Abstract
In this paper, we propose 0.863-approximation algorithm for MAX DICUT. The approximation ratio is better than the previously known result by Zwick, which is equal to 0.8596434254.
The algorithm solves the SDP relaxation problem proposed by Goemans and Williamson for the first time. We do not use the ‘rotation’ technique proposed by Feige and Goemans. We improve the approximation ratio by using hyperplane separation technique with skewed distribution function on the sphere. We introduce a class of skewed distribution functions defined on the 2-dimensional sphere satisfying that for any function in the class, we can design a skewed distribution functions on any dimensional sphere without decreasing the approximation ratio. We also searched and found a good distribution function defined on the 2-dimensional sphere numerically.
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References
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© 2001 Springer-Verlag Berlin Heidelberg
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Matuura, S., Matsui, T. (2001). 0.863-Approximation Algorithm for MAX DICUT. In: Goemans, M., Jansen, K., Rolim, J.D.P., Trevisan, L. (eds) Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques. RANDOM APPROX 2001 2001. Lecture Notes in Computer Science, vol 2129. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44666-4_17
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DOI: https://doi.org/10.1007/3-540-44666-4_17
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-42470-3
Online ISBN: 978-3-540-44666-8
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