Comparing the Theory and Practice of Spectral Algorithms to Combinatorial Flow Algorithms for ...

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Compares spectral algorithms and combinatorial flow algorithms for graph problems by examining their theoretical properties and practical performance; discusses specific spectral methods (e.g., eigenvector-based techniques) alongside combinatorial flow approaches (e.g., max-flow/min-cut), and evaluates when each approach succeeds or fails in practice.

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" chapters (14)

1. 0:00Intro
2. 2:16A generalization: quantity normalized cut
3. 3:29An intuitive clustering criterion
4. 10:04Two terms expressions and the Rayleigh ratio (Lemma 3.1, [H13])
5. 12:27The combinatorial versus the spectral continuous relaxations
6. 19:42It works because the problem can be formulated as "monotone integer program" Theorem
7. 27:18Scaling arcs weights
8. 28:07The Simplified equivalent graph
9. 28:57Solving the parametric min st cut
10. 34:21Comparison between NC' and the spectral method
11. 37:47Empirical testing for the general problems
12. 39:18Scalability of NC' versus the spectral algorithm (Shi)
13. 41:57A comparison of NC values of NC' with the sweep spectral algorithm
14. 51:02Conclusions