2015 IEEE 56th Annual Symposium on Foundations of Computer Science (FOCS) (2015)
Berkeley, CA, USA
Oct. 17, 2015 to Oct. 20, 2015
DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/FOCS.2015.24
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 &#x03A9;(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 , .
Approximation methods, Approximation algorithms, Eigenvalues and eigenfunctions, Algorithm design and analysis, Laplace equations, Resistance, Computer science
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.