Abstract
A (0, 1) matrix A is said to be ideal if all the vertices of the polytope Q(A) = {x: Ax ≥ 1,0 ≤ x ≤ 1} are integral. In this paper we consider the extension of the notion of ideality to (0, ±1) matrices. We associate with any (0, ±1) matrix A its disjoint completion A+ and we show that A is ideal if and only if a suitable (0, 1) matrix D(A+) is ideal. Moreover, we prove a Lehman-type characterization of minimally non-ideal (0, ±1) matrices that coincide with their disjoint completion.
Cite
CITATION STYLE
Nobili, P., & Sassano, A. (1995). (0,±1)ideal matrices. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 920, pp. 344–359). Springer Verlag. https://doi.org/10.1007/3-540-59408-6_63
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