We consider the problem of finding a maximum popular matching in a many-to-many matching setting with two-sided preferences and matroid constraints. This problem was proposed by Kamiyama [TCS 2020] and solved in the special case where matroids are base orderable. Utilizing a recently shown matroid exchange property, we show that the problem is tractable for arbitrary matroids.

翻译：我们考虑了在多种匹配环境中找到最大大众匹配点的问题,这种匹配点具有双向偏好和机器人限制。 这个问题是Kamiyama[TCS 2020]提出的,在机器人可以定型的特殊情况下解决了。 利用最近展示的机器人交换财产,我们证明对任意的机器人来说,这个问题是可以解决的。