Improved Approximation Algorithms for Maximum Cut andSatis ability Problems Using Semide nite Programming Michel

  • Michel X. Goemansy, David P. Williamsonz
  • Published 1995

Abstract

We present randomized approximation algorithms for the maximum cut (MAX CUT) and maximum 2-satissability (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 semideenite program and as an eigenvalue minimization problem. The best previously known approximation algorithms for these problems had performance guarantees of 1 2 for MAX CUT and 3 4 for MAX 2SAT. Slight extensions of our analysis lead to a .79607-approximation algorithm for the maximum directed cut problem (MAX DICUT) and a .758-approximation algorithm for MAX SAT, where the best previously known approximation algorithms had performance guarantees of 1 4 and 3 4 respectively. Our algorithm gives the rst substantial progress in approximating MAX CUT in nearly twenty years, and represents the rst use of semideenite programming in the design of approximation algorithms.

Cite this paper

@inproceedings{Goemansy1995ImprovedAA, title={Improved Approximation Algorithms for Maximum Cut andSatis ability Problems Using Semide nite Programming Michel}, author={Michel X. Goemansy and David P. Williamsonz}, year={1995} }