Improved sampling with applications to dynamic graph algorithms

  • Monika Rauch Henzinger
  • Mikkel Thorup
Session 6: Graph Algorithms
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1099)


We state a new sampling lemma and use it to improve the running time of dynamic graph algorithms.

For the dynamic connectivity problem the previously best randomized algorithm takes expected time O(log3n) per update, amortized over Ω(m) updates. Using the new sampling lemma, we improve its running time to O(log2n). There exists a lower bound in the cell probe model for the time per operation of Ω(log n/ log log n) for this problem.

Similarly improved running times are achieved for 2-edge connectivity, k-weight minimum spanning tree, and bipartiteness.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Monika Rauch Henzinger
    • 1
  • Mikkel Thorup
    • 2
  1. 1.Digital System Research CenterPalo Alto
  2. 2.Department of Computer ScienceUniversity of CopenhagenKbh. ØDenmark

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