Karger's Min-Cut Algorithm

Why it matters

Karger is elegant randomized graph algorithm. Understanding shapes randomized design.

The architecture

Contract random edge.

Merge endpoints.

Continue until 2 vertices.

Repeat O(n^2 log n) for success.

How it works end to end

Contraction: merge endpoints; keep parallel edges.

Success prob >= 2/n(n-1).

O(n^2 log n) reps for high confidence.

Karger-Stein: O(n^2 log^3 n) total.