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

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/FOCS.2015.24

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 &#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 [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

CITATIONS