2012/05/19 by Samuel Fiorini, Serge Massar, Sebastian Pokutta +2 · 4 citations
Computer Science · Mathematics · #Quantum Computing Algorithms and Architecture #Complexity and Algorithms in Graphs #Advanced Optimization Algorithms Research
paper · doi:10.1145/2213977.2213988
openalex publication_date 2012/05/19 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/29
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.