Conforti, Michele and Zambelli, Giacomo
(2006)
*Recognizing balanceable matrices.*
Mathematical Programming, 105 (2-3).
pp. 161-179.
ISSN 0025-5610

## Abstract

A 0/ ± 1 matrix is balanced if it does not contain a square submatrix with exactly two nonzero entries per row and per column in which the sum of all entries is 2 modulo 4. A 0/1 matrix is balanceable if its nonzero entries can be signed ±1 so that the resulting matrix is balanced. A signing algorithm due to Camion shows that the problems of recognizing balanced 0/ ± 1 matrices and balanceable 0/1 matrices are equivalent. Conforti, Cornu´ejols, Kapoor andVuˇskovi´c gave an algorithm to test if a 0/±1 matrix is balanced. Truemper has characterized balanceable 0/1 matrices in terms of forbidden submatrices. In this paper we give an algorithm that explicitly finds one of these forbidden submatrices or shows that none exists.

Item Type: | Article |
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Official URL: | http://www.springerlink.com/content/103081/ |

Additional Information: | © 2006 Springer-Verlag |

Divisions: | Management |

Subjects: | Q Science > QA Mathematics |

Date Deposited: | 26 Jan 2011 14:03 |

Last Modified: | 13 Sep 2024 22:08 |

URI: | http://eprints.lse.ac.uk/id/eprint/31723 |

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