A better approximation ratio for the vertex cover problem

@article{Karakostas2009ABA,
  title={A better approximation ratio for the vertex cover problem},
  author={George Karakostas},
  journal={Electron. Colloquium Comput. Complex.},
  year={2009}
}
  • George Karakostas
  • Published 2009
  • Computer Science, Mathematics
  • Electron. Colloquium Comput. Complex.
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… Expand
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TLDR
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It is shown that a large family of LP and SDP based algorithms fail to produce an approximation for Vertex Cover better than 2.36, and an integrality gap of 2 - o(lfloor)for Vertex cover SDPs obtained by tightening the standard LP relaxation with Omega(radiclog n/ log log n) rounds of LS+. Expand
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  • 21st Annual IEEE Conference on Computational Complexity (CCC'06)
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TLDR
It is conjecture that the new technique introduced to prove the lower bound for LS0, LS and LS+, the "fence" method, may lead to linear or nearly linear LS round lower bounds for VERTEX COVER, which are conjecture to be as large as the girth of the input graph for interesting graphs. Expand
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