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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.

Keywords

Approximation Ratio Semidefinite Program Geometric Program Annual IEEE Symposium Integer Quadratic Program 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Uriel Feige
    • 1
  1. 1.Weizmann InstituteRehovotIsrael

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