All Linear and Integer Programs Are Slim 3-Way Transportation Programs

@article{Loera2006AllLA,
title={All Linear and Integer Programs Are Slim 3-Way Transportation Programs},
author={Jes{\'u}s A. De Loera and Shmuel Onn},
journal={SIAM Journal on Optimization},
year={2006},
volume={17},
pages={806-821}
}

We show that any rational convex polytope is polynomial-time representable as a three-way linesum transportation polytope of “slim” (r, c, 3) format. This universality theorem has important consequences for linear and integer programming and for confidential statistical data disclosure. We provide a polynomial-time embedding of arbitrary linear programs and integer programs in such slim transportation programs and in bitransportation programs. Our construction resolves several standing problems… CONTINUE READING