Related papers: Computing exact minimum cuts without knowing the g…
We consider the minimum cut problem in undirected, weighted graphs. We give a simple algorithm to find a minimum cut that $2$-respects (cuts two edges of) a spanning tree $T$ of a graph $G$. This procedure can be used in place of the…
A minimum cycle basis of a weighted undirected graph $G$ is a basis of the cycle space of $G$ such that the total weight of the cycles in this basis is minimized. If $G$ is a planar graph with non-negative edge weights, such a basis can be…
We give a deterministic algorithm for finding the minimum (weight) cut of an undirected graph on $n$ vertices and $m$ edges using $\text{polylog}(n)$ calls to any maximum flow subroutine. Using the current best deterministic maximum flow…
We present a parallel algorithm for computing the minimum s-t cut in structured 3-dimensional proper order graphs arising from image segmentation problems. Proper order graphs are multi-column structures where vertices are arranged in…
A min-cut that seperates vertices s and t in a network is an edge set of minimum weight whose removal will disconnect s and t. This problem is the dual of the well known s-t max-flow problem. Several algorithms for the min-cut problem are…
Let $G=(V,E)$ be an undirected unweighted graph on $n$ vertices and $m$ edges. We address the problem of sensitivity oracle for all-pairs mincuts in $G$ defined as follows. Build a compact data structure that, on receiving any pair of…
We give an algorithm to find a minimum cut in an edge-weighted directed graph with $n$ vertices and $m$ edges in $\tilde O(n\cdot \max(m^{2/3}, n))$ time. This improves on the 30 year old bound of $\tilde O(nm)$ obtained by Hao and Orlin…
Given an undirected edge-weighted graph $G=(V,E)$ with $m$ edges and $n$ vertices, the minimum cut problem asks to find a subset of vertices $S$ such that the total weight of all edges between $S$ and $V \setminus S$ is minimized. Karger's…
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 $G$,…
We study algorithmic and structural aspects of connectivity in hypergraphs. Given a hypergraph $H=(V,E)$ with $n = |V|$, $m = |E|$ and $p = \sum_{e \in E} |e|$ the best known algorithm to compute a global minimum cut in $H$ runs in time…
A common way of partitioning graphs is through minimum cuts. One drawback of classical minimum cut methods is that they tend to produce small groups, which is why more balanced variants such as normalized and ratio cuts have seen more…
For $t\geq 3$, $K_{1, t}$ is called $t$-claw. In minimum $t$-claw deletion problem (\texttt{Min-$t$-Claw-Del}), given a graph $G=(V, E)$, it is required to find a vertex set $S$ of minimum size such that $G[V\setminus S]$ is $t$-claw free.…
Given an undirected, unweighted planar graph $G$ with $n$ vertices, we present a truly subquadratic size distance oracle for reporting exact shortest-path distances between any pair of vertices of $G$ in constant time. For any $\varepsilon…
We study the minimum cut problem in the presence of uncertainty and show how to apply a novel robust optimization approach, which aims to exploit the similarity in subsequent graph measurements or similar graph instances, without posing any…
We develop new $(1+\epsilon)$-approximation algorithms for finding the global minimum edge-cut in a directed edge-weighted graph, and for finding the global minimum vertex-cut in a directed vertex-weighted graph. Our algorithms are…
We consider the Global Minimum Vertex-Cut problem: given an undirected vertex-weighted graph $G$, compute a minimum-weight subset of its vertices whose removal disconnects $G$. The problem is closely related to Global Minimum Edge-Cut,…
In this paper, we consider two fundamental cut approximation problems on large graphs. We prove new lower bounds for both problems that are optimal up to logarithmic factors. The first problem is to approximate cuts in balanced directed…
In this paper, we present efficient pseudodeterministic algorithms for both the global minimum cut and minimum s-t cut problems. The running time of our algorithm for the global minimum cut problem is asymptotically better than the fastest…
We study the directed global minimum vertex-cut problem: given a directed vertex-weighted graph $G$, compute a vertex-cut $(L,S,R)$ in $G$ of minimum value, which is defined to be the total weight of all vertices in $S$. The problem,…
We present the first near-linear work and poly-logarithmic depth algorithm for computing a minimum cut in a graph, while previous parallel algorithms with poly-logarithmic depth required at least quadratic work in the number of vertices. In…