmundsson, J., Haverkort, H.J., Smid, M.H.M., Vigneron, A.: Sparse geometric graphs with small dilation. Comput. Geom. 40(3), 207–219 (2008)

3. Bose, P., Devroye, L., Löffler, M., Snoeyink, J., Verma, V.: The spanning ratio of the Delaunay triangulation is greater than $$\pi /2$$ π / 2 . In: CCCG, pp. 165–167 (2009)

4. Dumitrescu, A., Ebbers-Baumann, A., Grüne, A., Klein, R., Rote, G.: On geometric dilation and halving chords. In: Dehne, F.K.H.A., López-Ortiz, A., Sack, J.-R. (eds.) Algorithms and Data Structures. Proceedings of the 9th International Workshop, WADS 2005, Waterloo, Canada, 15–17 August, 2005. Lecture Notes in Computer Science, vol. 3608, pp. 244–255. Springer, Berlin (2005)

5. Dumitrescu, A., Ebbers-Baumann, A., Grüne, A., Klein, R., Rote, G.: On the geometric dilation of closed curves, graphs, and point sets. Comput. Geom. Theory Appl. 36(1), 16–38 (2007)

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