Randomized Rounding for Semidefinite Programs – Variations on the MAX CUT Example [chapter]

Uriel Feige
1999 Lecture Notes in Computer Science  
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
more » ... er improved approximation ratios for some special families of instances of MAX CUT, as well as for problems related to MAX CUT.
doi:10.1007/978-3-540-48413-4_20 fatcat:lrsup62rrbghtlhlydfowkx7be