The matching polytope has exponential extension complexity

@article{Rothvoss2014TheMP,
  title={The matching polytope has exponential extension complexity},
  author={Thomas Rothvoss},
  journal={Proceedings of the forty-sixth annual ACM symposium on Theory of computing},
  year={2014}
}
  • T. Rothvoss
  • Published 11 November 2013
  • Computer Science
  • Proceedings of the forty-sixth annual ACM symposium on Theory of computing
A popular method in combinatorial optimization is to express polytopes P, which may potentially have exponentially many facets, as solutions of linear programs that use few extra variables to reduce the number of constraints down to a polynomial. After two decades of standstill, recent years have brought amazing progress in showing lower bounds for the so called extension complexity, which for a polytope P denotes the smallest number of inequalities necessary to describe a higher dimensional… 

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It turns out that the high extension complexity for the matchingpolytope stem from the same source of hardness as for the correlation polytope: a direct sum structure.
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