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
On a Representation of the Matching Polytope Via Semidefinite Liftings
Mathematics of Operations Research
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
On the Matrix-Cut Rank of Polyhedra
Mathematics of Operations Research
A new multilayered PCP and the hardness of hypergraph vertex cover
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
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
Towards strong nonapproximability results in the Lovasz-Schrijver hierarchy
Proceedings of the thirty-seventh 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
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“Lift-and-project” procedures, which tighten linear relaxations over many rounds, yield many of the celebrated approximation algorithms of the past decade or so, even after only a constant number of rounds (e.g., for max-cut, max-3sat and sparsest-cut). Thus proving super-constant round lowerbounds on such procedures may provide evidence about the inapproximability of a problem. We prove an integrality gap of k–ε for linear relaxations obtained from the trivial linear relaxation for k-uniform hypergraph vertex cover by applying even Ω(loglog n) rounds of Lovász and Schrijver's LS lift-and-project procedure. In contrast, known PCP-based results only rule out k–1–ε approximations. Our gaps are tight since the trivial linear relaxation gives a k-approximation.