Neighbors of the Origin for Four by Three Matrices

David F. Shallcross
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David F. Shallcross: Cowles Foundation, Yale University, https://cowles.yale.edu/

No 916, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

Abstract: 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.

Keywords: Integer programming; neighborhood systems (search for similar items in EconPapers)
Pages: 11 pages
Date: 1989-06
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Published in Mathematics of Operations Research (1992), 17: 608-614

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