In this paper, we consider a matroid generalization of the stable matching problem. In particular, we consider the setting where preferences may contain ties. For this generalization, we propose a polynomial-time algorithm for the problem of checking the existence of a common independent set satisfying non-uniform stability, which is a common generalization of super-stability and strong stability.

翻译：本文考虑稳定匹配问题的拟阵推广。具体而言，我们研究偏好关系可能包含平局的情形。针对该推广问题，我们提出了一种多项式时间算法，用于检验满足非均匀稳定性的公共独立集的存在性——该稳定性是超稳定性和强稳定性的共同推广。