Spectral sparsification of graphs

Author: jhyx

August undefined, 2024

WebNov 3, 2024 · Distributed Graph Clustering and Sparsification. 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 algorithmic design methods for graph clustering. WebJul 14, 2024 · Graph sparsification is to approximate an arbitrary graph by a sparse graph and is useful in many applications, such as simplification of social networks, least squares problems, numerical solution of symmetric positive definite linear systems and etc.

Spectral Sparsification of Graphs: Theory and Algorithms

WebAug 14, 2024 · First, we introduce a novel triangle-aware sparsification scheme. Our scheme provably produces a spectral sparsifier with high probability [46, 47] on graphs that exhibit strong triadic closure, a hallmark property of real-world networks. WebSep 17, 2013 · A spectral sparsifier of a graph G is a sparse graph H on the same set of vertices such that the Laplacians of H and G are close, so that H captures the spectral behavior of G while being much cheaper to store and perform computations on. magic vs hornets score

Spectrum-preserving sparsification for visualization of big graphs

WebJan 22, 2024 · Spectral graph sparsification aims to find ultra-sparse subgraphs whose Laplacian matrix can well approximate the original Laplacian eigenvalues and eigenvectors. In recent years, spectral sparsification techniques have been extensively studied for accelerating various numerical and graph-related applications. Prior nearly-linear-time … WebJun 25, 2024 · Ahn et al. have worked on spectral sparsification of dynamic streaming graphs with the consideration that edges can be added to or deleted from the graph in the form of streams . This study shows that a graph can be sparsified with a randomized approach, which consumes \({\tilde{O}}(n^{5/3})\) space, by preserving the spectral … WebJun 4, 2024 · 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 optimal bounds on the sparsifier size are not known, mainly because the hypergraph Laplacian is non-linear, … ny state jury duty pay

Towards Scalable Spectral Sparsification of Directed Graphs

WebThis improves upon the spectral sparsifiers constructed by Spielman and Teng, which had O ( n log c n) edges for some large constant c, and upon the cut sparsifiers of Benczúr and Karger, which only satisfied these inequalities for x ∈ { 0, 1 } V. Webtion [8], where x is restricted to binary vector. Spectral sparsiﬁcation of a graph is a fundamental problem that has found application in randomized linear algebra [13, 33], graph problems [29], linear programming [34], and mathematics [37, 51]. There are many non-private algorithms for computing spectral sparsiﬁcation of graphs [2, 7, 35, ny state jr licensehttp://cs-www.cs.yale.edu/homes/spielman/PAPERS/CACMsparse.pdf magic vs hornets tickets

"WebApr 1, 2024 · Our spectral graph sparsification framework will guarantee the preservation of the key eigenvalues and eigenvectors within nearly-linear-sized spectrally-similar graph sparsifiers, achieving more efficient and effective compression of arbitrarily complex big graph data. Furthermore, based on intrinsic spectral graph properties, we propose a ... " - Spectral sparsification of graphs

Spectral sparsification of graphs

WebSpectral clustering algorithms provide approximate solutions to hard optimization problems that formulate graph partitioning in terms of the graph conductance. It is well understood that the quality of these approximate solutions is negatively. WebWe present the first single pass algorithm for computing spectral sparsifiers for graphs in the dynamic semi-streaming model. Given a single pass over a stream containing insertions and deletions of edges to a graph G, our algorithm maintains a randomized linear sketch of the incidence matrix of G into dimension O ( 1 ϵ 2 n p o l y l o g ( n)).

Did you know?

WebView jie-kdd-deeplearningday-2024.pdf from CSE NETWORKS at University of Washington. Graph Embedding and Reasoning Jie Tang Department of Computer Science and Technology Tsinghua University The WebAug 29, 2008 · We introduce a new notion of graph sparsificaiton based on spectral similarity of graph Laplacians: spectral sparsification requires that the Laplacian quadratic form of the sparsifier approximate that of the original. This is equivalent to saying that the Laplacian of the sparsifier is a good preconditioner for the Laplacian of the original.

WebAbstract. We introduce a new notion of graph sparsification based on spectral similarity of graph Laplacians: spectral sparsification requires that the Laplacian quadratic form of the … WebJan 21, 2024 · Abstract. Spectral sparsification is a general technique developed by Spielman et al. to reduce the number of edges in a graph while retaining its structural …

WebApr 1, 2024 · Spectral sparsifier and effective resistance The graph G can be presented by the following relation: G = ( V, E, w) Where, V, E, w are the vertices, links, and weights, respectively.

WebAug 1, 2013 · Spectral sparsifiers try to preserve properties of the spectrum of the combinatorial Laplacian, whereas cut-sparsifiers intend to preserve the connectivity of the …

WebFeb 18, 2024 · In this work, we propose feGRASS, a fast and effective graph spectral sparsification approach for the problem of large-scale power grid analysis and other … ny state kinship navigatorWebJul 28, 2010 · Spectral Sparsification of Graphs and Approximations of Matrices. We introduce a notion of what it means for one graph to be a good spectral approximation of … magic vs knicks play by playWebJun 3, 2024 · For the first time, we prove the existence of linear-sized spectral sparsifiers for general directed graphs, and introduce a practically-efficient yet unified spectral graph sparsification approach that allows sparsifying real-world, large-scale directed and undirected graphs with guaranteed preservation of the original graph spectra. ny state jobs general publicWebThe aforementioned method employs a sequence of algorithms based on the computation of the nearest Laplacian matrix and the subsequent sparsification of the corresponding graph. ... magic vs kings predictionWebApr 1, 2024 · Our spectral graph sparsification framework will guarantee the preservation of the key eigenvalues and eigenvectors within nearly-linear-sized spectrally-similar graph … ny state jobs examWebApr 1, 2024 · Our spectral graph sparsification framework will guarantee the preservation of the key eigenvalues and eigenvectors within nearly-linear-sized spectrally-similar graph sparsifiers, achieving more efficient and effective compression of … magic vs mavericks predictionWebAug 1, 2008 · We prove that every graph has a spectral sparsifier with a number of edges linear in its number of vertices. As linear-sized spectral sparsifiers of complete graphs are expanders, our sparsifiers of arbitrary graphs can be … magic vs knicks box score