Exponential Lower Bounds for Polytopes in Combinatorial Optimization

Aaron Snook will present the recent work of Samuel Fiorini, Serge Massar, Sebastian Pokutta, Hans Raj Tiwary, and Ronald de Wolf. They 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, they prove that this holds also for the cut polytope and the stable set polytope. These results were discovered through a new connection that they make between one-way quantum communication protocols and semidefinite programming reformulations of LPs.