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On Bounded Pitch Inequalities for the Min-Knapsack Polytope

  • Yuri Faenza
  • Igor MalinovićEmail author
  • Monaldo Mastrolilli
  • Ola Svensson
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10856)

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.

Notes

Acknowledgments

Supported by the Swiss National Science Foundation (SNSF) project 200020-169022 “Lift and Project Methods for Machine Scheduling Through Theory and Experiments”. Some of the work was done when the second and the third author visited the IEOR department of Columbia University, partially funded by a gift of the SNSF.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Yuri Faenza
    • 1
  • Igor Malinović
    • 2
    Email author
  • Monaldo Mastrolilli
    • 3
  • Ola Svensson
    • 2
  1. 1.Columbia UniversityNew York CityUSA
  2. 2.École Polytechnique Fédérale de LausanneLausanneSwitzerland
  3. 3.IDSIA LuganoMannoSwitzerland

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