The Lovász Theta Function and a Semidefinite Programming Relaxation of Vertex Cover
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On semidefinite programming relaxations for graph coloring and vertex cover
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Integrality gaps of 2 - o(1) for Vertex Cover SDPs in the Lovész-Schrijver Hierarchy
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Analytical and experimental comparison of six algorithms for the vertex cover problem
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Approximating vertex cover in dense hypergraphs
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Vertex cover in graphs with locally few colors
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The VLDB Journal — The International Journal on Very Large Data Bases
Approximating vertex cover using edge-based representations
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Theoretical Computer Science
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We reduce the approximation factor for the vertex cover to 2 − Θ (1/&sqrt;logn) (instead of the previous 2 − Θ ln ln n/2ln n obtained by Bar-Yehuda and Even [1985] and Monien and Speckenmeyer [1985]). The improvement of the vanishing factor comes as an application of the recent results of Arora et al. [2004] 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 by Arora et al. [2004]. 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 Arora et al. [2004] translates into the existence of a big independent set.