Faster Fully-Dynamic Minimum Spanning Forest

  • Jacob HolmEmail author
  • Eva Rotenberg
  • Christian Wulff-Nilsen
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9294)


We give a new data structure for the fully-dynamic minimum spanning forest problem in simple graphs. Edge updates are supported in O(log4n/loglogn) expected amortized time per operation, improving the O(log4n) amortized bound of Holm et al. (STOC ’98, JACM ’01). We also provide a deterministic data structure with amortized update time O(log4n logloglogn/loglogn). We assume the Word-RAM model with standard instructions.


Priority Queue Query Time Rank Tree Cluster Node Tree Edge 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Alstrup, S., Holm, J., de Lichtenberg, K., Thorup, M.: Maintaining information in fully dynamic trees with top trees. ACM Trans. Algorithms 1(2), 243–264 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Andersson, A., Hagerup, T., Nilsson, S., Raman, R.: Sorting in linear time? Journal of Computer and System Sciences 57(1), 74–93 (1998), See also STOC 1995Google Scholar
  3. 3.
    Eppstein, D., Galil, Z., Italiano, G.F., Nissenzweig, A.: Sparsification - a technique for speeding up dynamic graph algorithms. J. ACM 44(5), 669–696 (1997)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Frederickson, G.N.: Data structures for on-line updating of minimum spanning trees, with applications. SIAM Journal on Computing 14(4), 781–798 (1985), See also STOC 1983Google Scholar
  5. 5.
    Han, Y.: Deterministic sorting in O(nloglogn) time and linear space. J. Algorithms 50(1), 96–105 (2004), See also STOC 2002Google Scholar
  6. 6.
    Henzinger, M.R., King, V.: Fully dynamic 2-edge connectivity algorithm in polylogarithmic time per operation (1997)Google Scholar
  7. 7.
    Henzinger, M.R., King, V.: Randomized fully dynamic graph algorithms with polylogarithmic time per operation. J. ACM 46(4), 502–516 (1999), See also STOC 1995Google Scholar
  8. 8.
    Henzinger, M.R., Thorup, M.: Sampling to provide or to bound: With applications to fully dynamic graph algorithms. Random Structures and Algorithms 11(4), 369–379 (1997), See also ICALP 1996Google Scholar
  9. 9.
    Holm, J., de Lichtenberg, K., Thorup, M.: Poly-logarithmic deterministic fully-dynamic algorithms for connectivity, minimum spanning tree, 2-edge, and biconnectivity. J. ACM 48(4), 723–760 (2001), See also STOC 1998Google Scholar
  10. 10.
    Pǎtraşcu, M., Demaine, E.D.: Lower bounds for dynamic connectivity. In: Proc. 36th ACM Symposium on Theory of Computing (STOC), pp. 546–553 (2004)Google Scholar
  11. 11.
    Raman, R.: Fast algorithms for shortest paths and sorting (1996)Google Scholar
  12. 12.
    Thorup, M.: Near-optimal fully-dynamic graph connectivity. In: Proc. 32nd ACM Symposium on Theory of Computing (STOC), pp. 343–350 (2000)Google Scholar
  13. 13.
    Thorup, M.: Randomized sorting in O(nloglogn) time and linear space using addition, shift, and bit-wise boolean operations. J. Algorithms 42(2), 205–230 (2002), See also SODA 1997Google Scholar
  14. 14.
    Wulff-Nilsen, C.: Faster deterministic fully-dynamic graph connectivity. In: SODA, pp. 1757–1769 (2013)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Jacob Holm
    • 1
    Email author
  • Eva Rotenberg
    • 1
  • Christian Wulff-Nilsen
    • 1
  1. 1.Department of Computer ScienceUniversity of CopenhagenCopenhagenDenmark

Personalised recommendations