Abstract
MAX CUT is the problem of partitioning the vertices of a graph into two sets, maximizing the number of edges joining these sets. Goemans and Williamson gave an algorithm that approximates MAX CUT within a ratio of 0.87856. Their algorithm first uses a semidefinite programming relaxation of MAX CUT that embeds the vertices of the graph on the surface of an n dimensional sphere, and then cuts the sphere in two at random.
In this survey we shall review several variations of this algorithm which offer improved approximation ratios for some special families of instances of MAX CUT, as well as for problems related to MAX CUT.
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Feige, U. (1999). Randomized Rounding for Semidefinite Programs – Variations on the MAX CUT Example. In: Hochbaum, D.S., Jansen, K., Rolim, J.D.P., Sinclair, A. (eds) Randomization, Approximation, and Combinatorial Optimization. Algorithms and Techniques. RANDOM APPROX 1999 1999. Lecture Notes in Computer Science, vol 1671. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-48413-4_20
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DOI: https://doi.org/10.1007/978-3-540-48413-4_20
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