Why it matters

Matroid theory explains greedy success. Deep theoretical understanding.

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The architecture

Ground set + independence.

Hereditary + exchange properties.

Greedy on weighted matroid optimal.

Matroid + greedyGround setelements + weightsMatroid axiomshereditary + exchangeGreedyoptimal on matroidsMST is graphic matroid; scheduling is transversal matroid; family covers many greedies
Matroids.
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How it works end to end

Independence system + exchange.

Graphic matroid: MST.

Uniform matroid: k-choose problems.

Rado-Edmonds theorem.