Lectures 9-13

These lectures covered primarily the following four papers:

  1. Multi-way spectral partitioning and higher-order Cheeger inequalities
  2. Subexponential Algorithms for Unique Games and Related Problems
  3. Approximating the Expansion Profile and Almost Optimal Local Graph Clustering
  4. Finding Small Sparse Cuts Locally by Random Walk

I will post comprehensive lecture notes soon. We only used the subspace enumeration algorithm from (2) and the bulk of our analysis used the Lovasz-Siminovits-style arguments of (3) (see also (4)).

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2 thoughts on “Lectures 9-13

  1. Hi Prof. Lee, I am trying to learn things about spectral graph theory. Did you post the lecture notes about the papers you mentioned? I can’t find them either here or in your blog. Thanks! Tengyu

  2. Alas, I am being slow about these notes because I have been writing a survey version of Lectures 14-17 and, separately, another survey on Lecture 7-8. I would suggest that both papers 1,3, and 4 are easy to read. Papers (3) and (4) both contain a proof of the results in (2).

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