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arXiv · 1503.04717

On the existence of compact {\epsilon}-approximated formulations for knapsack in the original space

Yuri Faenza·Laura Sanità
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Abstract

We show that there exists a family of Knapsack polytopes such that, for each polytope P from this family and each {\epsilon} > 0, any {\epsilon}-approximated formulation of P in the original space R^n requires a number of inequalities that is super-polynomial in n. This answers a question by Bienstock and McClosky (2012). We also prove that, for any down-monotone polytope, an {\epsilon}-approximated formulation in the original space can be obtained with inequalities using at most O(min{log(n/{\epsilon}),n}/{\epsilon}) different coefficients.

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Yuri Faenza, Laura Sanità. 2015-03-16. On the existence of compact {\epsilon}-approximated formulations for knapsack in the original space. https://arxiv.org/abs/1503.04717

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