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International Conference on Integer Programming and Combinatorial Optimization

IPCO 2007: Integer Programming and Combinatorial Optimization pp 197–209Cite as

On a Generalization of the Master Cyclic Group Polyhedron

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4513))

Abstract

We study the Master Equality Polyhedron (MEP) which generalizes the Master Cyclic Group Polyhedron and the Master Knapsack Polyhedron.

We present an explicit characterization of the nontrivial facet-defining inequalities for MEP. This result generalizes similar results for the Master Cyclic Group Polyhedron by Gomory [9] and for the Master Knapsack Polyhedron by Araoz [1]. Furthermore, this characterization also gives a polynomial time algorithm for separating an arbitrary point from the MEP.

We describe how facet defining inequalities for the Master Cyclic Group Polyhedron can be lifted to obtain facet defining inequalities for the MEP, and also present facet defining inequalities for the MEP that cannot be obtained in such a way. Finally, we study the mixed-integer extension of the MEP and present an interpolation theorem that produces valid inequalities for general Mixed Integer Programming Problems using facets of the MEP.

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Author information

Authors and Affiliations

  1. Mathematical Sciences Department, IBM T. J. Watson Research Center, Yorktown Heights, NY, 10598,  

    Sanjeeb Dash & Oktay Günlük

  2. H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA, 30332,  

    Ricardo Fukasawa

Authors
  1. Sanjeeb Dash
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  2. Ricardo Fukasawa
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  3. Oktay Günlük
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Matteo Fischetti David P. Williamson

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© 2007 Springer Berlin Heidelberg

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Dash, S., Fukasawa, R., Günlük, O. (2007). On a Generalization of the Master Cyclic Group Polyhedron. In: Fischetti, M., Williamson, D.P. (eds) Integer Programming and Combinatorial Optimization. IPCO 2007. Lecture Notes in Computer Science, vol 4513. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72792-7_16

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  • DOI: https://doi.org/10.1007/978-3-540-72792-7_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-72791-0

  • Online ISBN: 978-3-540-72792-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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