Encyclopedia of Algorithms

2008 Edition
| Editors: Ming-Yang Kao

Planar Geometric Spanners

2005; Bose, Smid, Gudmundsson
  • Joachim Gudmundsson
  • Giri Narasimhan
  • Michiel Smid
Reference work entry
DOI: https://doi.org/10.1007/978-0-387-30162-4_294

Keywords and Synonyms

Geometric network; Dilation; Detour          

Problem Definition

Let S be a set of n points in the plane and let G be an undirected graph with vertex set S, in which each edge \( { (u,v) } \)

This is a preview of subscription content, log in to check access.

Recommended Reading

  1. 1.
    Aronov, B., de Berg, M., Cheong, O., Gudmundsson, J., Haverkort, H., Vigneron, A.: Sparse geometric graphs with small dilation. In: Proceedings of the 16th International Symposium on Algorithms and Computation. Lecture Notes in Computer Science, vol. 3827, pp. 50–59. Springer, Berlin (2005)Google Scholar
  2. 2.
    Bose, P., Gudmundsson, J., Smid, M.: Constructing plane spanners of bounded degree and low weight. Algorithmica 42, 249–264 (2005)MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Bose, P., Maheshwari, A., Narasimhan, G., Smid, M., Zeh, N.: Approximating geometric bottleneck shortest paths. Comput. Geom.: Theory Appl. 29, 233–249 (2004)Google Scholar
  4. 4.
    Bose, P., Morin, P.: Competitive online routing in geometric graphs. Theor. Comput. Sci. 324, 273–288 (2004)MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    Bose, P., Morin, P.: Online routing in triangulations. SIAM J. Comput. 33, 937–951 (2004)MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    Bose, P., Smid, M., Xu, D.: Diamond triangulations contain spanners of bounded degree. In: Proceedings of the 17th International Symposium on Algorithms and Computation. Lecture Notes in Computer Science, vol. 4288, pp. 173–182. Springer, Berlin (2006)Google Scholar
  7. 7.
    Chew, L.P.: There is a planar graph almost as good as the complete graph. In: Proceedings of the 2nd ACM Symposium on Computational Geometry, pp. 169–177 (1986)Google Scholar
  8. 8.
    Chew, L.P.: There are planar graphs almost as good as the complete graph. J. Comput. Syst. Sci. 39, 205–219 (1989)MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    Das, G., Joseph, D.: Which triangulations approximate the complete graph? In: Proceedings of the International Symposium on Optimal Algorithms. Lecture Notes in Computer Science, vol. 401, pp. 168–192. Springer, Berlin (1989)Google Scholar
  10. 10.
    Dobkin, D.P., Friedman, S.J., Supowit, K.J.: Delaunay graphs are almost as good as complete graphs. Discret. Comput. Geom. 5, 399–407 (1990)MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    Drysdale, R.L., McElfresh, S., Snoeyink, J.S.: On exclusion regions for optimal triangulations. Discrete Appl. Math. 109, 49–65 (2001)Google Scholar
  12. 12.
    Keil, J.M., Gutwin, C.A.: Classes of graphs which approximate the complete Euclidean graph. Discrete Comput. Geom. 7, 13–28 (1992)Google Scholar
  13. 13.
    Lee, A.W.: Diamonds are a plane graph's best friend. Master's thesis, School of Computer Science, Carleton University, Ottawa (2004)Google Scholar
  14. 14.
    Levcopoulos, C., Lingas, A.: There are planar graphs almost as good as the complete graphs and almost as cheap as minimum spanning trees. Algorithmica 8, 251–256 (1992)MathSciNetzbMATHCrossRefGoogle Scholar
  15. 15.
    Li, X.-Y., Wang, Y.: Efficient construction of low weighted bounded degree planar spanner. Int. J. Comput. Geom. Appl. 14, 69–84 (2004)zbMATHCrossRefGoogle Scholar
  16. 16.
    Narasimhan, G., Smid, M.: Geometric Spanner Networks. Cambridge University Press, Cambridge, UK (2007)zbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  • Joachim Gudmundsson
    • 1
  • Giri Narasimhan
    • 2
  • Michiel Smid
    • 3
  1. 1.DMiSTNational ICT Australia LtdAlexandriaAustralia
  2. 2.Department of Computer ScienceFlorida International UniversityMiamiUSA
  3. 3.School of Computer ScienceCarleton UniversityOttawaCanada