I'm looking for a reference on how to sample uniformly (and preferably efficiently, elegantly, etc.) from the vertices of a polytope. I gather that [enumerating vertices is hard](https://doi.org/10.1007/978-0-387-87363-3_17). I also note the MO questions [Uniformly Sampling from Convex Polytopes](https://mathoverflow.net/questions/9854/) and [Is it possible to sample uniformly on the surface of a high-dimensional polytope?](https://mathoverflow.net/questions/98027/). A bit of poking around Google Scholar hasn't turned anything up.



Sampling uniformly from the vertices of a polytope
Here is one efficient approach, performing a random walk with a rapid mixing time, that has been implemented for a particular class of polytopes, but which might well be adaptable to a more general setting: [Random Walks on the Vertices of Transportation Polytopes](http://homepages.inf.ed.ac.uk/mcryan/cdms-jour.pdf) (2008).


