Letchford, A N (2002) *Binary clutter inequalities for integer programs.* Working Paper. The Department of Management Science, Lancaster University.

## Abstract

We introduce a new class of valid inequalities for general integer linear programs, called binary clutter (BC) inequalities. They include the {0, 1/2}-cuts of Caprara and Fischetti as a special case and have some interesting connections to binary matroids, binary clutters and Gomory corner polyhedra. We show that the separation problem for BC-cuts is strongly NP-hard in general, but polynomially solvable in certain special cases. As a by-product we also obtain new conditions under which {0, 1/2}-cuts can be separated in polynomial time. These ideas are then illustrated using the Travelling Salesman Problem (TSP) as an example. This leads to an interesting link between the TSP and two apparently unrelated problems, the T-join and max-cut problems.

Item Type: | Monograph (Working Paper) |
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Additional Information: | This was eventually published as: A.N. Letchford (2003) Binary clutter inequalities for integer programs. Math. Program., 98(1-3), 201-221. |

Uncontrolled Keywords: | integer programming ; cutting planes ; matroid theory ; binary clutters ; travelling salesman problem |

Subjects: | |

Departments: | Lancaster University Management School > Management Science |

ID Code: | 48638 |

Deposited By: | ep_importer_pure |

Deposited On: | 11 Jul 2011 22:04 |

Refereed?: | No |

Published?: | Published |

Last Modified: | 09 Apr 2014 20:50 |

Identification Number: | |

URI: | http://eprints.lancs.ac.uk/id/eprint/48638 |

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