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.
Additional Metadata
THEME Null option (theme 11)
Journal Journal of the ACM
Project Quantum Algorithmics , Progress in quantum computing:Algorithms, communication, and applications
Note Published paper: DOI: 10.1145/2716307
Grant This work was funded by the European Commission 7th Framework Programme; grant id erc/615307 - Progress in quantum computing: Algorithms, communication, and applications (QPROGRESS)
Citation
Fiorini, S, Massar, S, Pokutta, S, Tiwary, H.R, & de Wolf, R. M. (2015). Exponential Lower Bounds for Polytopes in Combinatorial Optimization. Journal of the ACM, 62(2), 1–23.