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 algorithms for spectral sparsification. In addition to being an interesting concept, spectral sparsification has been an important tool in the design of nearly linear-time algorithms for solving systems of linear equations in symmetric, diagonally dominant matrices. The fast solution of these linear systems has already led to breakthrough results in combinatorial optimization, including a faster algorithm for finding approximate maximum flows and minimum cuts in an undirected network.
%0 Journal Article
%1 Batson:2013:SSG:2492007.2492029
%A Batson, Joshua
%A Spielman, Daniel A.
%A Srivastava, Nikhil
%A Teng, Shang-Hua
%C New York, NY, USA
%D 2013
%I ACM
%J Commun. ACM
%K cacm magazine sparsification
%N 8
%P 87--94
%R 10.1145/2492007.2492029
%T Spectral Sparsification of Graphs: Theory and Algorithms
%V 56
%X 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 algorithms for spectral sparsification. In addition to being an interesting concept, spectral sparsification has been an important tool in the design of nearly linear-time algorithms for solving systems of linear equations in symmetric, diagonally dominant matrices. The fast solution of these linear systems has already led to breakthrough results in combinatorial optimization, including a faster algorithm for finding approximate maximum flows and minimum cuts in an undirected network.
@article{Batson:2013:SSG:2492007.2492029,
abstract = {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 algorithms for spectral sparsification. In addition to being an interesting concept, spectral sparsification has been an important tool in the design of nearly linear-time algorithms for solving systems of linear equations in symmetric, diagonally dominant matrices. The fast solution of these linear systems has already led to breakthrough results in combinatorial optimization, including a faster algorithm for finding approximate maximum flows and minimum cuts in an undirected network.},
acmid = {2492029},
added-at = {2013-12-05T04:21:36.000+0100},
address = {New York, NY, USA},
author = {Batson, Joshua and Spielman, Daniel A. and Srivastava, Nikhil and Teng, Shang-Hua},
biburl = {https://www.bibsonomy.org/bibtex/288420b54fece9738cb9bdb87e8251e07/ytyoun},
doi = {10.1145/2492007.2492029},
interhash = {6022c1b47d6aca1f8c10365a377c4fe3},
intrahash = {88420b54fece9738cb9bdb87e8251e07},
issn = {0001-0782},
issue_date = {August 2013},
journal = {Commun. ACM},
keywords = {cacm magazine sparsification},
month = aug,
number = 8,
numpages = {8},
pages = {87--94},
publisher = {ACM},
timestamp = {2015-12-12T14:40:22.000+0100},
title = {Spectral Sparsification of Graphs: Theory and Algorithms},
volume = 56,
year = 2013
}