English

Gomory-Hu Trees in Quadratic Time

Data Structures and Algorithms 2021-12-03 v1

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 O~(n2.875)\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 O~(n2)\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].

Keywords

Cite

@article{arxiv.2112.01042,
  title  = {Gomory-Hu Trees in Quadratic Time},
  author = {Tianyi Zhang},
  journal= {arXiv preprint arXiv:2112.01042},
  year   = {2021}
}
R2 v1 2026-06-24T08:01:03.197Z