{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,5]],"date-time":"2025-10-05T14:34:35Z","timestamp":1759674875779,"version":"3.37.3"},"reference-count":24,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2018,10,3]],"date-time":"2018-10-03T00:00:00Z","timestamp":1538524800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"name":"Austrian Science Fund","award":["P25648-N25"],"award-info":[{"award-number":["P25648-N25"]}]},{"DOI":"10.13039\/501100002428","name":"Austrian Science Fund","doi-asserted-by":"publisher","award":["P27891"],"award-info":[{"award-number":["P27891"]}],"id":[{"id":"10.13039\/501100002428","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Glob Optim"],"published-print":{"date-parts":[[2019,3]]},"DOI":"10.1007\/s10898-018-0711-5","type":"journal-article","created":{"date-parts":[[2018,10,3]],"date-time":"2018-10-03T12:50:20Z","timestamp":1538571020000},"page":"547-565","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Rigorous packing of unit squares into a circle"],"prefix":"10.1007","volume":"73","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9730-5748","authenticated-orcid":false,"given":"Tiago","family":"Montanher","sequence":"first","affiliation":[],"role":[{"role":"author","vocab":"crossref"}]},{"given":"Arnold","family":"Neumaier","sequence":"additional","affiliation":[],"role":[{"role":"author","vocab":"crossref"}]},{"given":"Mih\u00e1ly","family":"Csaba Mark\u00f3t","sequence":"additional","affiliation":[],"role":[{"role":"author","vocab":"crossref"}]},{"given":"Ferenc","family":"Domes","sequence":"additional","affiliation":[],"role":[{"role":"author","vocab":"crossref"}]},{"given":"Hermann","family":"Schichl","sequence":"additional","affiliation":[],"role":[{"role":"author","vocab":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2018,10,3]]},"reference":[{"issue":"1","key":"711_CR1","doi-asserted-by":"crossref","first-page":"R126","DOI":"10.37236\/398","volume":"17","author":"W Bentz","year":"2010","unstructured":"Bentz, W.: Optimal packings of 13 and 46 unit squares in a square. Electron. J. Comb. 17(1), R126 (2010)","journal-title":"Electron. J. Comb."},{"issue":"4","key":"711_CR2","doi-asserted-by":"publisher","first-page":"709","DOI":"10.1007\/s10898-015-0395-z","volume":"65","author":"EG Birgin","year":"2016","unstructured":"Birgin, E.G., Lobato, R.D., Mart\u00ednez, J.M.: Packing ellipsoids by nonlinear optimization. J. Glob. Optim. 65(4), 709\u2013743 (2016)","journal-title":"J. Glob. Optim."},{"issue":"3","key":"711_CR3","doi-asserted-by":"publisher","first-page":"467","DOI":"10.1007\/s10898-016-0483-8","volume":"68","author":"EG Birgin","year":"2017","unstructured":"Birgin, E.G., Lobato, R.D., Mart\u00ednez, J.M.: A nonlinear programming model with implicit variables for packing ellipsoids. J. Glob. Optim. 68(3), 467\u2013499 (2017)","journal-title":"J. Glob. Optim."},{"issue":"6","key":"711_CR4","doi-asserted-by":"publisher","first-page":"735","DOI":"10.1057\/palgrave.jors.2602067","volume":"57","author":"EG Birgin","year":"2006","unstructured":"Birgin, E.G., Mart\u00ednez, J.M., Mascarenhas, W.F., Ronconi, D.P.: Method of sentinels for packing items within arbitrary convex regions. J. Oper. Res. Soc. 57(6), 735\u2013746 (2006)","journal-title":"J. Oper. Res. Soc."},{"issue":"3","key":"711_CR5","doi-asserted-by":"publisher","first-page":"786","DOI":"10.1016\/j.ejor.2007.01.054","volume":"191","author":"I Castillo","year":"2008","unstructured":"Castillo, I., Kampas, F.J., Pint\u00e9r, J.D.: Solving circle packing problems by global optimization: Numerical results and industrial applications. Eur. J. Oper. Res. 191(3), 786\u2013802 (2008)","journal-title":"Eur. J. Oper. Res."},{"key":"711_CR6","doi-asserted-by":"publisher","first-page":"1167","DOI":"10.1016\/j.jcta.2009.02.005","volume":"116","author":"F Chung","year":"2009","unstructured":"Chung, F., Graham, R.L.: Packing equal squares into a large square. J. Comb. Theory Ser. A 116, 1167\u20131175 (2009)","journal-title":"J. Comb. Theory Ser. A"},{"key":"711_CR7","doi-asserted-by":"publisher","first-page":"255","DOI":"10.1007\/s10898-014-0158-2","volume":"61","author":"F Domes","year":"2015","unstructured":"Domes, F., Neumaier, A.: Rigorous verification of feasibility. J. Glob. Optim. 61, 255\u2013278 (2015)","journal-title":"J. Glob. Optim."},{"issue":"1","key":"711_CR8","doi-asserted-by":"publisher","first-page":"9","DOI":"10.1016\/0097-3165(75)90099-0","volume":"19","author":"P Erd\u00f6s","year":"1975","unstructured":"Erd\u00f6s, P., Graham, R.L.: On packing squares with equal squares. J. Comb. Theory (A) 19(1), 9\u2013123 (1975)","journal-title":"J. Comb. Theory (A)"},{"key":"711_CR9","unstructured":"Friedman, E.: Erich packing center. http:\/\/www2.stetson.edu\/~efriedma\/packing.html . Accessed 4 Dec 2017"},{"key":"711_CR10","doi-asserted-by":"crossref","unstructured":"Friedman, E.: Packing unit squares in squares: a survey and new results. Electron. J. Comb. (2009)","DOI":"10.37236\/28"},{"key":"711_CR11","volume-title":"Global Optimization Using Interval Analysis","author":"ER Hansen","year":"1992","unstructured":"Hansen, E.R.: Global Optimization Using Interval Analysis. Marcel Dekker Inc., New York (1992)"},{"issue":"2","key":"711_CR12","doi-asserted-by":"publisher","first-page":"405","DOI":"10.1007\/s10898-013-0125-3","volume":"59","author":"J Kallrath","year":"2014","unstructured":"Kallrath, J., Rebennack, S.: Cutting ellipses from area-minimizing rectangles. J. Glob. Optim. 59(2), 405\u2013437 (2014)","journal-title":"J. Glob. Optim."},{"key":"711_CR13","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-2495-0","volume-title":"Rigorous Global Search: Continuous Problems","author":"RB Kearfott","year":"1996","unstructured":"Kearfott, R.B.: Rigorous Global Search: Continuous Problems. Kluwer Academic Publishers, Norwell (1996)"},{"issue":"2","key":"711_CR14","doi-asserted-by":"publisher","first-page":"299","DOI":"10.1145\/1141885.1141893","volume":"32","author":"M Lerch","year":"2006","unstructured":"Lerch, M., Tischler, G., Gudenberg, J.W.V., Hofschuster, W., Kr\u00e4mer, W.: Filib++, a fast interval library supporting containment computations. ACM Trans. Math. Softw. 32(2), 299\u2013324 (2006)","journal-title":"ACM Trans. Math. Softw."},{"issue":"2","key":"711_CR15","doi-asserted-by":"publisher","first-page":"353","DOI":"10.1016\/j.cam.2005.08.039","volume":"199","author":"MC Mark\u00f3t","year":"2007","unstructured":"Mark\u00f3t, M.C.: Interval methods for verifying structural optimality of circle packing configurations in the unit square. J. Comput. Appl. Math. 199(2), 353\u2013357 (2007)","journal-title":"J. Comput. Appl. Math."},{"key":"711_CR16","doi-asserted-by":"publisher","first-page":"193","DOI":"10.1137\/S1052623403425617","volume":"16","author":"MC Mark\u00f3t","year":"2005","unstructured":"Mark\u00f3t, M.C., Csendes, T.: A new verified optimization technique for the \u201cpacking circles in a unit square\u201d problems. SIAM J. Optim. 16, 193\u2013219 (2005)","journal-title":"SIAM J. Optim."},{"key":"711_CR17","doi-asserted-by":"publisher","first-page":"519","DOI":"10.1007\/978-3-319-95312-0_45","volume-title":"Fuzzy Information Processing","author":"WF Mascarenhas","year":"2018","unstructured":"Mascarenhas, W.F.: Moore: interval arithmetic in C++20. In: Barreto, G.A., Coelho, R. (eds.) Fuzzy Information Processing, pp. 519\u2013529. Springer, Cham (2018)"},{"issue":"2","key":"711_CR18","doi-asserted-by":"publisher","first-page":"247","DOI":"10.1590\/S1807-03022010000200008","volume":"29","author":"WF Mascarenhas","year":"2010","unstructured":"Mascarenhas, W.F., Birgin, E.G.: Using sentinels to detect intersections of convex and nonconvex polygons. Comput. Appl. Math. 29(2), 247\u2013267 (2010)","journal-title":"Comput. Appl. Math."},{"issue":"1","key":"711_CR19","doi-asserted-by":"crossref","first-page":"R37","DOI":"10.37236\/1934","volume":"12","author":"H Nagamochi","year":"2005","unstructured":"Nagamochi, H.: Packing unit squares in a rectangle. Electron. J. Comb. 12(1), R37 (2005)","journal-title":"Electron. J. Comb."},{"key":"711_CR20","series-title":"Encyclopedia of Mathematics and Its Applications","volume-title":"Interval Methods for Systems of Equations","author":"A Neumaier","year":"1990","unstructured":"Neumaier, A.: Interval Methods for Systems of Equations. Encyclopedia of Mathematics and Its Applications, vol. 37. Cambridge University Press, Cambridge (1990)"},{"issue":"4","key":"711_CR21","doi-asserted-by":"publisher","first-page":"541","DOI":"10.1007\/s10898-005-0937-x","volume":"33","author":"H Schichl","year":"2005","unstructured":"Schichl, H., Neumaier, A.: Interval analysis on directed acyclic graphs for global optimization. J. Glob. Optim. 33(4), 541\u2013562 (2005)","journal-title":"J. Glob. Optim."},{"key":"711_CR22","unstructured":"Specht, E.: Packomania. http:\/\/www.packomania.com\/ . Accessed 4 Dec 2017"},{"issue":"8","key":"711_CR23","first-page":"1","volume":"10","author":"W Stromquist","year":"2003","unstructured":"Stromquist, W.: Packing 10 or 11 unit squares in a square. Electron. J. Comb. 10(8), 1\u201311 (2003)","journal-title":"Electron. J. Comb."},{"key":"711_CR24","volume-title":"New Approaches to Circle Packing in a Square\u2014With Program Codes","author":"PG Szab\u00f3","year":"2008","unstructured":"Szab\u00f3, P.G., Mark\u00f3t, M.C., Csendes, T., Specht, E., Casado, L.G., Garc\u00eda, I.: New Approaches to Circle Packing in a Square\u2014With Program Codes. Springer, Berlin (2008)"}],"container-title":["Journal of Global Optimization"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10898-018-0711-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10898-018-0711-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10898-018-0711-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,11,11]],"date-time":"2020-11-11T23:20:29Z","timestamp":1605136829000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10898-018-0711-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,10,3]]},"references-count":24,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2019,3]]}},"alternative-id":["711"],"URL":"https:\/\/doi.org\/10.1007\/s10898-018-0711-5","relation":{},"ISSN":["0925-5001","1573-2916"],"issn-type":[{"type":"print","value":"0925-5001"},{"type":"electronic","value":"1573-2916"}],"subject":[],"published":{"date-parts":[[2018,10,3]]},"assertion":[{"value":"27 January 2018","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"25 September 2018","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"3 October 2018","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}