2026-07-23T00:18:16Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:24962 2026-02-09T08:02:40Z ddc:004 open_access

Reforming an Unfair Allocation by Exchanging Goods Yuen, Sheung Man Igarashi, Ayumi Kamiyama, Naoyuki Suksompong, Warut fair division indivisible goods envy-freeness exchanges Fairly allocating indivisible goods is a frequently occurring task in everyday life. Given an initial allocation of the goods, we consider the problem of reforming it via a sequence of exchanges to attain fairness in the form of envy-freeness up to one good (EF1). We present a vast array of results on the complexity of determining whether it is possible to reach an EF1 allocation from the initial allocation and, if so, the minimum number of exchanges required. In particular, we uncover several distinctions based on the number of agents involved and their utility functions. Furthermore, we derive essentially tight bounds on the worst-case number of exchanges needed to achieve EF1. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Sheung Man Yuen and Ayumi Igarashi and Naoyuki Kamiyama and Warut Suksompong 2025 Is Part Of LIPIcs, Volume 359, 36th International Symposium on Algorithms and Computation (ISAAC 2025) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ISAAC.2025.54 urn:nbn:de:0030-drops-249626 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.54 eng https://creativecommons.org/licenses/by/4.0/legalcode