This paper has two objectives. One is to give a linear time algorithm that solves the stable roommates problem (i.e., obtains one stable matching) using the stable marriage problem. The idea is that a stable matching of a roommate instance $I$ is a stable matching (that however must satisfy a certain condition) of some marriage instance $I'$. $I'$ is obtained just by making two copies of $I$, one for the men's table and the other for the women's table. The second objective is to investigate the possibility of reducing the roommate problem to the marriage problem (with a one-to-one correspondence between their stable matchings) in polynomial time. For a given $I$, we construct the rotation POSET $P$ of $I'$ and then we ``halve'' it to obtain $P'$, by which we can forget the above condition and can use all the closed subsets of $P'$ for all the stable matchings of $I$. Unfortunately, this approach works (runs in polynomial time) only for restricted instances.

翻译：本文有两个目标。其一，利用稳定婚姻问题给出一个线性时间算法，用于求解稳定室友问题（即获得一个稳定匹配）。其思路是：室友实例$I$的一个稳定匹配，就是某个婚姻实例$I'$（必须满足特定条件）的一个稳定匹配。$I'$仅通过将$I$复制两份得到，一份作为男性表，另一份作为女性表。其二，研究在多项式时间内将室友问题归约到婚姻问题（且两者稳定匹配之间存在一一对应关系）的可能性。对于给定的$I$，我们构造$I'$的旋转偏序集$P$，然后对其进行“对半分割”得到$P'$，从而可以忽略上述条件，并利用$P'$的所有封闭子集来对应$I$的所有稳定匹配。遗憾的是，该方法仅对受限实例有效（可在多项式时间内运行）。