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arXiv · 2610.11950

Computing Lower Bounds on the Non-negative Rank via SAT Solvers

Tilman Engel·Thomas Kalinowski·Matthias Schymura
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Abstract

Finding the extension complexity (xc) of a polytope is equivalent to finding the non-negative rank of its slack matrix. We provide a formulation for the rectangle and refined rectangle covering, bounding the non-negative rank of diverse non-negative matrices. While the bounds are known, our formulation enables us to use boolean satisfiability (SAT) solvers, which proves to be a strong tool. We obtain improved values for lower bounds on the non-negative rank of multiple matrices. In particular, we determined the xc of some regular polygons.

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Tilman Engel, Thomas Kalinowski, Matthias Schymura. 2026-10-08. Computing Lower Bounds on the Non-negative Rank via SAT Solvers. https://arxiv.org/abs/2610.11950

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