Yankee Swap: a Fast and Simple Fair Allocation Mechanism for Matroid Rank Valuations
This work addresses fair allocation problems in resource distribution settings, offering a more practical and faster solution, though it is incremental as it builds on known polynomial-time algorithms.
The paper tackles fair allocation of indivisible goods under matroid rank valuations by introducing a simple algorithm based on Yankee Swap that computes provably fair and efficient Lorenz dominating allocations, improving on existing methods in terms of simplicity and scalability.
We study fair allocation of indivisible goods when agents have matroid rank valuations. Our main contribution is a simple algorithm based on the colloquial Yankee Swap procedure that computes provably fair and efficient Lorenz dominating allocations. While there exist polynomial time algorithms to compute such allocations, our proposed method improves on them in two ways. (a) Our approach is easy to understand and does not use complex matroid optimization algorithms as subroutines. (b) Our approach is scalable; it is provably faster than all known algorithms to compute Lorenz dominating allocations. These two properties are key to the adoption of algorithms in any real fair allocation setting; our contribution brings us one step closer to this goal.