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Test sets for integer programs

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Abstract

In this paper I discuss various properties of the simplicial complex of maximal lattice free bodies associated with a matrixA. If the matrix satisfies some mild conditions, and isgeneric, the edges of the complex form the minimal test set for the family of integer programs obtained by selecting a particular row ofA as the objective function, and using the remaining rows to impose constraints on the integer variables.

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Authors and Affiliations

  1. Cowles Foundation, Yale University, 06520-8283, New Haven, CT, USA

    Herbert E. Scarf

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  1. Herbert E. Scarf
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Scarf, H.E. Test sets for integer programs. Mathematical Programming 79, 355–368 (1997). https://doi.org/10.1007/BF02614324

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