Constant Arboricity Spectral Sparsifiers

08/16/2018

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by   Timothy Chu, et al.

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We show that every graph is spectrally similar to the union of a constant number of forests. Moreover, we show that Spielman-Srivastava sparsifiers are the union of O(logn) forests. This result can be used to estimate boundaries of small subsets of vertices in nearly optimal query time.