Gomory-Hu Trees in Quadratic Time

12/02/2021

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by   Tianyi Zhang, et al.

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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 Õ(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 Õ(n^2). This quadratic upper bound is also obtained independently in an updated version by the same group of authors [AKL+, arXiv v2, 2021].