# On the Complexity of Fair House Allocation

arXiv: https://arxiv.org/abs/2106.06925 · HTML: https://mlsanity.com/paper/2106.06925/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Jun 2021.

## Built on by (most cited first, 1 of 1)

- [Graphical House Allocation](https://mlsanity.com/paper/2301.01323/) (2023)

## Abstract (arXiv)

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 n1-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.