Approximate Constraint Satisfaction Requires Large LP Relaxations
Computational Complexity
2016-02-09 v3 Data Structures and Algorithms
Combinatorics
Optimization and Control
Abstract
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 1/2 and any such linear program for Max 3-Sat has an integrality gap of 7/8.
Cite
@article{arxiv.1309.0563,
title = {Approximate Constraint Satisfaction Requires Large LP Relaxations},
author = {Siu On Chan and James R. Lee and Prasad Raghavendra and David Steurer},
journal= {arXiv preprint arXiv:1309.0563},
year = {2016}
}
Comments
29 pages; significant revisions, new references, simpler proofs