Super-stability is one of the stability concepts in the stable matching problem with ties. It is known that there may not exist a super-stable matching, and the existence of a super-stable matching can be checked in polynomial time. In this paper, we consider the problem of modifying an instance of the super-stable matching problem by deleting some bounded number of agents in such a way that there exists a super-stable matching in the modified instance. First, we prove that if we are allowed to delete agents on only one side, then our problem can be solved in polynomial time. Interestingly, this result is obtained by carefully observing the existing algorithm for checking the existence of a super-stable matching. In addition, we prove that if we are allowed to delete agents on both sides, then our problem is NP-complete.

翻译：超稳定性是带平局稳定匹配问题中的一种稳定性概念。已知超稳定匹配不一定存在，且其存在性可在多项式时间内判定。本文研究通过删除有限个代理来修改超稳定匹配问题实例，使得修改后的实例存在超稳定匹配。首先证明，若仅允许删除单侧代理，该问题可在多项式时间内求解。有趣的是，这一结果源于对现有超稳定匹配存在性判定算法的细致观察。此外，我们证明若允许删除双侧代理，该问题为NP完全的。