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Expander flows, geometric embeddings and graph partitioning

Expander flows, geometric embeddings and graph partitioning,10.1145/1007352.1007355,Sanjeev Arora,Satish Rao,Umesh V. Vazirani

Expander flows, geometric embeddings and graph partitioning   (Citations: 216)
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We give a O(√log n)-approximation algorithm for sparsest cut, 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 Rd, whose proof makes essential use of a phenomenon called measure concentration. We also describe an interesting and natural "certificate" for a graph's expansion, by embedding an n-node expander in it with appropriate dilation and congestion. We call this an expander flow.
Conference: ACM Symposium on Theory of Computing - STOC , pp. 222-231, 2004
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