Abstract
We close three open problems on 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 $$\mathcal{N}\mathcal{P}$$ -complete. We also show that, when the number of constraints of the LP relaxation is constant and its optimal solution is an extreme point, then the separation problems of both extended cover inequalities and weight inequalities can be solved in polynomial time. Moreover, we provide a natural generalization of (1, k)-configuration inequality which is easier to separate and contains the original (1, k)-configuration inequality as a strict sub-family.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.