Research on Formalization and Algorithms for the Stable Matching Problems Adapted to Real World

在稳定匹配问题中，每个人提交一个列表，根据他/她的偏好对异性成员进行排序。任务是找到一个匹配的属性称为稳定性。这个问题可以应用到现实世界中的许多分配问题，如分配居民到医院。在这项研究中，我们提出了这个问题的几个变体，以适应各种场合。我们还提出了有效的算法，以及证明了一些棘手的和不可逼近的。

In the stable matching problem, each person submits a list that orders members of the opposite gender based on his/her preference. The task is to find a matching with property called the stability. This problem can be applied to many real-world assignment problem, such as assigning residents to hospitals. In this research, we proposed several variants of this problem to adapt it to each occasion. We also proposed efficient algorithms for them, as well as proved some intractability and inapproximability.