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(m⋅n) time in the worst case to process a sequence of edge insertions, where n is the number of vertices in the graph and m is the total number of edges in the final graph. We also prove lower bounds for variations of this problem.
@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