Lodi, A and Letchford, A N (2002) *Polynomial-time separation of simple comb inequalities.* In: Integer Programming and Combinatorial Optimization. Lecture Notes in Computer Science . Springer, Berlin, pp. 93-108. ISBN 3-540-43676-6

## Abstract

The comb inequalities are a well-known class of facet-inducing inequalities for the Traveling Salesman Problem, defined in terms of certain vertex sets called the handle and the teeth. We say that a comb inequality is simple if the following holds for each tooth: either the intersection of the tooth with the handle has cardinality one, or the part of the tooth outside the handle has cardinality one, or both. The simple comb inequalities generalize the classical 2-matching inequalities of Edmonds, and also the so-called Chv´atal comb inequalities. In 1982, Padberg and Rao gave a polynomial-time algorithm for separating the 2-matching inequalities – i.e., for testing if a given fractional solution to an LP relaxation violates a 2-matching inequality. We extend this significantly by giving a polynomial-time algorithm for separating the simple comb inequalities. The key is a result due to Caprara and Fischetti.

Item Type: | Contribution in Book/Report/Proceedings |
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Additional Information: | The full version of this paper appeared as: L.K. Fleischer, A.N. Letchford & A. Lodi (2006) Polynomial-time separation of a superclass of simple comb inequalities. Math. Oper. Res., 31(4), 696-713. |

Uncontrolled Keywords: | travelling salesman problem |

Subjects: | |

Departments: | Lancaster University Management School > Management Science |

ID Code: | 46124 |

Deposited By: | ep_importer_pure |

Deposited On: | 11 Jul 2011 20:56 |

Refereed?: | Yes |

Published?: | Published |

Last Modified: | 21 Oct 2017 01:26 |

Identification Number: | |

URI: | http://eprints.lancs.ac.uk/id/eprint/46124 |

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