Hello everybody,

I posted this in r/math before but it was removed there (apologies for that). The suggestion was to post it here, so I copypasted it to here, hope that is permitted!

I'm currently reading up on Matroids which I, personally, find extremely interesting. I'm reading a paper about optimization on Matroids and their corresponding Polyhedra. Specifically, this paper makes use of an algorithm by Cunningham (1984): "Testing Membership in Matroid Polyhedra". The algorithm is also explained in Shrijvers excellent yet for an outsider hardcorely dense "Combanitorial Optimization: Polyhedra and Efficiency, Algorithms and Combinatorics, Vol. B", Theorem 40.4, but I find it extremely complicated to wrap my head around that stuff.

I know it is an extremely long shot, but I would honest-to-god like to understand how the Algorithm is supposed to work and how it optimizes. I tried looking for a matroid-related subreddit but unfortunately found none. If no one is capable (or willing) to engage with my oddly specific question, I absolutely understand.

Thanks and that's all, folks