Faster Worst-Case Update Time for Dynamic Subgraph Connectivity

Real-world networks are prone to breakdowns. Typically in the underlying graph G, besides the insertion or deletion of edges, the set of active vertices changes overtime. A vertex might work actively, or it might fail, and gets isolated temporarily. The active vertices are grouped as a set S. S is subjected to updates, i.e., a failed vertex restarts, or an active vertex fails, and gets deleted from S. Dynamic subgraph connectivity answers the queries on connectivity between any two active vertices in the subgraph of G induced by S. The problem is solved by a dynamic data structure, which supports the updates and answers the connectivity queries. In the general undirected graph, the best results for it include Õ(m) deterministic amortized update time, Õ(m) and Õ( √ mn) deterministic worst-case update time. In the paper, we propose a randomized data structure, which has Õ(m) worst-case update time.