Advertisement

Maintaining minimum spanning trees in dynamic graphs

  • Monika R. Henzinger
  • Valerie King
Session 15: Algorithms III
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1256)

Abstract

We present the first fully dynamic algorithm for maintaining a minimum spanning tree in time o(√n) per operation. To be precise, the algorithm uses O(n1/3 log n) amortized time per update operation. The algorithm is fairly simple and deterministic. An immediate consequence is the first fully dynamic deterministic algorithm for maintaining connectivity and, bipartiteness in amortized time O(n1/3 log n) per update, with O(1) worst case time per query.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    T. Corman, C. Leiserson, and Rivest. Introduction to Algorithms. MIT Press (1989), p. 381–399.Google Scholar
  2. 2.
    D. Eppstein, “Dynamic Euclidean minimum spanning trees and extrema of binary functions”, Disc. Comp. Geom. 13 (1995), 111–122.Google Scholar
  3. 3.
    D. Eppstein, Z. Galil, G. F. Italiano, “Improved Sparsification”, Tech. Report 93-20, Department of Information and Computer Science, University of California, Irvine, CA 92717.Google Scholar
  4. 4.
    D. Eppstein, Z. Galil, G. F. Italiano, A. Nissenzweig, “Sparsification — A Technique for Speeding up Dynamic Graph Algorithms” Proc. 33rd Symp. on Foundations of Computer Science, 1992, 60–69.Google Scholar
  5. 5.
    S. Even and Y. Shiloach, “An On-Line Edge-Deletion Problem”, J. ACM 28 (1981), 1–4.CrossRefGoogle Scholar
  6. 6.
    T. Feder and M. Mihail, “Balanced matroids”, Proc. 24th A Cm Symp. on Theory of Computing, 1992, 26–38.Google Scholar
  7. 7.
    G. N. Frederickson, “Data Structures for On-line Updating of Minimum Spanning Trees”, SIAM J. Comput., 14 (1985), 781–798.Google Scholar
  8. 8.
    G. N. Frederickson and M. A. Srinivas, “Algorithms and data structures for an expanded family of matroid intersection problems”, SIAM J. Corn-put. 18 (1989), 112–138.CrossRefGoogle Scholar
  9. 9.
    M. R. Henzinger and V. King. Randomized Dynamic Graph Algorithms with Polylogarithmic Time per Operation. Proc. 27th ACM Symp. on Theory of Computing, 1995, 519–527.Google Scholar
  10. 10.
    M. R. Henzinger and M. Thorup. Improved Sampling with Applications to Dynamic Graph Algorithms. To appear in Proc. 23rd International Colloquium on Automata, Languages, and Programming (ICALP), LNCS 1099, Springer-Verlag, 1996.Google Scholar
  11. 11.
    K. Mehlhorn. “Data Structures and Algorithms 1: Sorting and Searching”, Springer-Verlag, 1984.Google Scholar
  12. 12.
    H. Nagamochi and T. Ibaraki, “Linear time algorithms for finding a sparse k-connected spanning subgraph of a k-connected graph”, Algorithmica 7, 1992, 583–596.CrossRefGoogle Scholar
  13. 13.
    D. D. Sleator, R. E. Tarjan, “A data structure for dynamic trees” J. Comput. System Sci. 24, 1983, 362–381.CrossRefGoogle Scholar
  14. 14.
    R. E. Tarjan, Data Structures and Network Flow, SIAM (1983) p. 71.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Monika R. Henzinger
    • 1
  • Valerie King
    • 2
  1. 1.Systems Research CenterDigital Equipment CorporationPalo AltoUSA
  2. 2.Dept. of Computer ScienceUniversity of VictoriaVictoriaCanada

Personalised recommendations