A hierarchy of relaxation between the continuous and convex hull representations
SIAM Journal on Discrete Mathematics
.879-approximation algorithms for MAX CUT and MAX 2SAT
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
A threshold of ln n for approximating set cover (preliminary version)
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Some optimal inapproximability results
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
The importance of being biased
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
When Does the Positive Semidefiniteness Constraint Help in Lifting Procedures?
Mathematics of Operations Research
The Probable Value of the Lovász-Schrijver Relaxations for Maximum Independent Set
SIAM Journal on Computing
Proving Integrality Gaps without Knowing the Linear Program
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
A new multilayered PCP and the hardness of hypergraph vertex cover
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
A 7/8-Approximation Algorithm for MAX 3SAT?
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Rank Bounds and Integrality Gaps for Cutting Planes Procedures
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Expander flows, geometric embeddings and graph partitioning
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Eulogy: Michael (Misha) Alekhnovich 1978-2006
ACM SIGACT News
Compacting cuts: a new linear formulation for minimum cut
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Linear programming relaxations of maxcut
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
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 '07/RANDOM '07 Proceedings of the 10th International Workshop on Approximation and the 11th International Workshop on Randomization, and Combinatorial Optimization. Algorithms and Techniques
Exponential lower bounds and integrality gaps for tree-like Lovász-Schrijver procedures
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Tight rank lower bounds for the Sherali–Adams proof system
Theoretical Computer Science
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
Compacting cuts: A new linear formulation for minimum cut
ACM Transactions on Algorithms (TALG)
Optimal Sherali-Adams Gaps from Pairwise Independence
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
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
Integrality Gaps of $2-o(1)$ for Vertex Cover SDPs in the Lovász-Schrijver Hierarchy
SIAM Journal on 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
Exponential Lower Bounds and Integrality Gaps for Tree-Like Lovász-Schrijver Procedures
SIAM Journal on Computing
Lift-and-Project methods for set cover and knapsack
WADS'13 Proceedings of the 13th international conference on Algorithms and Data Structures
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Lovász and Schrijver described a generic method of tightening the LP and SDP relaxation for any 0-1 optimization problem. These tightened relaxations were the basis of several celebrated approximation algorithms (such as for max-cu , max-3sat, and sparsest cut).We prove strong inapproximability results in this model for well-known problems such as max-3sat, hypergraph vertex cover and set cover. We show that the relaxations produced by as many as Ω(n) rounds of the LS+ procedure do not allow nontrivial approximation, thus ruling out the possibility that the LS+ approach gives even slightly subexponential approximation algorithms for these problems.We also point out why our results are somewhat incomparable to known inapproximability results proved using PCPs, and formalize several interesting open questions.