[Scip] Scip for combinatorial enumeration and probability

[David Ruescas]

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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