Concepts of consistency have long played a key role in constraint programming but never developed in integer programming (IP). Consistency nonetheless plays a role in IP as well. For example, cutting planes can reduce backtracking by achieving various forms of consistency as well as by tightening the linear programming (LP) relaxation. We introduce a type of consistency that is particularly suited for 0–1 programming and develop the associated theory. We define a 0–1 constraint set as LP-consistent when any partial assignment that is consistent with its linear programming relaxation is consistent with the original 0–1 constraint set. We prove basic properties of LP-consistency, including its relationship with Chvátal-Gomory cuts and the integer hull. We show that a weak form of LP-consistency can reduce or eliminate backtracking in a way analogous to k-consistency. This work suggests a new approach to the reduction of backtracking in IP that focuses on cutting off infeasible partial assignments rather than fractional solutions.
CITATION STYLE
Davarnia, D., & Hooker, J. N. (2019). Consistency for 0–1 Programming. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 11494 LNCS, pp. 225–240). Springer Verlag. https://doi.org/10.1007/978-3-030-19212-9_15
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