On the Complexity of Fair House Allocation

2021/06/13 by Naoyuki Kamiyama, Pasin Manurangsi, Warut Suksompong · 1 citation
Computer Science · #cs.GT #cs.CC

paper · pdf · doi:10.1016/j.orl.2021.06.006

published as Operations Research Letters, 49(4):572-577 (2021)

arxiv created 2021/06/13 · arxiv updated 2021/07/15

Abstract

We study fairness in house allocation, where m houses are to be allocated among n agents so that every agent receives one house. We show that maximizing the number of envy-free agents is hard to approximate to within a factor of n^1-γ for any constant γ>0, and that the exact version is NP-hard even for binary utilities. Moreover, we prove that deciding whether a proportional allocation exists is computationally hard, whereas the corresponding problem for equitability can be solved efficiently.

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