A hierarchy of relaxation between the continuous and convex hull representations
SIAM Journal on Discrete Mathematics
A PCP characterization of NP with optimal amortized query complexity
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
The Probable Value of the Lovász-Schrijver Relaxations for Maximum Independent Set
SIAM Journal on Computing
An Explicit Exact SDP Relaxation for Nonlinear 0-1 Programs
Proceedings of the 8th International IPCO Conference on Integer Programming and Combinatorial Optimization
A Comparison of the Sherali-Adams, Lovász-Schrijver, and Lasserre Relaxations for 0--1 Programming
Mathematics of Operations Research
Towards strong nonapproximability results in the Lovasz-Schrijver hierarchy
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Gowers uniformity, influence of variables, and PCPs
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
New Lower Bounds for Vertex Cover in the Lovasz-Schrijver Hierarchy
CCC '06 Proceedings of the 21st Annual IEEE Conference on Computational Complexity
Tight integrality gaps for Lovasz-Schrijver LP relaxations of vertex cover and max cut
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
A Linear Round Lower Bound for Lovasz-Schrijver SDP Relaxations of Vertex Cover
CCC '07 Proceedings of the Twenty-Second Annual IEEE Conference on Computational Complexity
Linear programming relaxations of maxcut
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Approximation Algorithms Using Hierarchies of Semidefinite Programming Relaxations
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
Integrality gaps of 2 - o(1) for Vertex Cover SDPs in the Lovész-Schrijver Hierarchy
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
Approximation Resistant Predicates from Pairwise Independence
CCC '08 Proceedings of the 2008 IEEE 23rd Annual Conference on Computational Complexity
Improved Approximation Guarantees through Higher Levels of SDP Hierarchies
APPROX '08 / RANDOM '08 Proceedings of the 11th international workshop, APPROX 2008, and 12th international workshop, RANDOM 2008 on Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques
APPROX '08 / RANDOM '08 Proceedings of the 11th international workshop, APPROX 2008, and 12th international workshop, RANDOM 2008 on Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques
Linear Level Lasserre Lower Bounds for Certain k-CSPs
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Integrality gaps for Sherali-Adams relaxations
Proceedings of the forty-first annual ACM symposium on Theory of computing
Sherali-adams relaxations of the matching polytope
Proceedings of the forty-first annual ACM symposium on Theory of computing
CSP gaps and reductions in the lasserre hierarchy
Proceedings of the forty-first annual ACM symposium on Theory of computing
MaxMin allocation via degree lower-bounded arborescences
Proceedings of the forty-first annual ACM symposium on Theory of computing
Towards optimal integrality gaps for hypergraph vertex cover in the lovász-schrijver hierarchy
APPROX'05/RANDOM'05 Proceedings of the 8th international workshop on Approximation, Randomization and Combinatorial Optimization Problems, and Proceedings of the 9th international conference on Randamization and Computation: algorithms and techniques
More efficient queries in PCPs for NP and improved approximation hardness of maximum CSP
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
Integrality gaps of linear and semi-definite programming relaxations for Knapsack
IPCO'11 Proceedings of the 15th international conference on Integer programming and combinatoral optimization
Polynomial integrality gaps for strong SDP relaxations of Densest k-subgraph
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
IPCO'10 Proceedings of the 14th international conference on Integer Programming and Combinatorial Optimization
Linear vs. semidefinite extended formulations: exponential separation and strong lower bounds
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
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This work considers the problem of approximating fixed predicate constraint satisfaction problems (MAX k-CSP(P )). We show that if the set of assignments accepted by P contains the support of a balanced pairwise independent distribution over the domain of the inputs, then such a problem on n variables cannot be approximated better than the trivial (random) approximation, even using ***(n ) levels of the Sherali-Adams LP hierarchy. It was recently shown [3] that under the Unique Game Conjecture, CSPs with predicates with this condition cannot be approximated better than the trivial approximation. Our results can be viewed as an unconditional analogue of this result in the restricted computational model defined by the Sherali-Adams hierarchy. We also introduce a new generalization of techniques to define consistent "local distributions" over partial assignments to variables in the problem, which is often the crux of proving lower bounds for such hierarchies.