[Scip] Scip for combinatorial enumeration and probability

[Victor S. Miller]

I recommend looking at Latte, which implements a sophisticated algorithm of Barvinok to count solutions, and even to integrate a function over the solutions (i.e. Take a weighted sum ).

Victor

https://www.math.ucdavis.edu/~latte/

Sent from my iPhone

> On Sep 29, 2013, at 9:22, David Ruescas <fastness at gmail.com> wrote:
> 
> Hello scip,
> 
> I have a question which I'm not sure belongs on this list. If so, please let me know, apologies in advance.
> 
> I'm wondering whether using scip's solution counting capability is a viable approach for calculating probabilities over integer values. Consider this simple example
> 
> a + b = 25
> c + d = 34
> 
> a + c = 23
> b + d = 12
> 
> (numbers may be inconsistent, just made them up)
> 
> The question is, given the above constraints, what is the probability that a (or b,c,d) is equal to some number? In this simple example, it would be trivial to calculate this directly. But if the number of constraints is much larger the problem becomes more complex.
> 
> In such a scenario, one could in theory use scip to count the number of solutions overall, and then count the fraction of those that satisfy additional constraints (eg a = 10), hence obtaining a probability.
> 
> Does this use of scip make sense? Any pointers to literature on this topic?
> 
> Kind regards,
> 
> David
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