I am a researcher working at a public research institute. A research group from another country has published an algorithm in a peer-reviewed journal and provided a server implementation of it on their website (no public code). I have implemented the recipe of this algorithm as an open-source software tool, and I plan to release it for general academic usage and potentially commercial usage. I highlight commercial because a statement from the other research group at the end of their text establishes that the authors of the paper have filed a patent describing the design and composition of their software, due to commercial interests on their side (startup). Currently, that patent's status is pending, and it might be granted, or not.
I want to license my software with an MIT license (including commercial), yet currently, I do not fully understand the liability of my research institute or mine, in case the authors decide to claim a patent infringement. Am I or my research institution liable at this point, should opt for a non-commercial version of the MIT license (and which one), or does publishing the recipe of a method in a peer-reviewed allow reimplementing and licensing it with a commercial license by others, regardless of the commercial interests of the authors?