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We study fair allocation of indivisible goods when agents have matroid rankvaluations. Our main contribution is a simple algorithm based on the colloquialYankee Swap procedure that computes provably fair and efficient Lorenzdominating allocations. While there exist polynomial time algorithms to computesuch allocations, our proposed method improves on them in two ways. (a) Ourapproach is easy to understand and does not use complex matroid optimizationalgorithms as subroutines. (b) Our approach is scalable; it is provably fasterthan all known algorithms to compute Lorenz dominating allocations. These twoproperties are key to the adoption of algorithms in any real fair allocationsetting; our contribution brings us one step closer to this goal.

Yankee Swap: a Fast and Simple Fair Allocation Mechanism for Matroid Rank Valuations