Minimum Isolating Cuts: A New Tool for Solving Minimum Cut Problems

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Introduces a concrete procedure called isolating cuts lemma that, given a terminal set containing exactly one vertex from a small side, computes vertex-disjoint upper bounds and recovers each terminal’s s-t mincut using only O(log n) s-t max-flow calls; combines random sampling by rates ≈1/k to reduce global mincut to polylog max-flow calls and is derandomized to a deterministic polylog max-flow calls reduction. Extends to Steiner and all-pairs mincut (used to speed up Gomory-Hu tree construction), but fails for digraphs because cut symmetry and submodularity cannot be satisfied simultaneously.

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" chapters (9)

1. 0:00Introduction to isolating cuts
2. 1:38Min-cut background and context
3. 6:19Defining the isolating cut
4. 10:05The isolating cut lemma
5. 12:37Proving the isolating cut lemma
6. 21:01Deterministic and practical impact
7. 23:46Broader applications of the tool
8. 26:24All-pairs min-cut advancements
9. 35:38Future directions and conclusion