On the Complexity of Separating Cutting Planes for the Knapsack Polytope

Abstract

We close three open problems in the separation complexity of valid inequalities for the knapsack polytope. Specifically, we establish that the separation problems for extended cover inequalities, (1,k)-configuration inequalities, and weight inequalities are all NP-complete. We also give a number of special cases where the separation problem can be solved in polynomial time.