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arXiv · 1801.08850

On bounded pitch inequalities for the min-knapsack polytope

Yuri Faenza·Igor Malinović·Monaldo Mastrolilli·Ola Svensson
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Abstract

In the min-knapsack problem one aims at choosing a set of objects with minimum total cost and total profit above a given threshold. In this paper, we study a class of valid inequalities for min-knapsack known as bounded pitch inequalities, which generalize the well-known unweighted cover inequalities. While separating over pitch-1 inequalities is NP-hard, we show that approximate separation over the set of pitch-1 and pitch-2 inequalities can be done in polynomial time. We also investigate integrality gaps of linear relaxations for min-knapsack when these inequalities are added. Among other results, we show that, for any fixed $t$, the $t$-th CG closure of the natural linear relaxation has the unbounded integrality gap.

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Yuri Faenza, Igor Malinović, Monaldo Mastrolilli, Ola Svensson. 2018-01-26. On bounded pitch inequalities for the min-knapsack polytope. https://arxiv.org/abs/1801.08850

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