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. Before formally defining the problem, few preliminary definitions follow.
A graph is planar if it can be embedded in the plane so that no two edges intersect. In a dynamic framework, a planar graph that is committed to an embedding is called plane, and the general term planar is used only when changes in the embedding are allowed. An edge insertion that preserves the embedding is called embedding‐preserving, whereas it is called planarity‐preserving if it keeps the graph planar, even though its embedding can change; finally, an edge insertion is called arbitraryif it is not known to preserve planarity. Extensive work on dynamic graph algorithms has used ad hoc techniques to solve a number of problems such as minimum spanning forests, 2-edge‐connectivity and planarity testing for plane...
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Recommended Reading
Cimikowski, R.: Branch-and-bound techniques for the maximum planar subgraph problem. Int. J. Computer Math. 53, 135–147 (1994)
Eppstein, D., Galil, Z., Italiano, G.F., Nissenzweig, A.: Sparsification – a technique for speeding up dynamic graph algorithms. J. Assoc. Comput. Mach. 44(5), 669–696 (1997)
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)
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)
Eppstein, D., Italiano, G.F., Tamassia, R., Tarjan, R.E., Westbrook, J., Yung, M.: Maintenance of a minimum spanning forest in a dynamic plane graph. J. Algorithms 13, 33–54 (1992)
Frederickson, G.N.: Data structures for on-line updating of minimum spanning trees, with applications. SIAM J. Comput. 14, 781–798 (1985)
Frederickson, G.N.: Ambivalent data structures for dynamic 2-edge‐connectivity and k smallest spanning trees. SIAM J. Comput. 26(2), 484–538 (1997)
Galil, Z., Italiano, G.F., Sarnak, N.: Fully dynamic planarity testing with applications. J. ACM 48, 28–91 (1999)
Giammarresi, D., Italiano, G.F.: Decremental 2- and 3‐connectivity on planar graphs. Algorithmica 16(3):263–287 (1996)
Hershberger, J., Suri, M.R., Suri, S.: Data structures for two-edge connectivity in planar graphs. Theor. Comput. Sci. 130(1), 139–161 (1994)
Italiano, G.F., La Poutré, J.A., Rauch, M.: Fully dynamic planarity testing in planar embedded graphs. 1st Annual European Symposium on Algorithms, Bad Honnef, Germany, 30 September–2 October 1993
Tamassia, R.: A dynamic data structure for planar graph embedding. 15th Int. Colloq. Automata, Languages, and Programming. LNCS, vol. 317, pp. 576–590. Springer, Berlin (1988)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer-Verlag
About this entry
Cite this entry
Italiano, G. (2008). Fully Dynamic Planarity Testing. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-30162-4_157
Download citation
DOI: https://doi.org/10.1007/978-0-387-30162-4_157
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-387-30770-1
Online ISBN: 978-0-387-30162-4
eBook Packages: Computer ScienceReference Module Computer Science and Engineering