Simplex Transformations and Multiway Cut

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Uses the LP simplex embedding for multiway cut and replaces coordinatewise distortions with global, order-based transformations with dependencies plus a randomized mix of exponential-clock rounding and the CKR thresholding scheme. Proves a concrete approximation factor 1.29694 (previous best 1.309; integrality-hardness lower bound 1.2 under UGC). Gives the explicit cut-density analysis for infinitesimal edges, shows how the two building blocks and the dependent distortion combine to beat the previous coordinate-wise lower bound.

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" chapters (13)

1. 0:00Intro
2. 1:47Problem Definition (cont.)
3. 2:17Combinatorial Approach
4. 5:31Geometric Approach (cont.)
5. 10:33Edge Structure
6. 17:33Building Block II (cont.)
7. 20:29Multiple Building Blocks?
8. 22:12Algorithms Roadmap
9. 26:31Distorting the Simplex (cont.)
10. 27:56Feasible Distortion?
11. 29:30Case Study - Breaking the
12. 29:59Main Result
13. 30:24Open Questions