The Lovász Theta Function and a Semidefinite Programming Relaxation of Vertex Cover
SIAM Journal on Discrete Mathematics
The importance of being biased
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
O(√log n) approximation algorithms for min UnCut, min 2CNF deletion, and directed cut problems
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
On distance scales, embeddings, and efficient relaxations of the cut cone
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
The NP-completeness column: The many limits on approximation
ACM Transactions on Algorithms (TALG)
Minimum 2SAT-DELETION: Inapproximability results and relations to Minimum Vertex Cover
Discrete Applied Mathematics
Vertex cover might be hard to approximate to within 2-ε
Journal of Computer and System Sciences
On extracting consistent graphs in wireless sensor networks
International Journal of Sensor Networks
A better list heuristic for vertex cover
Information Processing Letters
The 0-1 inverse maximum stable set problem
Discrete Applied Mathematics
Distributed weighted vertex cover via maximal matchings
ACM Transactions on Algorithms (TALG)
On hard instances of approximate vertex cover
ACM Transactions on Algorithms (TALG)
APPROX '07/RANDOM '07 Proceedings of the 10th International Workshop on Approximation and the 11th International Workshop on Randomization, and Combinatorial Optimization. Algorithms and Techniques
Expander flows, geometric embeddings and graph partitioning
Journal of the ACM (JACM)
Analyses of simple hybrid algorithms for the vertex cover problem*
Evolutionary Computation
Vertex cover approximations on random graphs
WEA'07 Proceedings of the 6th international conference on Experimental algorithms
Vertex cover resists SDPs tightened by local hypermetric inequalities
IPCO'08 Proceedings of the 13th international conference on Integer programming and combinatorial optimization
On the approximability of the vertex cover and related problems
AAIM'10 Proceedings of the 6th international conference on Algorithmic aspects in information and management
The positive semidefinite Grothendieck problem with rank constraint
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Inapproximability of hypergraph vertex cover and applications to scheduling problems
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Approximated distributed minimum vertex cover algorithms for bounded degree graphs
COCOON'10 Proceedings of the 16th annual international conference on Computing and combinatorics
Minimum vertex cover in rectangle graphs
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
An approximation algorithm dependent on edge-coloring number for minimum maximal matching problem
Information Processing Letters
Minimum vertex cover in rectangle graphs
Computational Geometry: Theory and Applications
Local search with edge weighting and configuration checking heuristics for minimum vertex cover
Artificial Intelligence
Nearly optimal NP-hardness of vertex cover on k-uniform k-partite hypergraphs
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Kernels for the vertex cover problem on the preferred attachment model
WEA'06 Proceedings of the 5th international conference on Experimental Algorithms
How to trim a MST: A 2-Approximation algorithm for minimum cost-tree cover
ACM Transactions on Algorithms (TALG)
An edge-reduction algorithm for the vertex cover problem
Operations Research Letters
NuMVC: an efficient local search algorithm for minimum vertex cover
Journal of Artificial Intelligence Research
Flip distance between triangulations of a planar point set is APX-hard
Computational Geometry: Theory and Applications
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We reduce the approximation factor for Vertex Cover to $2 - \theta(\frac{1}{\sqrt{{\rm log} n}})$ (instead of the previous $2- \theta(\frac{{\rm log log} n}{{\rm log}\ n})$, obtained by Bar-Yehuda and Even [3], and by Monien and Speckenmeyer[11]). The improvement of the vanishing factor comes as an application of the recent results of Arora, Rao, and Vazirani [2] that improved the approximation factor of the sparsest cut and balanced cut problems. In particular, we use the existence of two big and well-separated sets of nodes in the solution of the semidefinite relaxation for balanced cut, proven in [2]. We observe that a solution of the semidefinite relaxation for vertex cover, when strengthened with the triangle inequalities, can be transformed into a solution of a balanced cut problem, and therefore the existence of big well-separated sets in the sense of [2] translates into the existence of a big independent set.