English

Incremental DFS Trees on Arbitrary Directed Graphs

Data Structures and Algorithms 2022-02-24 v3

Abstract

We present a new algorithm for maintaining a DFS tree of an arbitrary directed graph under any sequence of edge insertions. Our algorithm requires a total of O(mn)O(m\cdot n) time in the worst case to process a sequence of edge insertions, where nn is the number of vertices in the graph and mm is the total number of edges in the final graph. We also prove lower bounds for variations of this problem.

Keywords

Cite

@article{arxiv.1502.07206,
  title  = {Incremental DFS Trees on Arbitrary Directed Graphs},
  author = {Giorgio Ausiello and Paolo G. Franciosa and Giuseppe F. Italiano and Andrea Ribichini},
  journal= {arXiv preprint arXiv:1502.07206},
  year   = {2022}
}

Comments

The article contains a flaw in the complexity analysis

R2 v1 2026-06-22T08:37:47.121Z