Discussion
What does an integer programming approach contribute that propagation does not?
Answer: A
Relaxing the integrality requirement gives a linear program whose optimum bounds the true one, and that global bound prunes in a way local propagation cannot. Constraint programming supplies stronger local reasoning about complex combinatorial structures. Both handle discrete variables and can prove infeasibility, and neither is polynomial in general. Two techniques whose strengths are complementary rather than overlapping are natural candidates for combination, which is what hybrid solvers do.
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