Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming

@article{Goemans1995ImprovedAA,
title={Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming},
author={M. Goemans and David P. Williamson},
journal={J. ACM},
year={1995},
volume={42},
pages={1115-1145}
}

We present randomized approximation algorithms for the maximum cut (MAX CUT) and maximum 2-satisfiability (MAX 2SAT) problems that always deliver solutions of expected value at least.87856 times the optimal value. These algorithms use a simple and elegant technique that randomly rounds the solution to a nonlinear programming relaxation. This relaxation can be interpreted both as a semidefinite program and as an eigenvalue minimization problem. The best previously known approximation algorithms… CONTINUE READING