Spectral Sparsification in the Semi-Streaming Setting

Jonathan A. Kelner & Alex Levin
Let G be a graph with n vertices and m edges. A sparsifier of G is a sparse graph on the same vertex set approximating $G$ in some natural way. It allows us to say useful things about $G$ while considering much fewer than m edges. The strongest commonly-used notion of sparsification is spectral sparsification; H is a spectral sparsifier of G if the quadratic forms induced by the Laplacians of G and H approximate...