Abstract
Quantified Integer Programs (QIPs) are integer programs with variables being either existentially or universally quantified. They can be interpreted as a two-person zero-sum game with an existential and a universal player where the existential player tries to meet all constraints and the universal player intends to force at least one constraint to be not satisfied.
Originally, the universal player is only restricted to set the universal variables within their upper and lower bounds. We extend this idea by adding constraints for the universal variables, i.e., restricting the universal player to some polytope instead of the hypercube created by bounds. We also show how this extended structure can be polynomial-time reduced to a QIP.
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- 1.
An arborescence is a directed, rooted tree.
- 2.
The path is unique, because all nodes with level \(\ge n\) belong to existential variables and thus have only one successor in a strategy.
- 3.
except for auxiliary variable p in single-stage instances.
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Hartisch, M., Ederer, T., Lorenz, U., Wolf, J. (2016). Quantified Integer Programs with Polyhedral Uncertainty Set. In: Plaat, A., Kosters, W., van den Herik, J. (eds) Computers and Games. CG 2016. Lecture Notes in Computer Science(), vol 10068. Springer, Cham. https://doi.org/10.1007/978-3-319-50935-8_15
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DOI: https://doi.org/10.1007/978-3-319-50935-8_15
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