The Lovász Theta Function and a Semidefinite Programming Relaxation of Vertex Cover
SIAM Journal on Discrete Mathematics
On the power of unique 2-prover 1-round games
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
On semidefinite programming relaxations for graph coloring and vertex cover
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Improved Approximation Algorithms for the Vertex Cover Problem in Graphs and Hypergraphs
SIAM Journal on Computing
Expander flows, geometric embeddings and graph partitioning
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Local versus global properties of metric spaces
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Integrality gaps for sparsest cut and minimum linear arrangement problems
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Integrality gaps of 2 - o(1) for Vertex Cover SDPs in the Lovész-Schrijver Hierarchy
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
Local Global Tradeoffs in Metric Embeddings
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
A better approximation ratio for the vertex cover problem
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
A better approximation ratio for the vertex cover problem
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
Local Versus Global Properties of Metric Spaces
SIAM Journal on Computing
| Hi-index | 0.00 |
We consider the standard semidefinite programming (SDP) relaxation for VERTEX COVER to which all hypermetric inequalities supported on at most k vertices have been added. We show that the integrality gap for such SDPs remains 2-o(1) as long as k=O(√log n/ log log n). This extends successive results by Kleinberg-Goemans, Charikar and Hatami et al. which analyzed integrality gaps of the standard VERTEX COVER SDP relaxation as well as for SDPs tightened using triangle and pentagonal inequalities Our result is complementary but incomparable to a recent result by Georgiou et al. proving integrality gaps for VERTEX COVER SDPs in the Lovász-Schrijver hierarchy. One of our contributions is making explicit the difference between the SDPs considered by Georgiou et al. and those analyzed in the current paper.We do this by showing that VERTEX COVER SDPs in the Lovász-Schrijver hierarchy fail to satisfy any hypermetric constraints supported on independent sets of the input graph.