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MP

2007

2007

We present a probabilistic analysis of integer linear programs (ILPs). More speciﬁcally, we study ILPs in a so-called smoothed analysis in which it is assumed that ﬁrst an adversary speciﬁes the coeﬃcients of an integer program and then (some of) these coeﬃcients are randomly perturbed, e.g., using a Gaussian or a uniform distribution with small standard deviation. In this probabilistic model, we investigate structural properties of ILPs and apply them to the analysis of algorithms. For example, we prove a lower bound on the slack of the optimal solution. As a result of our analysis, we are able to specify the smoothed complexity of classes of ILPs in terms of their worst case complexity. For example, we obtain polynomial smoothed complexity for packing and covering problems with any ﬁxed number of constraints. Previous results of this kind were restricted to the case of binary programs.

Related Content

Added |
27 Dec 2010 |

Updated |
27 Dec 2010 |

Type |
Journal |

Year |
2007 |

Where |
MP |

Authors |
Heiko Röglin, Berthold Vöcking |

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