3 Approximate Constraint Satisfaction Requires Large LP Relaxations
Siu On Chan, Chan James, R. Lee, Prasad Raghavendra, David Steurer · 2014
We prove super-polynomial lower bounds on the size of linear programming relaxations for approximation versions of constraint satisfaction problems. We show that for these problems, polynomial-sized linear programs are exactly as powerful as programs arising from a constant number of rounds of the Sherali-Adams hierarchy. In particular, any polynomial-sized linear program for Max Cut has an integrality gap of 1