# 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={Michel X. 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…

## 3,441 Citations

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