Related papers: Cut Size Statistics of Graph Bisection Heuristics
Graph clustering is a fundamental computational problem with a number of applications in algorithm design, machine learning, data mining, and analysis of social networks. Over the past decades, researchers have proposed a number of…
Let $G$ be an $n$-vertex graph with $m$ edges. When asked a subset $S$ of vertices, a cut query on $G$ returns the number of edges of $G$ that have exactly one endpoint in $S$. We show that there is a bounded-error quantum algorithm that…
For many popular graph metric sparsifiers, such as spanners, emulators, and preservers, simple and elegant greedy algorithms are known that achieve state-of-the-art or existentially optimal tradeoffs between size and quality. The goal of…
Edge-centric distributed computations have appeared as a recent technique to improve the shortcomings of think-like-a-vertex algorithms on large scale-free networks. In order to increase parallelism on this model, edge partitioning -…
We present near-optimal algorithms for detecting small vertex cuts in the CONGEST model of distributed computing. Despite extensive research in this area, our understanding of the vertex connectivity of a graph is still incomplete,…
We study the problem of generating graphs with prescribed degree sequences for bipartite, directed, and undirected networks. We first propose a sequential method for bipartite graph generation and establish a necessary and sufficient…
The degree distribution is one of the most fundamental properties used in the analysis of massive graphs. There is a large literature on graph sampling, where the goal is to estimate properties (especially the degree distribution) of a…
A localized method to distribute paths on random graphs is devised, aimed at finding the shortest paths between given source/destination pairs while avoiding path overlaps at nodes. We propose a method based on message-passing techniques to…
We consider the problem of embedding the nodes of a hypergraph into Euclidean space under the assumption that the interactions arose through closeness to unknown hyperedge centres. In this way, we tackle the inverse problem associated with…
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…
We consider the task of drawing a graph on multiple horizontal layers, where each node is assigned a layer, and each edge connects nodes of different layers. Known algorithms determine the orders of nodes on each layer to minimize crossings…
We study the design of local algorithms for massive graphs. A local algorithm is one that finds a solution containing or near a given vertex without looking at the whole graph. We present a local clustering algorithm. Our algorithm finds a…
In the graph label selection problem, one is given an $n$-vertex graph and a budget $k$, and seeks to select $k$ vertices whose labels enable accurate prediction of the labels on the remaining vertices. This problem formalizes distilling a…
Community detection in graphs has many important and fundamental applications including in distributed systems, compression, image segmentation, divide-and-conquer graph algorithms such as nested dissection, document and word clustering,…
Graph neural networks are widely used tools for graph prediction tasks. Motivated by their empirical performance, prior works have developed generalization bounds for graph neural networks, which scale with graph structures in terms of the…
A local algorithm is a distributed algorithm that completes after a constant number of synchronous communication rounds. We present local approximation algorithms for the minimum dominating set problem and the maximum matching problem in…
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 $…
Hyperbolic random graphs inherit many properties that are present in real-world networks. The hyperbolic geometry imposes a scale-free network with a strong clustering coefficient. Other properties like a giant component, the small world…
Graph sparsification is a technique that approximates a given graph by a sparse graph with a subset of vertices and/or edges. The goal of an effective sparsification algorithm is to maintain specific graph properties relevant to the…
We design new algorithms for approximating 2CSPs on graphs with bounded threshold rank, that is, whose normalized adjacency matrix has few eigenvalues larger than $\varepsilon$, smaller than $-\varepsilon$, or both. Unlike on worst-case…