Abstract
We present a unified semidefinite programming hierarchies rounding approximation algorithm for a class of maximum graph bisection problems with improved approximation ratios. Under the above algorithmic framework, we show that the approximation ratios of Max-\(\frac{n}{2}\)-cut, Max-\(\frac{n}{2}\)-dense-subgraph, and Max-\(\frac{n}{2}\)-vertex-cover are equal to those of Max-\(\frac{n}{2}\)-uncut, Max-\(\frac{n}{2}\)-directed-cut, and Max-\(\frac{n}{2}\)-directed-uncut, respectively.
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Acknowledgments
The research of the first author is supported by NSF of China (No. 11071268). The second author’s research is supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) grant 283106. The third author’s research is supported by NSF of China (No. 11371001), Scientific Research Common Program of Beijing Municipal Commission of Education (No. KM201210005033), and China Scholarship Council. A preliminary version of this paper appears in Wu et al. (2013).
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Wu, C., Du, D. & Xu, D. An improved semidefinite programming hierarchies rounding approximation algorithm for maximum graph bisection problems. J Comb Optim 29, 53–66 (2015). https://doi.org/10.1007/s10878-013-9673-1
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DOI: https://doi.org/10.1007/s10878-013-9673-1