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Generalized Semimagic Squares for Digital Halftoning.

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Title: Generalized Semimagic Squares for Digital Halftoning.
Authors: Kawamura, Akitoshi kawamura@cs.toronto.edu
Source: Theory of Computing Systems. Oct2011, Vol. 49 Issue 3, p632-638. 7p.
Subjects: Theory of distributions (Functional analysis), Halftone process, Integer programming, Heuristic algorithms, Matrices (Mathematics), Irregularities of distribution (Number theory)
Abstract: Completing Aronov et al.'s study on zero-discrepancy matrices for digital halftoning, we determine all ( m, n, k, l) for which it is possible to put mn consecutive integers on an m× n board (with wrap-around) so that each k× l region has the same sum. For one of the cases where this is impossible, we give a heuristic method to find a matrix with small discrepancy. [ABSTRACT FROM AUTHOR]
Copyright of Theory of Computing Systems is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Generalized Semimagic Squares for Digital Halftoning.
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  Data: <searchLink fieldCode="AR" term="%22Kawamura%2C+Akitoshi%22">Kawamura, Akitoshi</searchLink><i> kawamura@cs.toronto.edu</i>
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  Data: Completing Aronov et al.'s study on zero-discrepancy matrices for digital halftoning, we determine all ( m, n, k, l) for which it is possible to put mn consecutive integers on an m× n board (with wrap-around) so that each k× l region has the same sum. For one of the cases where this is impossible, we give a heuristic method to find a matrix with small discrepancy. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Theory of Computing Systems is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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