, Volume 72, Issue 4, pp 995–1010 | Cite as

Augmenting Graphs to Minimize the Diameter

  • Fabrizio Frati
  • Serge Gaspers
  • Joachim GudmundssonEmail author
  • Luke Mathieson


We study the problem of augmenting a weighted graph by inserting edges of bounded total cost while minimizing the diameter of the augmented graph. Our main result is an FPT \(4\)-approximation algorithm for the problem.


Graph Algorithms Approximation algorithms Parametrized complexity 



A preliminary version of this paper was presented in [9]. FF acknowledges support from the Australian Research Council (grant DE140100708). SG acknowledges support from the Australian Research Council (grant DE120101761). JG acknowledges support from the Australian Research Council (grant FT100100755). NICTA is funded by the Australian Government as represented by the Department of Broadband, Communications and the Digital Economy and the Australian Research Council through the ICT Centre of Excellence program.


  1. 1.
    Alon, N., Gyárfás, A., Ruszinkó, M.: Decreasing the diameter of bounded degree graphs. J. Graph Theory 35, 161–172 (1999)CrossRefGoogle Scholar
  2. 2.
    Bilò, D., Gualà, L., Proietti, G.: Improved approximability and non-approximability results for graph diameter decreasing problems. Theor. Comput. Sci. 417, 12–22 (2012)zbMATHCrossRefGoogle Scholar
  3. 3.
    Chepoi, V., Vaxès, Y.: Augmenting trees to meet biconnectivity and diameter constraints. Algorithmica 33(2), 243–262 (2002)zbMATHMathSciNetCrossRefGoogle Scholar
  4. 4.
    Demaine, E.D., Zadimoghaddam, M.: Minimizing the diameter of a network using shortcut edges. In: Proceedings of the 12th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT), pp. 420–431 (2010)Google Scholar
  5. 5.
    Dodis, Y., Khanna, S.: Designing networks with bounded pairwise distance. In: Proceedings of the 31st Annual ACM Symposium on Theory of Computing (STOC), pp. 750–759 (1999)Google Scholar
  6. 6.
    Downey, R.G., Fellows, M.R.: Parameterized Complexity. Monographs in Computer Science, Springer (1999)CrossRefGoogle Scholar
  7. 7.
    Erdős, P., Rényi, A., Sós, V.T.: On a problem of graph theory. Studia Sci. Math. Hungar 1, 215–235 (1966)MathSciNetGoogle Scholar
  8. 8.
    Flum, J., Grohe, M.: Parameterized Complexity Theory, Texts in Theoretical Computer Science. An EATCS Series, vol. XIV. Springer, Berlin (2006)Google Scholar
  9. 9.
    Frati, F., Gaspers, S., Gudmundsson, J., Mathieson, L.: Augmenting graphs to minimize the diameter. In: Cai, L., Cheng, S.W., Lam, T.W. (eds.) International Symposium on Algorithms and Computation (ISAAC ’13). LNCS, vol. 8283, pp. 383–393. Springer (2013)Google Scholar
  10. 10.
    Fredman, M.L., Tarjan, R.E.: Fibonacci heaps and their uses in improved network optimization algorithms. J. ACM 34(3), 596–615 (1987)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Fredman, M.L., Willard, D.E.: Trans-dichotomous algorithms for minimum spanning trees and shortest paths. J. Comput. Syst. Sci. 48(3), 533–551 (1994)zbMATHMathSciNetCrossRefGoogle Scholar
  12. 12.
    Gao, Y., Hare, D.R., Nastos, J.: The parametric complexity of graph diameter augmentation. Discret. Appl. Math. 161(10–11), 1626–1631 (2013)zbMATHMathSciNetCrossRefGoogle Scholar
  13. 13.
    Grigorescu, E.: Decreasing the diameter of cycles. J. Graph Theory 43(4), 299–303 (2003)zbMATHMathSciNetCrossRefGoogle Scholar
  14. 14.
    Kapoor, S., Sarwat, M.: Bounded-diameter minimum-cost graph problems. Theory Comput. Syst. 41(4), 779–794 (2007)zbMATHMathSciNetCrossRefGoogle Scholar
  15. 15.
    Li, C.L., McCormick, S.T., Simchi-Levi, D.: On the minimum-cardinality-bounded-diameter and the bounded-cardinality-minimum-diameter edge addition problems. Oper. Res. Lett. 11(5), 303–308 (1992)zbMATHMathSciNetCrossRefGoogle Scholar
  16. 16.
    Marx, D.: Parameterized complexity and approximation algorithms. Comput. J. 51(1), 60–78 (2008)CrossRefGoogle Scholar
  17. 17.
    Niedermeier, R.: Invitation to Fixed-Parameter Algorithms. Oxford Lecture Series in Mathematics and its Applications, Oxford University Press, Oxford (2006)Google Scholar
  18. 18.
    Schoone, A.A., Bodlaender, H.L., van Leeuwen, J.: Diameter increase caused by edge deletion. J. Graph Theory 11, 409–427 (1997)CrossRefGoogle Scholar
  19. 19.
    Vazirani, V.V.: Approximation Algorithms. Springer, Berlin (2001)Google Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Fabrizio Frati
    • 1
  • Serge Gaspers
    • 2
    • 3
  • Joachim Gudmundsson
    • 1
    • 3
    Email author
  • Luke Mathieson
    • 4
  1. 1.University of SydneySydneyAustralia
  2. 2.University of New South WalesSydneyAustralia
  3. 3.NICTASydneyAustralia
  4. 4.Macquarie UniversitySydneyAustralia

Personalised recommendations