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2015 IEEE 56th Annual Symposium on Foundations of Computer Science (FOCS) (2015)
Berkeley, CA, USA
Oct. 17, 2015 to Oct. 20, 2015
ISSN: 0272-5428
ISBN: 978-1-4673-8191-8
pp: 250-269
ABSTRACT
We present the first almost-linear time algorithm for constructing linear-sized spectral sparsification for graphs. This improves all previous constructions of linear-sized spectral sparsification, which requires Ω(n2) time. A key ingredient in our algorithm is a novel combination of two techniques used in literature for constructing spectral sparsification: Random sampling by effective resistance, and adaptive constructions based on barrier functions [1], [3].
INDEX TERMS
Approximation methods, Approximation algorithms, Eigenvalues and eigenfunctions, Algorithm design and analysis, Laplace equations, Resistance, Computer science
CITATION

Y. T. Lee and H. Sun, "Constructing Linear-Sized Spectral Sparsification in Almost-Linear Time," 2015 IEEE 56th Annual Symposium on Foundations of Computer Science (FOCS), Berkeley, CA, USA, 2015, pp. 250-269.
doi:10.1109/FOCS.2015.24
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