Lecture : Flow - based Methods for Partitioning Graphs ( 1 of 2 )

Last time, we described the properties of expander graphs and showed that they have several “extremal” properties. Before that, we described a vanilla spectral partitioning algorithms, which led to the statement and proof of Cheeger’s Inequality. Recall that one direction viewed λ2 as a relaxation of the conductance or expansion problem; while the other direction gave a “quadratic” bound as well as a constructive proof of a graph partitioning algorithm. The basic idea was to compute a vector, show that it is a relaxation of the original problem, and show that one doesn’t loose too much in the process. Later, we will see that there are nice connections between these methods and low-dimensional spaces and hypothesized manifolds.