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FSTTCS

2001

Springer

2001

Springer

Semideﬁnite programming based approximation algorithms, such as the Goemans and Williamson approximation algorithm for the MAX CUT problem, are usually shown to have certain performance guarantees using local ratio techniques. Are the bounds obtained in this way tight? This problem was considered before by Karloﬀ [SIAM J. Comput., 29 (1999), pp. 336–350] and by Alon and Sudakov [Combin. Probab. Comput., 9 (2000), pp. 1–12]. Here we further extend their results and show, for the ﬁrst time, that the local analyses of the Goemans and Williamson MAX CUT algorithm, as well as its extension by Zwick, are tight for every possible relative size of the maximum cut in the sense that the expected value of the solutions obtained by the algorithms may be as small as the analyses ensure. We also obtain similar results for a related problem. Our approach is quite general and could possibly be applied to some additional problems and algorithms. Key words. MAX CUT, semideﬁnite programming, ...

Related Content

Added |
28 Jul 2010 |

Updated |
28 Jul 2010 |

Type |
Conference |

Year |
2001 |

Where |
FSTTCS |

Authors |
Uri Zwick |

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