The matching polytope has exponential extension complexity

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.

However, the central question in this field remained wide open: can the perfect matching polytope be written as an LP with polynomially many constraints?

We answer this question negatively. In fact, the extension complexity of the perfect matching polytope in a complete n-node graph is 2Omega(n).

Speaker Details

Thomas Rothvoss did his PhD in Mathematics in 2009 at EPFL in Switzerland under Friedrich Eisenbrand. Then he was a PostDoc at MIT working with Michel Goemans. Since January 2014 he is assistant professor in the Department of Mathematics at UW Seattle.

Thomas Rothvoss
University of Washington
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