Expander flows, geometric embeddings and graph partitioning
Sanjeev Arora, Satish B. Rao, Umesh V. Vazirani · Journal of the ACM · 2009
We give aO(√logn)-approximation algorithm for the sparsest cut, edge expansion, balanced separator, and graph conductance problems. This improves theO(logn)-approximation of Leighton and Rao (1988). We use a well-known semidefinite relaxation with triangle inequality constraints. Central to our analysis is a geometric theorem about projections of point sets inRd, whose proof makes essential use of a phenomenon called measure concentration. We also describe an interesting and natural “approximate certificate” for a graph's expansion, which involves embedding ann-node expander in it with appropriate dilation and congestion. We call this an expander flow.