Constructing Linear-Sized Spectral Sparsification in Almost-Linear Time
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 (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.
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