Expander flows, geometric embeddings and graph partitioning

We give a O( log n)-approximation algorithm for sparsest cut, edge expansion, balanced separator, and graph conductance problems. This improves the O(log n)-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 in d , 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 an n-node expander in it with appropriate dilation and congestion. We call this an expander flow.

• Type: Conference
• Year: 2004
• Where: STOC
• Authors: Sanjeev Arora, Satish Rao, Umesh V. Vazirani
• Keywords: Algorithms, Phenomenon Called Measure, STOC 2004, Triangle Inequality Constraints, Well-known Semidefinite Relaxation