Related papers: Multicritera Cuts and Size-Constrained $k$-cuts in…
We prove essentially tight lower bounds, conditionally to the Exponential Time Hypothesis, for two fundamental but seemingly very different cutting problems on surface-embedded graphs: the Shortest Cut Graph problem and the Multiway Cut…
We show the existence of an exact mimicking network of $k^{O(\log k)}$ edges for minimum multicuts over a set of terminals in an undirected graph, where $k$ is the total capacity of the terminals, as well as a method for computing a…
We consider the Minimum-$(k,\rho)$-$\mathrm{Shortcut}$ problem ($\min(k,\rho)\text{-}\mathrm{Shortcut}$), where the goal is to find the smallest set of shortcut edges such that every vertex in a given graph can reach its $\rho$ closest…
In this work, we resolve the query complexity of global minimum cut problem for a graph by designing a randomized algorithm for approximating the size of minimum cut in a graph, where the graph can be accessed through local queries like…
Minimum-weight cut (min-cut) is a basic measure of a network's connectivity strength. While the min-cut can be computed efficiently in the sequential setting [Karger STOC'96], there was no efficient way for a distributed network to compute…
We study a number of multi-route cut problems: given a graph G=(V,E) and connectivity thresholds k_(u,v) on pairs of nodes, the goal is to find a minimum cost set of edges or vertices the removal of which reduces the connectivity between…
Cuts in graphs are a fundamental object of study, and play a central role in the study of graph algorithms. The problem of sparsifying a graph while approximately preserving its cut structure has been extensively studied and has many…
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…
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…
An instance of the Connected Maximum Cut problem consists of an undirected graph G = (V, E) and the goal is to find a subset of vertices S $\subseteq$ V that maximizes the number of edges in the cut \delta(S) such that the induced graph…
In this paper, we present two approximation algorithms for the directed multi-multiway cut and directed multicut problems. The so called region growing paradigm \cite{1} is modified and used for these two cut problems on directed graphs. By…
There are many applications of graph cuts in computer vision, e.g. segmentation. We present a novel method to reformulate the NP-hard, k-way graph partitioning problem as an approximate minimal s-t graph cut problem, for which a globally…
The computational complexity of multicut-like problems may vary significantly depending on whether the terminals are fixed or not. In this work we present a comprehensive study of this phenomenon in two types of cut problems in directed…
We give an algorithm to find a mincut in an $n$-vertex, $m$-edge weighted directed graph using $\tilde O(\sqrt{n})$ calls to any maxflow subroutine. Using state of the art maxflow algorithms, this yields a directed mincut algorithm that…
We prove an approximate max-multiflow min-multicut theorem for bounded treewidth graphs. In particular, we show the following: Given a treewidth-$r$ graph, there exists a (fractional) multicommodity flow of value $f$, and a multicut of…
We study a generalization of the classic Global Min-Cut problem, called Global Label Min-Cut (or sometimes Global Hedge Min-Cut): the edges of the input (multi)graph are labeled (or partitioned into color classes or hedges), and removing…
We establish that in the large degree limit, the value of certain optimization problems on sparse random hypergraphs is determined by an appropriate Gaussian optimization problem. This approach was initiated in Dembo et. al.(2016) for…
A transversal of a hypergraph is a set of vertices intersecting each hyperedge. We design and analyze new exponential-time algorithms to enumerate all inclusion-minimal transversals of a hypergraph. For each fixed k>2, our algorithms for…
In this paper, we propose novel algorithms for inferring the Maximum a Posteriori (MAP) solution of discrete pairwise random field models under multiple constraints. We show how this constrained discrete optimization problem can be…
We study graph ordering problems with a min-max objective. A classical problem of this type is cutwidth, where given a graph we want to order its vertices such that the number of edges crossing any point is minimized. We give a $…