Fully Dynamic Planarity Testing
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...
- 3.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
- 11.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 1993Google Scholar
- 12.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)Google Scholar