On finding 2-cuts and 3-edge-connected components in parallel
Abstract
Given a connected undirected multigraph G (a graph that may contain parallel edges), the algorithm of [19] finds the 3-edge-connected components of in linear time using an innovative graph contraction technique based on a depth-first search. In [21], it was shown that the algorithm can be extended to produce a Mader construction sequence for each 3-edge-connected component, a cactus representation of the 2-cuts (cut-pairs) of each 2-edge-connected component of , and the 1-cuts (bridges) at the same time. In this paper, we further extend the algorithm of [19] to generate the 2-cuts and the 3-edge-connected components of simultaneously in linear time by performing only one depth-first search over the input graph. Previously known algorithms solve the two problems separately in multiple phases.
Cite
@article{arxiv.2306.14103,
title = {On finding 2-cuts and 3-edge-connected components in parallel},
author = {Yung H. Tsin},
journal= {arXiv preprint arXiv:2306.14103},
year = {2023}
}
Comments
14 pages, 2 figures. arXiv admin note: text overlap with arXiv:2002.04727