Two-prover one-round proof systems: their power and their problems (extended abstract)
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
An approximation algorithm for MAX DICUT with given sizes of parts
APPROX '00 Proceedings of the Third International Workshop on Approximation Algorithms for Combinatorial Optimization
Approximating the value of two power proof systems, with applications to MAX 2SAT and MAX DICUT
ISTCS '95 Proceedings of the 3rd Israel Symposium on the Theory of Computing Systems (ISTCS'95)
Improved Rounding Techniques for the MAX 2-SAT and MAX DI-CUT Problems
Proceedings of the 9th International IPCO Conference on Integer Programming and Combinatorial Optimization
ISAAC '02 Proceedings of the 13th International Symposium on Algorithms and Computation
Fast SDP algorithms for constraint satisfaction problems
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Towards Sharp Inapproximability for Any 2-CSP
SIAM Journal on Computing
Improved approximation algorithms for MAX NAE-SAT and MAX SAT
WAOA'05 Proceedings of the Third international conference on Approximation and Online Algorithms
Rounding two and three dimensional solutions of the SDP relaxation of MAX CUT
APPROX'05/RANDOM'05 Proceedings of the 8th international workshop on Approximation, Randomization and Combinatorial Optimization Problems, and Proceedings of the 9th international conference on Randamization and Computation: algorithms and techniques
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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.