A better approximation ratio for the vertex cover problem

George Karakostas
2009 ACM Transactions on Algorithms  
We reduce the approximation factor for Vertex Cover to 2 − Θ( 1 √ log n ) (instead of the previous 2 − Θ( log log n log n ), obtained by , and by Monien and Speckenmeyer [10]). The improvement of the vanishing factor comes as an application of the recent results of Arora, Rao, and Vazirani [1] 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
more » ... the semidefinite relaxation for balanced cut, proven in [1] . 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 [1] translates into the existence of a big independent set.
doi:10.1145/1597036.1597045 fatcat:ilxodfx7c5fbtmp7qpz3melx24