The geometric dilation of finite point sets

Algorithmica (New York)

Volumn 44, Issue 2, 2006, Pages 137-149

  Ebbers Baumann, Annette ^a   Grüne, Ansgar ^a   Klein, Rolf ^a  

^a UNIVERSITY OF BONN   (Germany)

Author keywords

Computational geometry; Detour; Dilation; Graph; Network; Spanner; Stretch factor; Transportation network

Indexed keywords

ALGORITHMS; FINITE ELEMENT METHOD; GEOMETRY; GRAPH THEORY; INFORMATION THEORY; MATHEMATICAL MODELS; SET THEORY;

DETOUR; DILATION; GRAPH; NETWORK; SPANNER; STRETCH FACTOR; TRANSPORTATION NETWORK;

COMPUTATIONAL GEOMETRY;

EID: 30744448164     PISSN: 01784617     EISSN: 14320541     Source Type: Journal    
DOI: 10.1007/s00453-005-1203-9     Document Type: Conference Paper

References (15)

1. P. Agarwal, R. Klein, Ch. Knauer, and M. Sharir. Computing the detour of polygonal curves. Technical Report B 02-03, FU Berlin, January 2002.
2. O. Aichholzer, F. Aurenhammer, Ch. Icking, R. Klein, E. Langetepe, and G. Rote. Generalized self-approaching curves. Discrete Appl. Math., 109:3-24, 2001.
3. P. Bose, J. Gudmundsson, and M. Smid. Constructing plane spanners of bounded degree and low weight. In Proc. 10th Europ. Symp. Algorithms, Volume 2461 of Lecture Notes in Computer Science, pages 234-246. Springer-Verlag, Berlin, 2001.
4. D. Z. Chen, G. Das, and M. Smid. Lower bounds for computing geometric spanners and approximate shortest paths. Discrete Appl. Math., 110:151-167, 2001.
5. A. Ebbers-Baumann, R. Klein, E. Langetepe, and A. Lingas. A fast algorithm for approximating the detour of a polygonal chain. Comput. Geom., 27:123-134, 2004.
6. D. Eppstein. Spanning trees and spanners. In J.-R. Sack and J. Urrutia, editors, Handbook of Computational Geometry, pages 425-461. Elsevier, Amsterdam, 1999.
7. A. Grüne. Umwege in Polygonen. Diplomarbeit, Universität Bonn, 2002.
8. A. Grüne, R. Klein, and E. Langetepe. Computing the detour of polygons. In Abstracts 19th Europ. Workshop Computational Geometry, pages 61-64. University of Bonn, 2003.
9. J. Gudmundsson, Ch. Levcopoulos, G. Narasimhan, and M. Smid. Approximate distance oracles revisited. In Proc. 13th Internat. Symp. ISAAC '02, pages 357-368. Volume 2518 of Lecture Notes in Computer Science. Springer-Verlag, Berlin, 2002.
10. Ch. Icking, R. Klein, and E. Langetepe. Self-approaching curves. Math. Proc. Cambridge Philos. Soc., 125:441-453, 1999.
11. R. Kusner and J.M. Sullivan. On distortion and thickness of knots. In Topology and Geometry in Polymer Science, pages 67-78. Volume 103 of IMA. Springer, New York, 1998.
12. S. Langerman, P. Morin, and M. Soss. Computing the maximum detour and spanning ratio of planar chains, trees and cycles. In Proc. 19th Internat. Symp. Theoretical Aspects of Computer Science, STACS '02, pages 250-261. Volume 2285 of Lecture Notes in Computer Science. Springer-Verlag, Berlin, 2002.
13. S. Langerman, P. Morin, and M. Soss. Computing the maximum detour and spanning ratio of planar chains, trees and cycles. In Proc. 19th Internat. Symp. Theoretical Aspects of Computer Science, STACS '02, pages 250-261. Volume 2285 of Lecture Notes in Computer Science. Springer-Verlag, Berlin, 2002.
14. J. Matoušek. Lectures on Discrete Geometry, Chapter II. Volume 212 of Graduate Texts in Mathematics. Springer, New York, 2002.
15. G. Narasimhan and M. Smid. Approximating the stretch factor of Euclidean graphs. SIAM J. Comput., 30:978-989, 2000.