Two polynomial-time algorithms are proposed for multilevel fair allocation under matroid-rank preferences, one generic with efficiency and fairness guarantees and one extending General Yankee Swap with efficiency guarantees and strong practical fairness.
Murota.Discrete Convex Analysis, volume 10 ofMonographs on Discrete Mathematics and Applications
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Matroids satisfy a generalized basis exchange where for X and Y in the symmetric difference of bases A and B there exist U and V containing them with |U|=|V| at most rank(X+Y) such that A-U+V and B+U-V are bases, plus a framework for Grassmann-Plücker extensions in characteristic-zero representable
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Multilevel Fair Allocation with Matroid-Rank Preferences
Two polynomial-time algorithms are proposed for multilevel fair allocation under matroid-rank preferences, one generic with efficiency and fairness guarantees and one extending General Yankee Swap with efficiency guarantees and strong practical fairness.
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Generalizing the Multiple Exchange Property for Matroid Bases
Matroids satisfy a generalized basis exchange where for X and Y in the symmetric difference of bases A and B there exist U and V containing them with |U|=|V| at most rank(X+Y) such that A-U+V and B+U-V are bases, plus a framework for Grassmann-Plücker extensions in characteristic-zero representable