Spectral sparsification of graphs

Author: tpom

August undefined, 2024

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. 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.

Spectral Sparsification of Graphs SIAM Journal on …

WebApproximating a given graph by a graph with fewer edges or vertices is called sparsification. The notion of approximation that is most relevant to this workshop is the … 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 … hajo hosen

Graph Sparsification by Effective Resistances SIAM Journal on Computing

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 … WebWelcome Computer Science WebJun 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. pirkan opisto

[2007.07161] Graph Sparsification by Universal Greedy Algorithms

Spectrum-preserving sparsification for visualization of big …

http://cs-www.cs.yale.edu/homes/spielman/PAPERS/CACMsparse.pdf Web2 days ago · Graph sparsification is the approximation of an arbitrary graph by a sparse graph. We explain what it means for one graph to be a spectral approximation of another and review the development of ... pirkanmaan yrittäjät lehtiWebAug 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. hajoi

"WebGiven a pair of graphs 𝐀 and 𝐁, the problems of deciding whether there exists either a homomorphism or an isomorphism from 𝐀 to 𝐁 have received a lot of attention. ... We further investigate the more general problem of spectral sparsification and make some first steps towards sparsification of continuous valued CSPs. Show less ... " - Spectral sparsification of graphs

Spectral sparsification of graphs

WebAug 1, 2013 · Graph sparsification is the approximation of an arbitrary graph by a sparse graph. We explain what it means for one graph to be a spectral approximation of another and review the... WebNov 4, 2024 · Spectral graph sparsification aims to find ultra-sparse subgraphs whose Laplacian matrix can well approximate the original Laplacian eigenvalues and …

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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. Web1 day ago · We propose an algorithm for recovering simultaneously a sparse topology and the cable parameters of any network, combining in an iterative procedure the resolution of algebraic fitting convex problems and techniques of spectral graph sparsification. The algorithm is tested on several electrical networks.

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 … WebJul 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 …

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. instead of “σ-spectral approximation” wherever it won’t create confusion. We … Download PDF Abstract: We introduce a new notion of graph sparsificaiton based …

WebTo construct a spectral sparsifier of an arbitrary unweighted graph, we first apply Theorem 3 to find a (1/log 2 n)-spectral decomposition of the graph in which the boundary has at …

WebThis work proves that MCPS is NP-hard already on directed acyclic graphs (DAGs), and introduces the family of laminar series-parallel graphs (LSPs), a generalization of DSPs that also includes cyclic and very dense graphs. We introduce and discuss the Minimum Capacity-Preserving Subgraph (MCPS) problem: given a directed graph and a retention … pirkan pyöräily tuloksetWebDec 11, 2024 · It is proved that every graph has a spectral sparsifier with a number of edges linear in its number of vertices, and an elementary deterministic polynomial time … hajo in assamWebJul 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. pirkanpoikaWebAug 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 … hajo herrmannWebThe aforementioned method employs a sequence of algorithms based on the computation of the nearest Laplacian matrix and the subsequent sparsification of the corresponding graph. ... ha johnsWebSpectral Sparsification in Dynamic Graph Streams. In: Raghavendra, P., Raskhodnikova, S., Jansen, K., Rolim, J.D.P. (eds) Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques. APPROX RANDOM 2013 2013. Lecture Notes in Computer Science, vol 8096. ha joint formulaWebSpectral Sparsification in Dynamic Graph Streams. In: Raghavendra, P., Raskhodnikova, S., Jansen, K., Rolim, J.D.P. (eds) Approximation, Randomization, and Combinatorial … pirkei avot 5:7