Faster CutEquivalent Trees in Simple Graphs
Abstract
Let $G = (V, E)$ be an undirected connected simple graph on $n$ vertices. A cutequivalent tree of $G$ is an edgeweighted tree on the same vertex set $V$, such that for any pair of vertices $s, t\in V$, the minimum $(s, t)$cut in the tree is also a minimum $(s, t)$cut in $G$, and these two cuts have the same cut value. In a recent paper [Abboud, Krauthgamer and Trabelsi, 2021], the authors propose the first subcubic time algorithm for constructing a cutequivalent tree. More specifically, their algorithm has $\widetilde{O}(n^{2.5})$ running time. In this paper, we improve the running time to $\hat{O}(n^2)$ if almostlinear time maxflow algorithms exist. Also, using the currently fastest maxflow algorithm by [van den Brand et al, 2021], our algorithm runs in time $\widetilde{O}(n^{17/8})$.
 Publication:

arXiv eprints
 Pub Date:
 June 2021
 DOI:
 10.48550/arXiv.2106.03305
 arXiv:
 arXiv:2106.03305
 Bibcode:
 2021arXiv210603305Z
 Keywords:

 Computer Science  Data Structures and Algorithms
 EPrint:
 Fix typos