📦 Set Cover

Band 6 — The Saturn transformer. Cover all elements with the fewest sets.

Elements: 30 Sets: 15

Ready

Each row is a set. Coloured = covers this element.

Algorithm: Greedy Approximation

At each step, pick the set that covers the most uncovered elements. Guarantees O(ln n) approximation ratio. Simple, fast, and hard to beat in practice. O(m × n) where m = number of sets, n = number of elements.

Why This Matters

Set Cover governs resource allocation — server placement, ad targeting, sensor coverage. The Saturn transformer finds the minimal covering structure.