The Complexity of Recognizing Facets for the Knapsack Polytope
Optimization and Control
2025-10-21 v3 Computational Complexity
Abstract
The complexity class DP is the class of all languages that are the intersection of a language in NP and a language in coNP. It was conjectured that recognizing a facet for the knapsack polytope is DP-complete. We provide a positive answer to this conjecture. Moreover, despite the \DP-hardness of the recognition problem, we give a polynomial time algorithm for deciding if an inequality with a fixed number of distinct coefficients defines a facet of a knapsack polytope.
Cite
@article{arxiv.2211.03311,
title = {The Complexity of Recognizing Facets for the Knapsack Polytope},
author = {Rui Chen and Haoran Zhu},
journal= {arXiv preprint arXiv:2211.03311},
year = {2025}
}