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Journal of Combinatorial Optimization

, Volume 31, Issue 3, pp 1111–1129 | Cite as

Implicit cover inequalities

  • Agostinho AgraEmail author
  • Cristina Requejo
  • Eulália Santos
Article

Abstract

In this paper we consider combinatorial optimization problems whose feasible sets are simultaneously restricted by a binary knapsack constraint and a cardinality constraint imposing the exact number of selected variables. In particular, such sets arise when the feasible set corresponds to the bases of a matroid with a side knapsack constraint, for instance the weighted spanning tree problem and the multiple choice knapsack problem. We introduce the family of implicit cover inequalities which generalize the well-known cover inequalities for such feasible sets and discuss the lifting of the implicit cover inequalities. A computational study for the weighted spanning tree problem is reported.

Keywords

Cover inequalities Weighted minimal spanning tree problem Lifting Matroidal knapsack 

Notes

Acknowledgments

Research partially funded by CIDMA (Centro de Investigação e Desenvolvimento em Matemática e Aplicações) through the FCT (Fundação para a Ciência e a Tecnologia) within project PEst-OE/MAT/UI4106/2014, and by FCT through program COMPETE: FCOMP-01-0124-FEDER-041898 within project EXPL/MAT-NAN/1761/2013.

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Agostinho Agra
    • 1
    Email author
  • Cristina Requejo
    • 1
  • Eulália Santos
    • 2
  1. 1.CIDMA and Department of MathematicsUniversity of AveiroAveiroPortugal
  2. 2.CIDMAISLA-Higher Institute of LeiriaLeiriaPortugal

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