Linear vs. semidefinite extended formulations
Samuel Fiorinia, Serge Massara, Sebastian Pokuttab, Hans Raj Tiwarya, Ronald de Wolfc
- aUniversité libre de Bruxelles, Brussels, Belgium
- bFriedrich-Alexander Universität, Erlangen, Germany
- cCWI and University of Amsterdam, Amsterdam, Netherlands
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Abstract
We solve a 20-year old problem posed by Yannakakis and prove that there exists no polynomial-size linear program (LP) whose associated polytope projects to the traveling salesman polytope, even if the LP is not required to be symmetric. Moreover, we prove that this holds also for the cut polytope and the stable set polytope. These results were discovered through a new connection that we make between one-way quantum communication protocols and semidefinite programming reformulations of LPs.
TL;DRA 20-year old problem posed by Yannakakis is solved and it is proved that there exists no polynomial-size linear program (LP) whose associatedpolytope projects to the traveling salesman polytope, even if the LP is not required to be symmetric. (Semantic Scholar)