Incremental Algorithm for Maintaining a DFS Tree for Undirected Graphs

Abstract

Depth First Search (DFS) tree is a fundamental data structure for graphs used in solving various algorithmic problems. However, very few results are known for maintaining DFS tree in a dynamic environment--insertion or deletion of edges. We present the first algorithm for maintaining a DFS tree for an undirected graph under insertion of edges. For processing any arbitrary online sequence of edge insertions, this algorithm takes total $$O(n^2)$$O(n2) time.