Fall 2013

Spectral Sparsification of Graphs

Tuesday, September 17th, 2013 2:45 pm3:30 pm

Add to Calendar

Many important properties of an undirected graph manifest themselves spectrally in the eigenvalues or quadratic forms of matrices related to the graph. For instance, the connectivity structure, electrical properties, and random walk behavior of a graph are determined by its Laplacian matrix. A spectral sparsifier of a graph G is a sparse graph H on the same set of vertices such that the Laplacians of H and G are close, so that H captures the spectral behavior of G while being much cheaper to store and perform computations on. We survey a line of work showing that a nearly linear size spectral sparsifier exists for every graph and can be computed in the one pass streaming model with small update time per edge, and discuss possible improvements which could make this algorithm more useful in practice.