相关论文: A Sketching Algorithm for Spectral Graph Sparsific…

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…

In cut sparsification, all cuts of a hypergraph $H=(V,E,w)$ are approximated within $1\pm\epsilon$ factor by a small hypergraph $H'$. This widely applied method was generalized recently to a setting where the cost of cutting each hyperedge…

In second-order optimization, a potential bottleneck can be computing the Hessian matrix of the optimized function at every iteration. Randomized sketching has emerged as a powerful technique for constructing estimates of the Hessian which…

We consider straight line drawings of a planar graph $G$ with possible edge crossings. The \emph{untangling problem} is to eliminate all edge crossings by moving as few vertices as possible to new positions. Let $fix(G)$ denote the maximum…

Call a simple graph $H$ of order $n$ well-separable, if by deleting a separator set of size $o(n)$ the leftover will have components of size at most $o(n)$. We prove, that bounded degree well-separable spanning subgraphs are easy to embed:…

We give an algorithm to compute a one-dimensional shape-constrained function that best fits given data in weighted-$L_{\infty}$ norm. We give a single algorithm that works for a variety of commonly studied shape constraints including…

We call a graph $G$ separable if a balanced separator can be computed for $G$ of size $O(n^c)$ with $c<1$. Many real-world graphs are separable such as graphs of bounded genus, graphs of constant treewidth, and graphs excluding a fixed…

We prove that there is a randomized polynomial-time algorithm that given an edge-weighted graph $G$ excluding a fixed-minor $Q$ on $n$ vertices and an accuracy parameter $\varepsilon>0$, constructs an edge-weighted graph~$H$ and an…

Subexponential parameterized algorithms are known for a wide range of natural problems on planar graphs, but the techniques are usually highly problem specific. The goal of this paper is to introduce a framework for obtaining…

Whether or not the Sparsest Cut problem admits an efficient $O(1)$-approximation algorithm is a fundamental algorithmic question with connections to geometry and the Unique Games Conjecture. Revisiting spectral algorithms for Sparsest Cut,…

We consider the following stochastic matching problem on both weighted and unweighted graphs: A graph $G(V, E)$ along with a parameter $p \in (0, 1)$ is given in the input. Each edge of $G$ is realized independently with probability $p$.…

While the harmonic function solution performs well in many semi-supervised learning (SSL) tasks, it is known to scale poorly with the number of samples. Recent successful and scalable methods, such as the eigenfunction method focus on…

Graph Crossing Number is a fundamental problem with various applications. In this problem, the goal is to draw an input graph $G$ in the plane so as to minimize the number of crossings between the images of its edges. Despite extensive…

Subgraph Isomorphism is a very basic graph problem, where given two graphs $G$ and $H$ one is to check whether $G$ is a subgraph of $H$. Despite its simple definition, the Subgraph Isomorphism problem turns out to be very broad, as it…

We study graph partitioning problems from a min-max perspective, in which an input graph on n vertices should be partitioned into k parts, and the objective is to minimize the maximum number of edges leaving a single part. The two main…

The Max-Cut problem is a well known combinatorial optimization problem. In this paper we describe a fast approximation method. Given a graph G, we want to find a cut whose size is maximal among all possible cuts. A cut is a partition of the…

We study the Requirement Cut problem, a generalization of numerous classical graph partitioning problems including Multicut, Multiway Cut, $k$-Cut, and Steiner Multicut among others. Given a graph with edge costs, terminal groups $(S_1,…

The minimum cut problem in an undirected and weighted graph $G$ is to find the minimum total weight of a set of edges whose removal disconnects $G$. We completely characterize the quantum query and time complexity of the minimum cut problem…

The notion of code sparsification was introduced by Khanna, Putterman and Sudan (arxiv.2311.00788), as an analogue to the the more established notion of cut sparsification in graphs and hypergraphs. In particular, for $\alpha\in (0,1)$ an…

We design an algorithm for approximating the size of \emph{Max Cut} in dense graphs. Given a proximity parameter $\varepsilon \in (0,1)$, our algorithm approximates the size of \emph{Max Cut} of a graph $G$ with $n$ vertices, within an…