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SIAM Journal on Discrete Mathematics
A lift-and-project cutting plane algorithm for mixed 0-1 programs
Mathematical Programming: Series A and B
MAX-CUT has a randomized approximation scheme in dense graphs
Random Structures & Algorithms
How good is the Goemans-Williamson MAX CUT algorithm?
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Polynomial time approximation schemes for dense instances of NP -hard problems
Journal of Computer and System Sciences
On the integrality ratio of semidefinite relaxations of MAX CUT
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
An Explicit Equivalent Positive Semidefinite Program for Nonlinear 0-1 Programs
SIAM Journal on Optimization
Proving Integrality Gaps without Knowing the Linear Program
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
The regularity lemma and approximation schemes for dense problems
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Property testing and its connection to learning and approximation
FOCS '96 Proceedings of the 37th 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
Random sampling and approximation of MAX-CSPs
Journal of Computer and System Sciences - STOC 2002
A Comparison of the Sherali-Adams, Lovász-Schrijver, and Lasserre Relaxations for 0--1 Programming
Mathematics of Operations Research
Optimal Inapproximability Results for Max-Cut and Other 2-Variable CSPs?
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Towards strong nonapproximability results in the Lovasz-Schrijver hierarchy
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Tight integrality gaps for Lovasz-Schrijver LP relaxations of vertex cover and max cut
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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
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
Max cut and the smallest eigenvalue
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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
Robust Algorithms for on Minor-Free Graphs Based on the Sherali-Adams Hierarchy
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
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ACM Transactions on Algorithms (TALG)
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IPCO'11 Proceedings of the 15th international conference on Integer programming and combinatoral optimization
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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
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ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
Proceedings of the 5th conference on Innovations in theoretical computer science
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It is well-known that the integrality gap of the usual linear programming relaxation for Maxcut is 2 - ε. For general graphs, we prove that for any ε and any fixed bound k, adding linear constraints of support bounded by k does not reduce the gap below 2 - ε. We generalize this to prove that for any ε and any fixed bound k, strengthening the usual linear programming relaxation by doing κ rounds of Sherali-Adams lift-and-project does not reduce the gap below 2 - ε. On the other hand, we prove that for dense graphs, this gap drops to 1 + ε after adding all linear constraints of support bounded by some constant depending on ε.