, Volume 80, Issue 3, pp 935–976 | Cite as

Improved Spanning Ratio for Low Degree Plane Spanners

  • Prosenjit Bose
  • Darryl Hill
  • Michiel Smid
Part of the following topical collections:
  1. Special Issue on Theoretical Informatics


We describe an algorithm that builds a plane spanner with a maximum degree of 8 and a spanning ratio of \({\approx }4.414\) with respect to the complete graph. This is the best currently known spanning ratio for a plane spanner with a maximum degree of less than 14.


Computational geometry Graphs Graph theory Plane Spanners Spanning graph Spanning ratio Degree Bounded degree 


  1. 1.
    Benson, R.V.: Euclidean Geometry and Convexity. McGraw-Hill, New York (1966)MATHGoogle Scholar
  2. 2.
    Bonichon, N., Gavoille, C., Hanusse, N., Perković, L.: Plane spanners of maximum degree six. In: Abramsky, S., Gavoille, C., Kirchner, C., auf der Heide, F.M., Spirakis, P. (eds.) Automata, Languages and Programming, Volume 6198 of Lecture Notes in Computer Science, pp. 19–30. Springer, Berlin (2010)Google Scholar
  3. 3.
    Bonichon, N., Kanj, I., Perković, L., Xia, G.: There are plane spanners of degree 4 and moderate stretch factor. Discrete Comput. Geom. 53(3), 514–546 (2015)MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Bose, P., Carmi, P., Chaitman-Yerushalmi, L.: On bounded degree plane strong geometric spanners. J. Discrete Algorithms 15, 16–31 (2012)MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Bose, P., Gudmundsson, J., Smid, M.: Constructing plane spanners of bounded degree and lowweight. Algorithmica 42(3), 249–264 (2005)MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Bose, P., Keil, J.M.: On the stretch factor of the constrained Delaunay triangulation. In: 3rd International Symposium on Voronoi Diagrams in Science and Engineering, ISVD 2006, Banff, Alberta, Canada, July 2–5, 2006, pp. 25–31. IEEE Computer Society (2006)Google Scholar
  7. 7.
    Bose, P., Smid, M.H.M., Xu, D.: Delaunay and diamond triangulations contain spanners of bounded degree. Int. J. Comput. Geom. Appl. 19, 119–140 (2009)MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Chew, P: There is a planar graph almost as good as the complete graph. In: Proceedings of the Second Annual Symposium on Computational Geometry, SCG ’86, pp. 169–177. ACM, New York, NY, USA (1986)Google Scholar
  9. 9.
    Dobkin, D.P., Friedman, S.J., Supowit, K.J.: Delaunay graphs are almost as good as complete graphs. Discrete Comput. Geom. 5(1), 399–407 (1990)MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Kanj, I., Perkovic, L., Türkoglu, D.: Degree four plane spanners: simpler and better. In: Fekete, S., Lubiw, A. (eds.) 32nd International Symposium on Computational Geometry (SoCG 2016), Volume 51 of Leibniz International Proceedings in Informatics (LIPIcs), pp. 45:1–45:15, Dagstuhl, Germany. Schloss Dagstuhl–Leibniz-Zentrum fuer Informatik (2016)Google Scholar
  11. 11.
    Kanj, I.A., Perković, L., Xia, G.: On spanners and lightweight spanners of geometric graphs. SIAM J. Comput. 39(6), 2132–2161 (2010)MathSciNetCrossRefMATHGoogle Scholar
  12. 12.
    Keil, J.M., Gutwin, C.A.: Classes of graphs which approximate the complete euclidean graph. Discrete Comput. Geom. 7(1), 13–28 (1992)MathSciNetCrossRefMATHGoogle Scholar
  13. 13.
    Li, X.-Y., Wang, Y.: Efficient construction of low weight bounded degree planar spanner. In: Warnow, T., Zhu, B. (eds.) Computing and Combinatorics, Volume 2697 of Lecture Notes in Computer Science, pp. 374–384. Springer, Berlin (2003)Google Scholar
  14. 14.
    Xia, G.: The stretch factor of the delaunay triangulation is less than 1.998. SIAM J. Comput. 42(4), 1620–1659 (2013)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.School of Computer ScienceCarleton UniversityOttawaCanada

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