Linear vs. semidefinite extended formulations: exponential separation and strong lower bounds

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.

Authors

• Samuel Fiorini
• Serge Massar
• Sebastian Pokutta
• Hans Raj Tiwary
• Ronald de Wolf

Keywords

• combinatorial optimization
• communication complexity
• linear programming
• quantum communication complexity
• semidefinite programming