On the Complexity of Recognizing Integrality and Total Dual Integrality of the {0, 1/2}-Closure

The {0, 12}-closure of a rational polyhedron {x : Ax ≤ b} is obtained by adding all Gomory-Chvátal cuts that can be derived from the linear system Ax ≤ b using multipliers in {0, 12}. We show that deciding whether the {0, 1 2}-closure coincides with the integer hull is strongly NP-hard. A direct consequence of our proof is that, testing whether the linear description of the {0, 12}-closure derived from Ax ≤ b is totally dual integral, is strongly NP-hard.

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