Encyclopedia of Algorithms

2008 Edition
| Editors: Ming-Yang Kao

Fully Dynamic Higher Connectivity for Planar Graphs

1998; Eppstein, Galil, Italiano, Spencer
  • Giuseppe F. Italiano
Reference work entry
DOI: https://doi.org/10.1007/978-0-387-30162-4_155

Keywords and Synonyms

Fully dynamic edge connectivity; Fully dynamic vertex connectivity          

Problem Definition

In this entry, the problem of maintaining a dynamic planar graph subject to edge insertions and edge deletions that preserve planarity but that can change the embedding is considered. In particular, in this problem one is concerned with the problem of efficiently maintaining information about edge and vertex connectivity in such a dynamically changing planar graph. The algorithms to solve this problem must handle insertions that keep the graph planar without regard to any particular embedding of the graph. The interested reader is referred to the chapter “Fully Dynamic Planarity Testing” of this encyclopedia for algorithms to learn how to check efficiently whether a graph subject to edge insertions and deletions remains planar (without regard to any particular embedding).

Before defining formally the problems considered here, a few preliminary definitions follow.

Given...

This is a preview of subscription content, log in to check access.

Recommended Reading

  1. 1.
    Galil Z., Italiano G.F., Sarnak N.: Fully dynamic planarity testing with applications. J. ACM 48, 28–91 (1999)MathSciNetGoogle Scholar
  2. 2.
    Eppstein D., Galil Z., Italiano G.F., Spencer T.H.: Separator based sparsification I: planarity testing and minimum spanning trees. J. Comput. Syst. Sci., Special issue of STOC 93 52(1), 3–27 (1996)Google Scholar
  3. 3.
    Eppstein D., Galil Z., Italiano G.F., Spencer T.H.: Separator based sparsification II: edge and vertex connectivity. SIAM J. Comput. 28, 341–381 (1999)MathSciNetGoogle Scholar
  4. 4.
    Giammarresi D., Italiano G.F.: Decremental 2- and 3‑connectivity on planar graphs. Algorithmica 16(3), 263–287 (1996)MathSciNetzbMATHGoogle Scholar
  5. 5.
    Hershberger J., M.R., Suri S.: Data structures for two-edge connectivity in planar graphs. Theor. Comput. Sci. 130(1), 139–161 (1994)MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  • Giuseppe F. Italiano
    • 1
  1. 1.Department of Information and Computer SystemsUniversity of RomeRomeItaly