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Experimental Study of Geometric t-Spanners

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Algorithms – ESA 2005 (ESA 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3669))

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Abstract

The construction of t-spanners of a given point set has received a lot of attention, especially from a theoretical perspective. In this paper we perform the first extensive experimental study of the properties of t-spanners. The main aim is to examine the quality of the produced spanners in the plane. We implemented the most common t-spanner algorithms and tested them on a number of different point sets. The experiments are discussed and compared to the theoretical results and in several cases we suggest modifications that are implemented and evaluated. The quality measurements that we consider are the number of edges, the weight, the maximum degree, the diameter and the number of crossings.

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References

  1. 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)

    Article  MATH  MathSciNet  Google Scholar 

  2. 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 (1995)

    Google Scholar 

  3. Bose, P., Gudmundsson, J., Morin, P.: Ordered theta graphs. Computational Geometry: Theory and Applications 28, 11–18 (2004)

    MATH  MathSciNet  Google Scholar 

  4. 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)

    Article  MATH  MathSciNet  Google Scholar 

  5. Clarkson, K.L.: Approximation algorithms for shortest path motion planning. In: Proc. 19th ACM Symposium on Computational Geometry, pp. 56–65 (1987)

    Google Scholar 

  6. Czumaj, A., Lingas, A.: Fast approximation schemes for euclidean multi-connectivity problems. In: Welzl, E., Montanari, U., Rolim, J.D.P. (eds.) ICALP 2000. LNCS, vol. 1853, pp. 856–868. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  7. Eppstein, D.: Spanning trees and spanners. In: Sack, J.-R., Urrutia, J. (eds.) Handbook of Computational Geometry, pp. 425–461. Elsevier Science Publishers, Amsterdam (2000)

    Chapter  Google Scholar 

  8. Farley, A.M., Proskurowski, A., Zappala, D., Windisch, K.J.: Spanners and message distribution in networks. Discrete Applied Mathematics 137(2), 159–171 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  9. Gudmundsson, J., Levcopoulos, C., Narasimhan, G.: Improved greedy algorithms for constructing sparse geometric spanners. SIAM Journal of Computing 31(5), 1479–1500 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  10. Gudmundsson, J., Levcopoulos, C., Narasimhan, G., Smid, M.: Approximate distance oracles for geometric graph. In: Proc. 13th ACM-SIAM Symposium on Discrete Algorithms (2002)

    Google Scholar 

  11. 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)

    Google Scholar 

  12. Keil, J.M., Gutwin, C.A.: Classes of graphs which approximate the complete Euclidean graph. Discrete and Computational Geometry 7, 13–28 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  13. Li, X.-Y.: Applications of computational geomety in wireless ad hoc networks. In: Cheng, X.-Z., Huang, X., Du, D.-Z. (eds.) Ad Hoc Wireless Networking. Kluwer, Dordrecht (2003)

    Google Scholar 

  14. Mehlhorn, K., Näher, S.: LEDA: A Platform for Combinatorial and Geometric Computing. Cambridge University Press, Cambridge (2000)

    Google Scholar 

  15. Navarro, G., Paredes, R.: Practical construction of metric t-spanners. In: Proc. 5th Workshop on Algorithm Engineering and Experiments, pp. 69–81. SIAM Press, Philadelphia (2003)

    Google Scholar 

  16. Navarro, G., Paredes, R., Chávez, E.: t-spanners as a data structure for metric space searching. In: Laender, A.H.F., Oliveira, A.L. (eds.) SPIRE 2002. LNCS, vol. 2476, pp. 298–309. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  17. Purchase, H.C.: Which aesthetic has the greatest effect on human understanding? In: DiBattista, G. (ed.) GD 1997. LNCS, vol. 1353, pp. 248–261. Springer, Heidelberg (1997)

    Chapter  Google Scholar 

  18. 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)

    Google Scholar 

  19. Ruppert, J., Seidel, R.: Approximating the d-dimensional complete Euclidean graph. In: Proc. 3rd Canadian Conference on Computational Geometry, pp. 207–210 (1991)

    Google Scholar 

  20. Sigurd, M., Zachariasen, M.: Construction of minimum-weight spanners. In: Albers, S., Radzik, T. (eds.) ESA 2004. LNCS, vol. 3221, pp. 797–808. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

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Farshi, M., Gudmundsson, J. (2005). Experimental Study of Geometric t-Spanners. In: Brodal, G.S., Leonardi, S. (eds) Algorithms – ESA 2005. ESA 2005. Lecture Notes in Computer Science, vol 3669. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11561071_50

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  • DOI: https://doi.org/10.1007/11561071_50

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-29118-3

  • Online ISBN: 978-3-540-31951-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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