Approximating the Expansion Profile and Almost Optimal Local Graph Clustering

  title={Approximating the Expansion Profile and Almost Optimal Local Graph Clustering},
  author={Shayan Oveis Gharan and Luca Trevisan},
  journal={2012 IEEE 53rd Annual Symposium on Foundations of Computer Science},
Spectral partitioning is a simple, nearly-linear time, algorithm to find sparse cuts, and the Cheeger inequalities provide a worst-case guarantee of the quality of the approximation found by the algorithm. Local graph partitioning algorithms [1], [2], [3] run in time that is nearly linear in the size of the output set, and their approximation guarantee is worse than the guarantee provided by the Cheeger inequalities by a poly-logarithmic logΩ(1) n factor. It has been an open problem to design a… CONTINUE READING
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