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Neighbors of the Origin for Four by Three Matrices

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Scarf has defined a neighborhood system for families of integer programs where the right-hand side is allowed to vary. This system depends on a matrix A of constraint and objective function coefficients of the integer programs. This paper characterizes the set of neighbors of the origin when A is four by three; showing that it may be described as the set of integer vectors in a union of two-dimensional polyhedra, where the number of polyhedra is quadratic in the bit size of A.

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  • David F. Shallcross, 1989. "Neighbors of the Origin for Four by Three Matrices," Cowles Foundation Discussion Papers 916, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:916
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    File URL: https://cowles.yale.edu/sites/default/files/files/pub/d09/d0916.pdf
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    Keywords

    Integer programming; neighborhood systems;

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