Del Pia, Alberto and Zambelli, Giacomo
(2009)
*Half-integral vertex covers on bipartite bidirected graphs: total dual integrality and cut-rank.*
SIAM Journal on Discrete Mathematics, 23
(3).
pp. 1281-1296.
ISSN 0895-4801

## Abstract

In this paper we study systems of the form $b\leq Mx\leq d$, $l\leq x\leq u$, where $M$ is obtained from a totally unimodular matrix with two nonzero elements per row by multiplying by 2 some of its columns, and where $b,d,l,u$ are integral vectors. We give an explicit description of a totally dual integral system that describes the integer hull of the polyhedron $P$ defined by the above inequalities. Since the inequalities of such a totally dual integral system are Chvátal inequalities for $P$, our result implies that the matrix $M$ has cut-rank 1. We also derive a strongly polynomial time algorithm to find an integral optimal solution for the dual of the problem of minimizing a linear function with integer coefficients over the aforementioned totally dual integral system.

Item Type: | Article |
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Official URL: | http://scitation.aip.org/sidma |

Additional Information: | ©2009 Society for Industrial and Applied Mathematics |

Library of Congress subject classification: | Q Science > QA Mathematics |

Sets: | Departments > Management |

Rights: | http://www.lse.ac.uk/library/usingTheLibrary/academicSupport/OA/depositYourResearch.aspx |

Date Deposited: | 25 Jan 2011 13:23 |

URL: | http://eprints.lse.ac.uk/31687/ |

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