Towards strong nonapproximability results in the Lovasz-Schrijver hierarchy
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Discrete Applied Mathematics
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
How hard is it to approximate the best Nash equilibrium?
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
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
On linear and semidefinite programming relaxations for hypergraph matching
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
How well can primal-dual and local-ratio algorithms perform?
ACM Transactions on Algorithms (TALG)
Inapproximability of NP-complete variants of nash equilibrium
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
How Hard Is It to Approximate the Best Nash Equilibrium?
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
Statistical algorithms and a lower bound for detecting planted cliques
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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Lov{ász and Schrijver [SIAM J. Optim., 1 (1991), pp. 166--190] devised a lift-and-project method that produces a sequence of convex relaxations for the problem of finding in a graph an independent set (or a clique) of maximum size. Each relaxation in the sequence is tighter than the one before it, while the first relaxation is already at least as strong as the Lov{ász theta function [IEEE Trans. Inform. Theory, 25 (1979), pp. 1--7]. We show that on a random graph Gn,1/2, the value of the rth relaxation in the sequence is roughly \rule{0pt}{7pt}$\smash{\sqrt{\rule{0pt}{7pt}\smash{n/2^r}}}$, almost surely. It follows that for those relaxations known to be efficiently computable, namely, for r=O(1), the value of the relaxation is comparable to the theta function. Furthermore, a perfectly tight relaxation is almost surely obtained only at the $r=\Theta(\log n)$ relaxation in the sequence.