# Envy-Freeness in House Allocation Problems

arXiv: https://arxiv.org/abs/1905.00468 · HTML: https://mlsanity.com/paper/1905.00468/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 May 2019.

## Built on by (most cited first, 5 of 5)

- [Temporal Fair Division of Indivisible Items](https://mlsanity.com/paper/2410.14593/) (2024)
- [Two-Sided Matching Meets Fair Division](https://mlsanity.com/paper/2107.07404/) (2021)
- [Fairness in Repeated Matching: A Maximin Perspective](https://mlsanity.com/paper/2510.04624/) (2025)
- [Reforming an Envy-Free Matching](https://mlsanity.com/paper/2207.02641/) (2022)
- [Graphical House Allocation](https://mlsanity.com/paper/2301.01323/) (2023)

## Abstract (arXiv)

We consider the house allocation problem, where m houses are to be assigned to n agents so that each agent gets exactly one house. We present a polynomial-time algorithm that determines whether an envy-free assignment exists, and if so, computes one such assignment. We also show that an envy-free assignment exists with high probability if the number of houses exceeds the number of agents by a logarithmic factor.