# On a generalization of the master cyclic group polyhedron

@article{Dash2007OnAG, title={On a generalization of the master cyclic group polyhedron}, author={Sanjeeb Dash and Ricardo Fukasawa and Oktay G{\"u}nl{\"u}k}, journal={Mathematical Programming}, year={2007}, volume={125}, pages={1-30} }

AbstractWe study the master equality polyhedron (MEP) which generalizes the
master cyclic group polyhedron (MCGP) and the master knapsack polyhedron (MKP).
We present an explicit characterization of the polar of the nontrivial facet-defining
inequalities for MEP. This result generalizes similar results for the MCGP by Gomory
(1969) and for the MKP by Araóz (1974). Furthermore, this characterization gives a
polynomial time algorithm for separating an arbitrary point from MEP. We describe
how…

## 11 Citations

### The master equality polyhedron with multiple rows

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This paper defines the notion of a polaroid, a set containing all nontrivial facet defining inequalities, and shows how to use linear programming (LP) to efficiently solve the separation problem for the MEP when the polaroid has a compact polyhedral description.

### The Master Equality Polyhedron: Two-Slope Facets and Separation Algorithm

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This thesis presents our findings about the Master Equality Polyhedron (MEP), an extension of Gomory’s Master Group Polyhedron. We prove a theorem analogous to Gomory and Johnson’s two-slope theorem…

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This survey surveys recent research on mixed-integer rounding (MIR) inequalities and a generalization, namely the two-step MIR inequalities defined by Dash and Gunluk (2006), and gives a short proof of the well-known fact that the MIR closure of a polyhedral set is a polyhedron.

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The Steinitz lemma is used to prove an upper bound of τ(d) ≤ dd+o(d), and based on a construction of Alon and Vũ, a lower bound is obtained, contributing to understanding the master equality polyhedron with multiple rows defined by Dash et al.

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