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arXiv · 2211.03311

The Complexity of Recognizing Facets for the Knapsack Polytope

Rui Chen·Haoran Zhu
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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.

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Rui Chen, Haoran Zhu. 2022-11-07. The Complexity of Recognizing Facets for the Knapsack Polytope. https://arxiv.org/abs/2211.03311

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