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Recognizing balanceable matrices

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

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Identification Number: 10.1007/s10107-005-0647-7


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
Official URL:
Additional Information: © 2006 Springer-Verlag
Divisions: Management
Subjects: Q Science > QA Mathematics
Date Deposited: 26 Jan 2011 14:03
Last Modified: 16 May 2024 00:30

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