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arXiv · 1508.03261

Constructing Linear-Sized Spectral Sparsification in Almost-Linear Time

Yin Tat Lee·He Sun
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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 $\Omega(n^2)$ 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.

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Yin Tat Lee, He Sun. 2015-08-13. Constructing Linear-Sized Spectral Sparsification in Almost-Linear Time. https://arxiv.org/abs/1508.03261

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