Related papers: Similarity-Aware Spectral Sparsification by Edge F…

A graph G'(V,E') is an \eps-sparsification of G for some \eps>0, if every (weighted) cut in G' is within (1\pm \eps) of the corresponding cut in G. A celebrated result of Benczur and Karger shows that for every undirected graph G, an…

Spectral hypergraph sparsification, an attempt to extend well-known spectral graph sparsification to hypergraphs, has been extensively studied over the past few years. For undirected hypergraphs, Kapralov, Krauthgamer, Tardos, and…

We describe a simple algorithm for spectral graph sparsification, based on iterative computations of weighted spanners and uniform sampling. Leveraging the algorithms of Baswana and Sen for computing spanners, we obtain the first…

Large data applications rely on storing data in massive, sparse graphs with millions to trillions of nodes. Graph-based methods, such as node prediction, aim for computational efficiency regardless of graph size. Techniques like localized…

Graph neural networks have been successful for machine learning, as well as for combinatorial and graph problems such as the Subgraph Isomorphism Problem and the Traveling Salesman Problem. We describe an approach for computing graph…

Graph-based methods have been demonstrated as one of the most effective approaches for semi-supervised learning, as they can exploit the connectivity patterns between labeled and unlabeled data samples to improve learning performance.…

Cut and spectral sparsification of graphs have numerous applications, including e.g. speeding up algorithms for cuts and Laplacian solvers. These powerful notions have recently been extended to hypergraphs, which are much richer and may…

In this paper, we present a construction of a `matching sparsifier', that is, a sparse subgraph of the given graph that preserves large matchings approximately and is robust to modifications of the graph. We use this matching sparsifier to…

Traditional classification tasks learn to assign samples to given classes based solely on sample features. This paradigm is evolving to include other sources of information, such as known relations between samples. Here we show that, even…

Generative graph models struggle to scale due to the need to predict the existence or type of edges between all node pairs. To address the resulting quadratic complexity, existing scalable models often impose restrictive assumptions such as…

Sparsification aims at extracting a reduced core of associations that best preserves both the dynamics and topology of networks while reducing the computational cost of simulations. We show that the semi-metric topology of complex networks…

The network reconfiguration problem seeks to find a rooted tree $T$ such that the energy of the (unique) feasible electrical flow over $T$ is minimized. The tree requirement on the support of the flow is motivated by operational constraints…

Graph sparsification aims to reduce the number of edges of a graph while maintaining its structural properties. In this paper, we propose the first general and effective information-theoretic formulation of graph sparsification, by taking…

Compression and sparsification algorithms are frequently applied in a preprocessing step before analyzing or optimizing large networks/graphs. In this paper we propose and study a new framework contracting edges of a graph (merging vertices…

Graph Neural Networks (GNNs) are widely used to perform different machine learning tasks on graphs. As the size of the graphs grows, and the GNNs get deeper, training and inference time become costly in addition to the memory requirement.…

We introduce a new algorithmic framework for designing dynamic graph algorithms in minor-free graphs, by exploiting the structure of such graphs and a tool called vertex sparsification, which is a way to compress large graphs into small…

We introduce a new spectral method for image segmentation that incorporates long range relationships for global appearance modeling. The approach combines two different graphs, one is a sparse graph that captures spatial relationships…

This paper investigates the recovery of a node-domain sparse graph signal from the output of a graph filter. This problem, which is often referred to as the identification of the source of a diffused sparse graph signal, is seminal in the…

Graph sparsification aims to reduce the number of edges of a network while maintaining its accuracy for given tasks. In this study, we propose a novel method called GSGAN, which is able to sparsify networks for community detection tasks.…

To cope with the complexity of large networks, a number of dimensionality reduction techniques for graphs have been developed. However, the extent to which information is lost or preserved when these techniques are employed has not yet been…