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

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