Conforti, Michele, Gerards, Bert and Zambelli, Giacomo
(2007)
*Mixed-integer vertex covers on bipartite graphs.*
In: Fischetti, Matteo and Williamson, David .P., (eds.)
Integer Programming and Combinatorial Optimization.
Lecture notes in computer science (4513).
Springer, Berlin, Germany, pp. 324-336.
ISBN 9783540727927

## Abstract

Let A be the edge-node incidence matrix of a bipartite graph G = (U,V;E), I be a subset of the nodes of G, and b be a vector such that 2b is integral. We consider the following mixed-integer set: We characterize conv(X(G,b,I)) in its original space. That is, we describe a matrix (C,d) such that conv(X(G,b,I)) = {x : Cx ≥ d}. This is accomplished by computing the projection onto the space of the x-variables of an extended formulation, given in [1], for conv(X(G,b,I)). We then give a polynomial-time algorithm for the separation problem for conv(X(G,b,I)), thus showing that the problem of optimizing a linear function over the set X(G,b,I) is solvable in polynomial time.

Item Type: | Book Section |
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Official URL: | http://www.informatik.uni-trier.de/~ley/db/conf/ip... |

Additional Information: | © 2007 Springer-Verlag Berlin Heidelberg |

Divisions: | Management |

Subjects: | Q Science > Q Science (General) Q Science > QA Mathematics |

Sets: | Departments > Management |

Date Deposited: | 25 Jan 2011 13:53 |

Last Modified: | 30 Jan 2019 13:57 |

Projects: | 12th International IPCO Conference, Ithaca, NY, USA |

URI: | http://eprints.lse.ac.uk/id/eprint/31690 |

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