Abstract
The construction of t-spanners of a given point set has received a lot of attention, especially from a theoretical perspective. We experimentally study the performance of the most common construction algorithms for points in the Euclidean plane. In a previous paper [10] we considered the properties of the produced graphs from five common algorithms. We consider several additional algorithms and focus on the running times. This is the first time an extensive comparison has been made between the running times of construction algorithms of t-spanners.
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Similar content being viewed by others
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
Althöfer, I., Das, G., Dobkin, D.P., Joseph, D., Soares, J.: On sparse spanners of weighted graphs. Discrete & Computational Geometry 9(1), 81–100 (1993)
Arya, S., Das, G., Mount, D.M., Salowe, J.S., Smid, M.: Euclidean spanners: short, thin, and lanky. In: Proc. 27th ACM Symposium on Theory of Computing, pp. 489–498. ACM Press, New York (1995)
Arya, S., Mount, D.M., Smid, M.: Randomized and deterministic algorithms for geometric spanners of small diameter. In: Proc. 35th IEEE Symposium on Foundations of Computer Science, pp. 703–712. IEEE Computer Society Press, Los Alamitos (1994)
Arya, S., Mount, D.M., Smid, M.: Dynamic algorithms for geometric spanners of small diameter: Randomized solutions. Computational Geometry: Theory and Applications 13(2), 91–107 (1999)
Bose, P., Gudmundsson, J., Morin, P.: Ordered theta graphs. Computational Geometry: Theory and Applications 28, 11–18 (2004)
Callahan, P.B., Kosaraju, S.R.: A decomposition of multidimensional point sets with applications to k-nearest-neighbors and n-body potential fields. Journal of the ACM 42, 67–90 (1995)
Clarkson, K.L.: Approximation algorithms for shortest path motion planning. In: Proceedings of the 19th ACM Symposium on the Theory of Computing, pp. 56–65. ACM Press, New York (1987)
Das, G., Narasimhan, G.: A fast algorithm for constructing sparse Euclidean spanners. International Journal of Computational Geometry and Applications 7, 297–315 (1997)
Davis, R.B. (2005), http://www.robertnz.net/nr03doc.htm
Farshi, M., Gudmundsson, J.: Experimental study of geometric t-spanners. In: Brodal, G.S., Leonardi, S. (eds.) ESA 2005. LNCS, vol. 3669, pp. 556–567. Springer, Heidelberg (2005)
Gudmundsson, J., Levcopoulos, C., Narasimhan, G.: Improved greedy algorithms for constructing sparse geometric spanners. SIAM Journal of Computing 31(5), 1479–1500 (2002)
Keil, J.M.: Approximating the complete Euclidean graph. In: Karlsson, R., Lingas, A. (eds.) SWAT 1988. LNCS, vol. 318, pp. 208–213. Springer, Heidelberg (1988)
Keil, J.M., Gutwin, C.A.: Classes of graphs which approximate the complete Euclidean graph. Discrete and Computational Geometry 7, 13–28 (1992)
Li, X.-Y.: Applications of computational geometry in wireless ad hoc networks. In: Cheng, X.-Z., Huang, X., Du, D.-Z. (eds.) Ad Hoc Wireless Networking, Kluwer Academic Publishers, Dordrecht (2003)
Narasimhan, G., Smid, M.: Geometric spanner networks. Cambridge University Press, Cambridge (2007)
Navarro, G., Paredes, R.: Practical construction of metric t-spanners. In: Proc. 5th Workshop on Algorithm Engineering and Experiments, pp. 69–81. SIAM Press (2003)
Rao, S., Smith, W.D.: Approximating geometrical graphs via spanners and banyans. In: Proc. 30th ACM Symposium on the Theory of Computing, pp. 540–550. ACM, New York (1998)
Sigurd, M., Zachariasen, M.: Construction of minimum-weight spanners. In: Albers, S., Radzik, T. (eds.) ESA 2004. LNCS, vol. 3221, Springer, Heidelberg (2004)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer Berlin Heidelberg
About this paper
Cite this paper
Farshi, M., Gudmundsson, J. (2007). Experimental Study of Geometric t-Spanners: A Running Time Comparison. In: Demetrescu, C. (eds) Experimental Algorithms. WEA 2007. Lecture Notes in Computer Science, vol 4525. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72845-0_21
Download citation
DOI: https://doi.org/10.1007/978-3-540-72845-0_21
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-72844-3
Online ISBN: 978-3-540-72845-0
eBook Packages: Computer ScienceComputer Science (R0)