Dynamic Connectivity: Connecting to Networks and Geometry

Dynamic connectivity is a well-studied problem, but so far the most compelling progress has been confined to the edge-update model: maintain an understanding of connectivity in an undirected graph, subject to edge insertions and deletions. In this paper, we study two more challenging, yet equally fundamental problems: Subgraph connectivity asks to maintain an understanding of connectivity under vertex updates: updates can turn vertices on and off, and queries refer to the subgraph induced by on vertices. (For instance, this is closer to applications in networks of routers, where node faults may occur.) We describe a data structure supporting vertex updates in O(m2/3 ) amortized time, where m denotes the number of edges in the graph. This greatly improves over the previous result [Chan, STOC’02], which required fast matrix multiplication and had an update time of O(m0.94 ). The new data structure is also simpler. Geometric connectivity asks to maintain a dynamic set of n geometric o...

• Type: Conference
• Year: 2008
• Where: FOCS
• Authors: Timothy M. Chan, Mihai Patrascu, Liam Roditty
• Keywords: Dynamic Connectivity, FOCS 2008, Theoretical Computer Science, Update Time, Vertex Updates