Related papers: Graph reduction with spectral and cut guarantees

We consider the problem of sampling from data defined on the nodes of a weighted graph, where the edge weights capture the data correlation structure. As shown recently, using spectral graph theory one can define a cut-off frequency for the…

The interference imposes a significant negative impact on the performance of wireless networks. With the continuous deployment of larger and more sophisticated wireless networks, reducing interference in such networks is quickly being…

Graph representation learning plays an important role in many graph mining applications, but learning embeddings of large-scale graphs remains a problem. Recent works try to improve scalability via graph summarization -- i.e., they learn…

Dimensionality reduction techniques map data represented on higher dimensions onto lower dimensions with varying degrees of information loss. Graph dimensionality reduction techniques adopt the same principle of providing latent…

One of the most important combinatorial optimization problems is graph coloring. There are several variations of this problem involving additional constraints either on vertices or edges. They constitute models for real applications, such…

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 machine learning, graph embedding algorithms seek low-dimensional representations of the input network data, thereby allowing for downstream tasks on compressed encodings. Recently, within the framework of network renormalization,…

The edit distance between two graphs is a widely used measure of similarity that evaluates the smallest number of vertex and edge deletions/insertions required to transform one graph to another. It is NP-hard to compute in general, and a…

In graph modification problems, one is given a graph G and the goal is to apply a minimum number of modification operations (such as edge deletions) to G such that the resulting graph fulfills a certain property. For example, the Cluster…

Conformal prediction provides rigorous, distribution-free uncertainty guarantees, but often yields prohibitively large prediction sets in structured domains such as routing, planning, or sequential recommendation. We introduce "graph-based…

We consider the minimum-cut partitioning of a graph into more than two parts using spectral methods. While there exist well-established spectral algorithms for this problem that give good results, they have traditionally not been well…

Reconfiguring two shortest paths in a graph means modifying one shortest path to the other by changing one vertex at a time so that all the intermediate paths are also shortest paths. This problem has several natural applications, namely:…

The graph is one of the most widely used mathematical structures in engineering and science because of its representational power and inherent ability to demonstrate the relationship between objects. The objective of this work is to…

The Bandwidth Problem seeks for a simultaneous permutation of the rows and columns of the adjacency matrix of a graph such that all nonzero entries are as close as possible to the main diagonal. This work focuses on investigating novel…

The most commonly used method to tackle the graph partitioning problem in practice is the multilevel approach. During a coarsening phase, a multilevel graph partitioning algorithm reduces the graph size by iteratively contracting nodes and…

Graph sparsification has been studied extensively over the past two decades, culminating in spectral sparsifiers of optimal size (up to constant factors). Spectral hypergraph sparsification is a natural analogue of this problem, for which…

We generalize the notion of quasirandom which concerns a class of equivalent properties that random graphs satisfy. We show that the convergence of a graph sequence under the spectral distance is equivalent to the convergence using the…

Graph compression is a data analysis technique that consists in the replacement of parts of a graph by more general structural patterns in order to reduce its description length. It notably provides interesting exploration tools for the…

Graph Neural Networks (GNNs) have demonstrated significant achievements in processing graph data, yet scalability remains a substantial challenge. To address this, numerous graph coarsening methods have been developed. However, most…

Sparse recovery can recover sparse signals from a set of underdetermined linear measurements. Motivated by the need to monitor large-scale networks from a limited number of measurements, this paper addresses the problem of recovering sparse…