Lecture 04 / 13 : Graph Sampling and Sparsification

In previous lectures, we discussed various topics on graph: sparsest cut, clustering which finds small k-cuts, max flow, multicommodity flow, etc. For very large graphs, we’d like to ask “instead of regular approximation algorithms which run in polynomial time, can we find any near-linear time algorithm for minimum cut or maximum flow problems?”. A simple idea is for a given graph G, to solve the problem on a sparse subgraph with the same number of nodes of G that preserves some properties of the original graph like distance or cuts, rather than on the original graph, and formally is called graph sparsification with sampling.