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arXiv · 2608.30669

Reaching Fairness by Reallocating Goods

Robert Bredereck·Eva Deltl·Tanmay Inamdar·Pallavi Jain·Pranjal Pandey·Bin Sun
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Abstract

Fair allocation of indivisible goods has largely been studied under the assumption that no prior allocation exists. Motivated by practical settings with pre-existing (and possibly unfair) allocations, we study how to achieve fairness through limited reallocations. Building on recent work on reformability/reallocations, we consider three fairness notions---envy-freeness (EF), envy-freeness up to one good (EF1), and envy-freeness up to any good (EFX)---and optimize the number of goods reallocated. We analyze both the classical and parameterized complexity of these problems, providing a comprehensive analysis across multiple fairness notions.

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Robert Bredereck, Eva Deltl, Tanmay Inamdar, Pallavi Jain, Pranjal Pandey, Bin Sun. 2026-08-31. Reaching Fairness by Reallocating Goods. https://arxiv.org/abs/2608.30669

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