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.
@article{arxiv.1905.00468,
title = {Envy-Freeness in House Allocation Problems},
author = {Jiarui Gan and Warut Suksompong and Alexandros A. Voudouris},
journal= {arXiv preprint arXiv:1905.00468},
year = {2019}
}