# A Knapsack Intersection Hierarchy Applied to All-or-Nothing Flow in Trees

@inproceedings{Jozefiak2022AKI, title={A Knapsack Intersection Hierarchy Applied to All-or-Nothing Flow in Trees}, author={Adam Jozefiak and F. Bruce Shepherd and Noah Weninger}, year={2022} }

We introduce a natural knapsack intersection hierarchy for strengthening linear programming relaxations of packing integer programs, i.e., max{wx : x ∈ P ∩{0, 1}} where P = {x ∈ [0, 1] : Ax ≤ b} and A, b, w ≥ 0. The t level P t corresponds to adding cuts associated with the integer hull of the intersection of any t knapsack constraints (rows of the constraint matrix). This model captures the maximum possible strength of “t-row cuts”, an approach often used by solvers for small t. If A is m × n…

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