Letchford, A N and Sorensen, M M (2008) *Binary positive semidefinite matrices and associated integer polytopes.* In: Integer Programming and Combinatorial Optimization : Proceedings of the 13th International IPCO Conference. Lecture Notes in Computer Science . Springer, Berlin, pp. 125-139. ISBN 3540688862

## Abstract

We consider the positive semidefinite (psd) matrices with binary entries. We give a characterisation of such matrices, along with a graphical representation. We then move on to consider the associated integer polytopes. Several important and well-known integer polytopes (the cut, boolean quadric, multicut and clique partitioning polytopes) are shown to arise as projections of binary psd polytopes. Finally, we present various valid inequalities for binary psd polytopes, and show how they relate to inequalities known for the simpler polytopes mentioned. Along the way, we answer an open question in the literature on the max-cut problem, by showing that the so-called k-gonal inequalities define a polytope.

Item Type: | Contribution in Book/Report/Proceedings |
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Additional Information: | The full version of this paper appeared as: A.N. Letchford & M.M. Sørensen (2012) Binary positive semidefinite matrices and associated integer polytopes. Math. Program., 131(1), 253-271. |

Subjects: | |

Departments: | Lancaster University Management School > Management Science |

ID Code: | 46938 |

Deposited By: | ep_importer_pure |

Deposited On: | 11 Jul 2011 21:09 |

Refereed?: | Yes |

Published?: | Published |

Last Modified: | 19 Jun 2018 05:47 |

Identification Number: | |

URI: | http://eprints.lancs.ac.uk/id/eprint/46938 |

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