Questions like these appeared in this forum in several guises (and have been answered, see, e.g.,
viewtopic.php?f=8&t=1693).
I am aware, however, that for non-experts it may not be obvious that these questions are essentially the same.
So I answer them again.
1. When I calculate the H-representation from the V-representation,
can I get some output from polymake on the progress, while it is computing to estimate how long it takes?
No. Essentially there is almost no way to do this, however desirable this may be. The only convex hull code which I know to have such an option is lrs (which is interfaced from polymake), but this is intrinsically not very reliable (which is not the fault of the lrs authors).
2. What is the fastest method of the available algorithms for doing this?
This is entirely impossible to say without knowing something about the input. polymake's default is ppl, and this often works well, but there are notable exceptions.
My best offer is a comprehensive set of tests documented in:
- Benjamin Assarf, Ewgenij Gawrilow, Katrin Herr, Michael Joswig, Benjamin Lorenz, Andreas Paffenholz and Thomas Rehn. Computing convex hulls and counting integer points with polymake. Math. Program. Comput. 9 (2017), no. 1, 1-38. https://link.springer.com/article/10.10 ... 016-0104-z
The main contribution in that paper are some "rules of thumb", which hopefully help you at least a bit.
