Progress while computing H-representation

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polymake_rulez44
Posts: 6
Joined: 30 Aug 2019, 10:42

Progress while computing H-representation

Postby polymake_rulez44 » 05 Dec 2019, 16:58

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?

2. What is the fastest method of the available algorithms for doing this?

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joswig
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Posts: 247
Joined: 24 Dec 2010, 11:10

Re: Progress while computing H-representation

Postby joswig » 06 Dec 2019, 11:35

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.

polymake_rulez44
Posts: 6
Joined: 30 Aug 2019, 10:42

Re: Progress while computing H-representation

Postby polymake_rulez44 » 09 Dec 2019, 13:33

Thank you very much for your answer.

If you have an server with multiple cores (like 20), which algorithm can make use of this? Where do i find information on this?

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joswig
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Posts: 247
Joined: 24 Dec 2010, 11:10

Re: Progress while computing H-representation

Postby joswig » 10 Dec 2019, 11:25

If you have an server with multiple cores (like 20), which algorithm can make use of this? Where do i find information on this?
Again, please consult that paper ;-)

There are currently two parallel convex hull codes available (that I am aware of): normaliz and lrs (in its mplrs version).
The polymake interface makes use of the parallelization in normaliz. Yet, the differences in running time may be much
larger than any potential advantage from parallelization. It needs to stressed that each convex hull code interfaced
by or being part of polymake has a scenario in which it is (much) superior to all others.


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