Year: 2021
Type: preprint
Abstract: Gomory-Hu tree [Gomory and Hu, 1961] is a succinct representation of pairwise minimum cuts in an undirected graph. When the input graph has general edge weights, classic algorithms need at least cubic running time to compute a Gomory-Hu tree. Very recently, the authors of [AKL+, arXiv v1, 2021] have improved the running time to $\tilde{O}(n^{2.875})$ which breaks the cubic barrier for the first time. In this paper, we refine their approach and improve the running time to $\tilde{O}(n^2)$. This quadratic upper bound is also obtained independently in an updated version by the same group of authors [AKL+, arXiv v2, 2021].
Source: arXiv (Cornell University)
Author: Zhang, Tianyi
Institution: Tel Aviv University
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3216100562