Exponential Lower Bounds for Polytopes in Combinatorial Optimization
Combinatorics
2015-03-16 v5 Computational Complexity
Quantum Physics
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.
Keywords
Cite
@article{arxiv.1111.0837,
title = {Exponential Lower Bounds for Polytopes in Combinatorial Optimization},
author = {Samuel Fiorini and Serge Massar and Sebastian Pokutta and Hans Raj Tiwary and Ronald de Wolf},
journal= {arXiv preprint arXiv:1111.0837},
year = {2015}
}
Comments
19 pages, 4 figures. This version of the paper will appear in the Journal of the ACM. The earlier conference version in STOC'12 had the title "Linear vs. Semidefinite Extended Formulations: Exponential Separation and Strong Lower Bounds"