Why it matters

Matroid intersection generalizes matching. Powerful but niche.

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The architecture

Two matroid oracles.

Augmenting paths in exchange graph.

Iterate.

Matroid intersectionTwo matroidsM1, M2Exchange graphaugment pathsResultmax common indep setCunningham 1986; Edmonds 1970; generalizes bipartite matching
Matroid intersection.
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How it works end to end

Cunningham 1986.

Edmonds 1970.

Bipartite matching special case.