A hierarchy of relaxation between the continuous and convex hull representations
SIAM Journal on Discrete Mathematics
Proving Integrality Gaps without Knowing the Linear Program
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
New Lower Bounds for Vertex Cover in the Lovasz-Schrijver Hierarchy
CCC '06 Proceedings of the 21st Annual IEEE Conference on Computational Complexity
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
Max cut and the smallest eigenvalue
Proceedings of the forty-first annual ACM symposium on Theory of computing
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
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
Approximate Lasserre integrality gap for unique games
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Towards Sharp Inapproximability for Any 2-CSP
SIAM Journal on Computing
Local Global Tradeoffs in Metric Embeddings
SIAM Journal on Computing
How well can primal-dual and local-ratio algorithms perform?
ACM Transactions on Algorithms (TALG)
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
Sherali-Adams relaxations and indistinguishability in counting logics
Proceedings of the 3rd Innovations in Theoretical Computer Science Conference
Polynomial integrality gaps for strong SDP relaxations of Densest k-subgraph
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
On the rank of cutting-plane proof systems
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
Exponential Lower Bounds and Integrality Gaps for Tree-Like Lovász-Schrijver Procedures
SIAM Journal on Computing
Proceedings of the 5th conference on Innovations in theoretical computer science
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We study linear programming relaxations of Vertex Cover and Max Cutarising from repeated applications of the "lift-and-project" method of Lovasz and Schrijver starting from the standard linear programming relaxation. For Vertex Cover, Arora, Bollobas, Lovasz and Tourlakis prove thatthe integrality gap remains at least 2-ε after Ωε(log n) rounds, where n is the number ofvertices, and Tourlakis proves that integrality gap remains at least 1.5-ε after Ω((log n)2) rounds. Fernandez de laVega and Kenyon prove that the integrality gap of Max Cut is at most 12 + ε after any constant number of rounds. (Theirresult also applies to the more powerful Sherali-Adams method. We prove that the integrality gap of Vertex Cover remains at least 2-ε after Ωε (n) rounds, and that theintegrality gap of Max Cut remains at most 1/2 +ε after Ωε(n) rounds.