On the Complexity of Fair House Allocation
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.
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.
Research Areas
