Fully Polynomial-Time Approximation Schemes for Fair Rent Division
研究了在一般效用函数下公平分配公寓房间和租金的算法，提出了完全多项式时间近似方案，解决了此前仅适用于拟线性效用的局限，对匹配市场均衡计算也有贡献。
We study the problem of fair rent division that entails splitting the rent and allocating the rooms of an apartment among agents in a fair manner (i.e., under the imposed rents, no agent has a strictly stronger preference for any other agent’s room). The utility functions specify the cardinal preferences of the agents for the rooms for every possible room rent. Although envy-free solutions are guaranteed to exist under reasonably general utility functions, efficient algorithms for finding them were known only for quasilinear utilities. This work addresses this notable gap and develops a fully polynomial-time approximation scheme for fair rent division with minimal assumptions on the utility functions. Envy-free solutions correspond to equilibria of a two-sided matching market with monetary transfers; hence, this work also provides efficient algorithms for finding approximate equilibria in such markets. We complement the algorithmic results by proving that the fair rent division problem lies in the intersection of the complexity classes polynomial parity arguments on directed graphs and polynomial local search.