Advertisement

Fully dynamic 2-edge-connectivity in planar graphs

  • John Hershberger
  • Monika Rauch
  • Subhash Suri
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 621)

Abstract

We propose a data structure for maintaining 2-edge connectivity information dynamically in a planar graph. The data structure requires linear storage and preprocessing time for its construction, supports online updates (insertion and deletion of an edge) in O(log2n) time, and answers a query (whether two vertices are in the same 2-connected component) in O(log n) time. The previous best algorithm for this problem required O(log3n) time for updates.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    A. V. Aho, J. Hopcroft, and J. D. Ullman. The design and analysis of computer algorithms. Addison-Wesley, Reading, MA, 1974.Google Scholar
  2. 2.
    D. Eppstein, G. Italiano, R. Tamassia, R. E. Tarjan, J. Westbrook, and M. Yung. “Maintenance of a minimum spanning forest in a dynamic planar graph” Proc. of 1st SODA, 1990.Google Scholar
  3. 3.
    G. N. Frederickson. “Data structures for online updating of minimum spanning trees.” SIAM J. on Computing (14), 1985, 781–798.Google Scholar
  4. 4.
    G. N. Frederickson. “Ambivalent data structures for dynamic 2-edge connectivity and k smallest spanning trees.” Proc. of 32nd FOCS, 1991.Google Scholar
  5. 5.
    Z. Galil and G. Italiano. “Fully dynamic algorithms for edge connectivity problems.” Proc. of 23rd STOC, 1991.Google Scholar
  6. 6.
    F. Harary. Graph Theory. Addison-Wesley, Reading, Massachusetts, 1969.Google Scholar
  7. 7.
    J. H. Hopcroft and R. E. Tarjan. “Dividing a graph into tri-connected components.” SIAM J. on Computing, 1973.Google Scholar
  8. 8.
    G. L. Miller and V. Ramachandran. “A new graph triconnectivity algorithm and its parallelization.” Proc. 19th STOC, 1987.Google Scholar
  9. 9.
    R. E. Tarjan. Data Structures and Network Algorithms. Society for Industrial and Applied Mathematics, Philadelphia, 1983.Google Scholar
  10. 10.
    R. E. Tarjan. “Depth-first search and linear graph algorithms.” SIAM J. on Computing, 1972.Google Scholar
  11. 11.
    R. E. Tarjan and U. Vishkin. “An efficient parallel biconnectivity algorithm.” SIAM J. of Computing, pp. 862–874, 1985.Google Scholar
  12. 12.
    J. Westbrook and R. E. Tarjan. “Maintaining bridge-connected and bi-connected components on-line.” Tech Report, Princeton University, 1989.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • John Hershberger
    • 1
  • Monika Rauch
    • 2
  • Subhash Suri
    • 3
  1. 1.DEC Systems Research CenterUSA
  2. 2.Princeton UniversityUSA
  3. 3.Bell Communications ResearchUSA

Personalised recommendations