House allocation refers to the problem where $m$ houses are to be allocated to $n$ agents so that each agent receives one house. Since an envy-free house allocation does not always exist, we consider finding such an allocation in the presence of subsidy. We show that computing an envy-free allocation with minimum subsidy is NP-hard in general, but can be done efficiently if $m$ differs from $n$ by an additive constant or if the agents have identical utilities.

翻译：房屋分配问题是指将$m$套房屋分配给$n$个代理人，使得每个代理人获得一套房屋。由于无嫉妒的房屋分配并非总是存在，我们考虑在存在补贴的情况下寻找此类分配。我们证明，计算最小补贴下的无嫉妒分配在一般情况下是NP难的，但如果$m$与$n$相差一个加性常数，或者代理人具有相同效用，则可以高效求解。