# Recognizing Cartesian products of matrices and polytopes

@article{Aprile2020RecognizingCP, title={Recognizing Cartesian products of matrices and polytopes}, author={Manuel Aprile and Michele Conforti and Yuri Faenza and Samuel Fiorini and Tony Huynh and Marco Macchia}, journal={ArXiv}, year={2020}, volume={abs/2002.02264} }

The 1-product of matrices $S_1 \in \mathbb{R}^{m_1 \times n_1}$ and $S_2 \in \mathbb{R}^{m_2 \times n_2}$ is the matrix in $\mathbb{R}^{(m_1+m_2) \times (n_1n_2)}$ whose columns are the concatenation of each column of $S_1$ with each column of $S_2$. Our main result is a polynomial time algorithm for the following problem: given a matrix $S$, is $S$ a 1-product, up to permutation of rows and columns? Our main motivation is a close link between the 1-product of matrices and the Cartesian product…

## 4 Citations

### Slack matrices, k-products, and 2-level polytopes

- Mathematics, Computer ScienceArXiv
- 2021

In this paper, we study algorithmic questions concerning products of matrices and their consequences for recognition algorithms for polyhedra. The 1-product of matrices S1 ∈ R m1×n1 , S2 ∈ R m2×n2 is…

### Submodular functions

- Physics
- 2021

These notes contain examples of submodular functions and describe certain algorithms for optimizing them. They are intended for students from the M.Sc. class IEORE4008 Computational Discrete…

### Slack matrices, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e20" altimg="si15.svg"><mml:mi>k</mml:mi></mml:math>-products, and 2-level polytopes

- MathematicsDiscrete Applied Mathematics
- 2022

### Extended formulations for matroid polytopes through randomized protocols

- MathematicsOper. Res. Lett.
- 2022

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