Related papers: A computational study of Gomory-Hu construction tr…
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…
The construction of cut trees (also known as Gomory-Hu trees) for a given graph enables the minimum-cut size of the original graph to be obtained for any pair of vertices. Cut trees are a powerful back-end for graph management and mining,…
A cut tree (or Gomory-Hu tree) of an undirected weighted graph G=(V,E) encodes a minimum s-t-cut for each vertex pair {s,t} \subseteq V and can be iteratively constructed by n-1 maximum flow computations. They solve the multiterminal…
The Gomory-Hu tree or cut tree (Gomory and Hu, 1961) is a classic data structure for reporting $(s,t)$ mincuts (and by duality, the values of $(s,t)$ maxflows) for all pairs of vertices $s$ and $t$ in an undirected graph. Gomory and Hu…
Given an $m$-edge, undirected, weighted graph $G=(V,E,w)$, a Gomory-Hu tree $T$ (Gomory and Hu, 1961) is a tree over the vertex set $V$ such that all-pairs mincuts in $G$ are preserved exactly in $T$. In this article, we give the first…
Given an undirected, weighted $n$-vertex graph $G = (V, E, w)$, a Gomory-Hu tree $T$ is a weighted tree on $V$ such that for any pair of distinct vertices $s, t \in V$, the Min-$s$-$t$-Cut on $T$ is also a Min-$s$-$t$-Cut on $G$. Computing…
Every undirected graph $G$ has a (weighted) cut-equivalent tree $T$, commonly named after Gomory and Hu who discovered it in 1961. Both $T$ and $G$ have the same node set, and for every node pair $s,t$, the minimum $(s,t)$-cut in $T$ is…
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…
Given an undirected graph $G=(V,E,w)$, a Gomory-Hu tree $T$ (Gomory and Hu, 1961) is a tree on $V$ that preserves all-pairs mincuts of $G$ exactly. We present a simple and efficient randomized reduction from Gomory-Hu trees to polylog…
Given an undirected graph $G=(V,E,w)$, a Gomory-Hu tree $T$ (Gomory and Hu, 1961) is a tree on $V$ that preserves all-pairs mincuts of $G$ exactly. We present a simple, efficient reduction from Gomory-Hu trees to polylog maxflow…
We give an $n^{2+o(1)}$-time algorithm for finding $s$-$t$ min-cuts for all pairs of vertices $s$ and $t$ in a simple, undirected graph on $n$ vertices. We do so by constructing a Gomory-Hu tree (or cut equivalent tree) in the same running…
For an undirected $n$-vertex graph $G$ with non-negative edge-weights, we consider the following type of query: given two vertices $s$ and $t$ in $G$, what is the weight of a minimum $st$-cut in $G$? We solve this problem in preprocessing…
Gomory-Hu (GH) Trees are a classical sparsification technique for graph connectivity. It is one of the fundamental models in combinatorial optimization which also continually finds new applications, most recently in social network analysis.…
Gomory and Hu proved that if $ G $ is a finite graph with non-negative weights on its edges, then there exists a tree $ T $ (called now Gomory-Hu tree) on $ V(G) $ such that for all $ u\neq v\in V(G) $ there is an $ e\in E(T) $ such that…
Min-Cut queries are fundamental: Preprocess an undirected edge-weighted graph, to quickly report a minimum-weight cut that separates a query pair of nodes $s,t$. The best data structure known for this problem simply builds a cut-equivalent…
Due to their computational complexity, graph cuts for cluster detection and identification are used mostly in the form of convex relaxations. We propose to utilize the original graph cuts such as Ratio, Normalized or Cheeger Cut to detect…
We devise new cut sparsifiers that are related to the classical sparsification of Nagamochi and Ibaraki [Algorithmica, 1992], which is an algorithm that, given an unweighted graph $G$ on $n$ nodes and a parameter $k$, computes a subgraph…
We present the first non-trivial algorithm for the all-pairs minimum cut problem in the cut-query model. Given cut-query access to an unweighted graph $G=(V,E)$ with $n$ vertices, our randomized algorithm constructs a Gomory-Hu tree of $G$,…
The minimum cut problem for an undirected edge-weighted graph asks us to divide its set of nodes into two blocks while minimizing the weight sum of the cut edges. In this paper, we engineer the fastest known exact algorithm for the problem.…
A tree-packing is a collection of spanning trees of a graph. It has been a useful tool for computing the minimum cut in static, dynamic, and distributed settings. In particular, [Thorup, Comb. 2007] used them to obtain his dynamic min-cut…