Which Nonnegative Matrices Are Slack Matrices?
Jo\~ao Gouveia, Roland Grappe, Volker Kaibel, Kanstantsin Pashkovich,, Richard Z. Robinson, Rekha R. Thomas
TL;DR
This paper characterizes slack matrices of cones and polytopes within all nonnegative matrices, providing an algorithm to identify them and connecting the problem to the complex polyhedral verification challenge.
Contribution
It offers a complete characterization of slack matrices and introduces an algorithm to determine if a matrix is a slack matrix, linking to the polyhedral verification problem.
Findings
Provided a characterization of slack matrices among nonnegative matrices
Developed an algorithm for recognizing slack matrices
Connected the recognition problem to polyhedral verification complexity
Abstract
In this paper we characterize the slack matrices of cones and polytopes among all nonnegative matrices. This leads to an algorithm for deciding whether a given matrix is a slack matrix. The underlying decision problem is equivalent to the polyhedral verification problem whose complexity is unknown.
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Taxonomy
Topicsgraph theory and CDMA systems · Computational Geometry and Mesh Generation · Advanced Graph Theory Research