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Recognizing balanceable matrices

By Michele Conforti and Giacomo Zambelli

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

Topics: QA Mathematics
Publisher: Springer
Year: 2006
DOI identifier: 10.1007/s10107-005-0647-7
OAI identifier: oai:eprints.lse.ac.uk:31723
Provided by: LSE Research Online
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