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Master corner polyhedron: Vertices

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  • Shlyk, Vladimir A.

Abstract

We focus on the vertices of the master corner polyhedron (MCP), a fundamental object in the theory of integer linear programming. We introduce two combinatorial operations that transform vertices to their neighbors. This implies that each MCP can be defined by the initial vertices regarding these operations; we call them support vertices. We prove that the class of support vertices of all MCPs over a group is invariant under automorphisms of this group and describe MCP vertex bases. Among other results, we characterize its irreducible points, establish relations between a vertex and the nontrivial facets that pass through it, and prove that this polyhedron is of diameter 2.

Suggested Citation

  • Shlyk, Vladimir A., 2013. "Master corner polyhedron: Vertices," European Journal of Operational Research, Elsevier, vol. 226(2), pages 203-210.
    • Handle: RePEc:eee:ejores:v:226:y:2013:i:2:p:203-210
    DOI: 10.1016/j.ejor.2012.11.011
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    References listed on IDEAS

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    1. Kianfar, Kiavash & Fathi, Yahya, 2010. "Generating facets for finite master cyclic group polyhedra using n-step mixed integer rounding functions," European Journal of Operational Research, Elsevier, vol. 207(1), pages 105-109, November.
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    3. Balas, Egon, 2002. "Some thoughts on the development of integer programming during my research career - lecture delivered upon receiving the EURO Gold Medal, July 9, 2001, Rotterdam," European Journal of Operational Research, Elsevier, vol. 141(1), pages 1-7, August.
    4. Valentin Borozan & Gérard Cornuéjols, 2009. "Minimal Valid Inequalities for Integer Constraints," Mathematics of Operations Research, INFORMS, vol. 34(3), pages 538-546, August.
    5. DEY, Santanu S. & WOLSEY, Laurence A., 2010. "Constrained infinite group relaxations of MIPS," LIDAM Reprints CORE 2314, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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