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
Integrality gaps for Sherali-Adams relaxations
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
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
Hardness amplification in proof complexity
Proceedings of the forty-second ACM symposium on Theory of computing
Graph expansion and the unique games conjecture
Proceedings of the forty-second ACM symposium on Theory of computing
Approximating sparsest cut in graphs of bounded treewidth
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on 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
Integrality Gaps of $2-o(1)$ for Vertex Cover SDPs in the Lovász-Schrijver Hierarchy
SIAM Journal on Computing
Polynomial integrality gaps for strong SDP relaxations of Densest k-subgraph
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Exponential Lower Bounds and Integrality Gaps for Tree-Like Lovász-Schrijver Procedures
SIAM Journal on Computing
| Hi-index | 0.00 |
We study semidefinite programming relaxations of Vertex Cover arising from repeated applications of the LS+ "lift-and-project" method of Lovasz and Schrijver starting from the standard linear programming relaxation. Goemans and Kleinberg prove that after one round of LS+ the integrality gap remains arbitrarily close to 2. Charikar proves an integrality gap of 2, later strengthened by Hatami, Magen, and Markakis, for stronger relaxations that are, however, incomparable with two rounds of LS+. Subsequent work by Georgiou, Magen, Pitassi, and Tourlakis shows that the integrality gap remains 2 - \varepsilon after \Omega(\sqrt {\frac{{\log n}} {{\log \log n}}} ) rounds [?]. We prove that the integrality gap remains at least 7/6 - \varepsilon after c_{\varepsilon}n rounds, where n is the number of vertices and c_\varepsilon \ge 0 is a constant that depends only on \varepsilon.