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Improved Approximation Algorithms for Maximum Cut and Satisfiability Problems Using Semidefinite Programming (1995)

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by M. X. Goemans , D.P. Williamson
Venue:Journal of the ACM
Citations:1208 - 13 self
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BibTeX

@ARTICLE{Goemans95improvedapproximation,
    author = {M. X. Goemans and D.P. Williamson},
    title = {Improved Approximation Algorithms for Maximum Cut and Satisfiability Problems Using Semidefinite Programming},
    journal = {Journal of the ACM},
    year = {1995},
    volume = {42},
    pages = {1115--1145}
}

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Abstract

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 for these problems had performance guarantees of ...

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