We consider a many-to-one variant of the stable matching problem. More concretely, we consider the variant of the stable matching problem where one side has a matroid constraint. Furthermore, we consider the situation where the preference of each agent may contain ties. In this setting, we consider the problem of checking the existence of a strongly stable matching, and finding a strongly stable matching if a strongly stable matching exists. We propose a polynomial-time algorithm for this problem.

翻译：更具体地说,我们考虑稳定匹配问题的变体。我们考虑稳定匹配问题的变体,如果一方有机器人限制。此外,我们考虑每个代理商的偏好可能包含关联的情况。在这种背景下,我们考虑检查是否存在一个非常稳定的匹配,如果存在一个非常稳定的匹配,则寻找一个非常稳定的匹配。我们为此提出一个多时算法。