On the existence of compact {\epsilon}-approximated formulations for knapsack in the original space
Optimization and Control
2015-03-18 v1 Discrete Mathematics
Combinatorics
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.
Keywords
Cite
@article{arxiv.1503.04717,
title = {On the existence of compact {\epsilon}-approximated formulations for knapsack in the original space},
author = {Yuri Faenza and Laura Sanità},
journal= {arXiv preprint arXiv:1503.04717},
year = {2015}
}