Separator-Based Sparsification II: Edge and Vertex Connectivity

We consider the problem of maintaining a dynamic planar graph subject to edge insertions and edge deletions that preserve planarity but that can change the embedding. We describe algorithms and data structures for maintaining information about 2- and 3-vertex-connectivity, and 3- and 4-edge-connectivity in a planar graph in O(n1/2) amortized time per insertion, deletion, or connectivity query. All of the data structures handle insertions that keep the graph planar without regard to any particular embedding of the graph. Our algorithms are based on a new type of sparsification combined with several properties of separators in planar graphs. Key words. analysis of algorithms, dynamic data structures, edge connectivity, vertex connectivity, planar graphs AMS subject classifications. 68P05, 68Q20, 68R10 PII. S0097539794269072

• Type: Journal
• Year: 1998
• Where: SIAMCOMP
• Authors: David Eppstein, Zvi Galil, Giuseppe F. Italiano, Thomas H. Spencer
• Keywords: Data Structures, Dynamic Planar Graph, Planar Graphs, SIAMCOMP 1998