# Incremental Algorithm for Maintaining a DFS Tree for Undirected Graphs

Incremental Algorithm for Maintaining a DFS Tree for Undirected Graphs 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 ( n 2 ) time. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Algorithmica Springer Journals

# Incremental Algorithm for Maintaining a DFS Tree for Undirected Graphs

, Volume 79 (2) – Aug 26, 2016
18 pages

/lp/springer_journal/incremental-algorithm-for-maintaining-a-dfs-tree-for-undirected-graphs-b5BgvzJUl4
Publisher
Springer US
Subject
Computer Science; Algorithm Analysis and Problem Complexity; Theory of Computation; Mathematics of Computing; Algorithms; Computer Systems Organization and Communication Networks; Data Structures, Cryptology and Information Theory
ISSN
0178-4617
eISSN
1432-0541
D.O.I.
10.1007/s00453-016-0204-1
Publisher site
See Article on Publisher Site

### 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 ( n 2 ) time.

### Journal

AlgorithmicaSpringer Journals

Published: Aug 26, 2016

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