{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,11]],"date-time":"2026-04-11T00:59:16Z","timestamp":1775869156673,"version":"3.50.1"},"reference-count":13,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2007,6,27]],"date-time":"2007-06-27T00:00:00Z","timestamp":1182902400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Theory Comput Syst"],"published-print":{"date-parts":[[2008,2]]},"DOI":"10.1007\/s00224-007-9005-x","type":"journal-article","created":{"date-parts":[[2007,6,28]],"date-time":"2007-06-28T20:32:47Z","timestamp":1183062767000},"page":"143-156","source":"Crossref","is-referenced-by-count":6,"title":["A Generalization of Magic Squares with Applications to Digital Halftoning"],"prefix":"10.1007","volume":"42","author":[{"given":"Boris","family":"Aronov","sequence":"first","affiliation":[]},{"given":"Tetsuo","family":"Asano","sequence":"additional","affiliation":[]},{"given":"Yosuke","family":"Kikuchi","sequence":"additional","affiliation":[]},{"given":"Subhas C.","family":"Nandy","sequence":"additional","affiliation":[]},{"given":"Shinji","family":"Sasahara","sequence":"additional","affiliation":[]},{"given":"Takeaki","family":"Uno","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2007,6,27]]},"reference":[{"key":"9005_CR1","doi-asserted-by":"crossref","unstructured":"Aggarwal, A., Klawe, M., Moran, S., Shor, P., Wilber, R.: Geometric applications of a matrix searching algorithm. In: Proc. 2nd ACM Symposium on Computational Geometry, pp.\u00a0285\u2013292 (1986)","DOI":"10.1145\/10515.10546"},{"issue":"2","key":"9005_CR2","first-page":"159","volume":"E86-D","author":"T. Asano","year":"2003","unstructured":"Asano, T.: Digital halftoning: algorithm engineering challenges. IEICE Trans. Inf. Syst. E86-D(2), 159\u2013178 (2003)","journal-title":"IEICE Trans. Inf. Syst."},{"key":"9005_CR3","unstructured":"Asano, T., Obokata, K., Katoh, N., Tokuyama, T.: Matrix rounding under the L p -discrepancy measure and its application to digital halftoning. In: Proc. ACM-SIAM Symposium on Discrete Algorithms, San Francisco, pp. 896\u2013904 (2002)"},{"key":"9005_CR4","series-title":"Lecture Notes in Comput. Sci.","doi-asserted-by":"crossref","DOI":"10.1007\/3-540-36586-9","volume-title":"Theoretical Foundations of Computer Vision: Geometry, Morphology, and Computational Imaging","author":"T. Asano","year":"2003","unstructured":"Asano, T., Katoh, N., Obokata, K., Tokuyama, T.: Combinatorial and geometric problems related to digital halftoning. In: Theoretical Foundations of Computer Vision: Geometry, Morphology, and Computational Imaging. Lecture Notes in Comput. Sci., vol.\u00a02616. Springer, New York (2003)"},{"key":"9005_CR5","unstructured":"Bayer, B.E.: An optimum method for two-level rendition of continuous-tone pictures. In: Conference Record, IEEE International Conference on Communications, vol. 1, pp. (26-11)\u2013(26-15) (1973)"},{"key":"9005_CR6","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511626371","volume-title":"The Discrepancy Method: Randomness and Complexity","author":"B. Chazelle","year":"2000","unstructured":"Chazelle, B.: The Discrepancy Method: Randomness and Complexity. Cambridge University Press, Cambridge (2000)"},{"key":"9005_CR7","unstructured":"Heinz, H.D.: Magic squares, magic stars & other patterns. Web site, http:\/\/www.geocities.com\/CapeCanaveral\/Launchpad\/4057\/"},{"key":"9005_CR8","series-title":"Fundamental Algorithms","volume-title":"The Art of Computer Programming, Volume 1","author":"D.E. Knuth","year":"1997","unstructured":"Knuth, D.E.: The Art of Computer Programming, Volume 1, Fundamental Algorithms, 3rd edn. Addison-Wesley, Reading (1997)","edition":"3"},{"key":"9005_CR9","volume-title":"Geometric Discrepancy","author":"J. Matou\u0161ek","year":"1991","unstructured":"Matou\u0161ek, J.: Geometric Discrepancy. Springer, New York (1991)"},{"issue":"11","key":"9005_CR10","doi-asserted-by":"crossref","first-page":"1920","DOI":"10.1364\/JOSAA.9.001920","volume":"9","author":"T. Mitsa","year":"1992","unstructured":"Mitsa, T., Parker, K.J.: Digital halftoning technique using a\u00a0blue-noise mask. J. Opt. Soc. Am. A 9(11), 1920\u20131929 (1992)","journal-title":"J. Opt. Soc. Am. A"},{"issue":"1","key":"9005_CR11","doi-asserted-by":"crossref","first-page":"56","DOI":"10.1109\/5.3288","volume":"76","author":"R.A. Ulichney","year":"1988","unstructured":"Ulichney, R.A.: Dithering with blue noise. Proc. IEEE 76(1), 56\u201379, (1988)","journal-title":"Proc. IEEE"},{"key":"9005_CR12","series-title":"Proc. SPIE","doi-asserted-by":"crossref","first-page":"332","DOI":"10.1117\/12.152707","volume-title":"IS&T\/SPIE Symposium on Electronic Imaging Science and Technology, Proceedings of Conf. Human Vision, Visual Processing and Digital Display IV","author":"R. Ulichney","year":"1993","unstructured":"Ulichney, R.: The void-and-cluster method for dither array generation. In: Allebach, J. (ed.) IS&T\/SPIE Symposium on Electronic Imaging Science and Technology, Proceedings of Conf. Human Vision, Visual Processing and Digital Display IV. Proc. SPIE, vol.\u00a01913, pp.\u00a0332\u2013343. Wiley, New York (1993)"},{"key":"9005_CR13","doi-asserted-by":"crossref","first-page":"92","DOI":"10.1117\/12.165114","volume":"3","author":"M. Yao","year":"1994","unstructured":"Yao, M., Parker, K.J.: Modified approach to the construction of a blue noise mask. J. Electron. Imag. 3, 92\u201397 (1994)","journal-title":"J. Electron. Imag."}],"container-title":["Theory of Computing Systems"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00224-007-9005-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00224-007-9005-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00224-007-9005-x","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,24]],"date-time":"2019-05-24T11:51:34Z","timestamp":1558698694000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00224-007-9005-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,6,27]]},"references-count":13,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2008,2]]}},"alternative-id":["9005"],"URL":"https:\/\/doi.org\/10.1007\/s00224-007-9005-x","relation":{},"ISSN":["1432-4350","1433-0490"],"issn-type":[{"value":"1432-4350","type":"print"},{"value":"1433-0490","type":"electronic"}],"subject":[],"published":{"date-parts":[[2007,6,27]]}}}