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- W4300943503 abstract "The Gomory-Hu tree, or a cut tree, is a classic data structure that stores minimum $s$-$t$ cuts of an undirected weighted graph for all pairs of nodes $(s,t)$. We propose a new approach for computing the cut tree based on a reduction to the problem that we call OrderedCuts. Given a sequence of nodes $s,v_1,ldots,v_ell$, its goal is to compute minimum ${s,v_1,ldots,v_{i-1}}$-$v_i$ cuts for all $iin[ell]$. We show that the cut tree can be computed by $tilde O(1)$ calls to OrderedCuts. We also establish new results for OrderedCuts that may be of independent interest. First, we prove that all $ell$ cuts can be stored compactly with $O(n)$ space in a data structure that we call an OC tree. We define a weaker version of this structure that we call depth-1 OC tree, and show that it is sufficient for constructing the cut tree. Second, we prove results that allow divide-and-conquer algorithms for computing OC tree. We argue that the existence of divide-and-conquer algorithms makes our new approach a good candidate for a practical implementation." @default.
- W4300943503 created "2022-10-04" @default.
- W4300943503 creator A5021390142 @default.
- W4300943503 date "2022-08-03" @default.
- W4300943503 modified "2023-10-18" @default.
- W4300943503 title "OrderedCuts: A new approach for computing Gomory-Hu tree" @default.
- W4300943503 doi "https://doi.org/10.48550/arxiv.2208.02000" @default.
- W4300943503 hasPublicationYear "2022" @default.
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