{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,14]],"date-time":"2025-10-14T11:15:13Z","timestamp":1760440513040},"reference-count":13,"publisher":"World Scientific Pub Co Pte Lt","issue":"05","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Found. Comput. Sci."],"published-print":{"date-parts":[[2006,10]]},"abstract":"<jats:p> Let R be a rectangle with given area a(R), height h(R) and width w(R), and r<jats:sub>1<\/jats:sub>, r<jats:sub>2<\/jats:sub>, \u2026, r<jats:sub>n<\/jats:sub> be n soft rectangles, where we mean by a soft rectangle a rectangle r whose area a(r) is prescribed but whose aspect ratio \u03c1(r) is allowed to be changed. In this paper, we consider the problem of packing n soft rectangles r<jats:sub>1<\/jats:sub>, r<jats:sub>2<\/jats:sub>, \u2026, r<jats:sub>n<\/jats:sub> into R. We prove that, if a(R) \u2265 \u03a3<jats:sub>1\u2264i\u2264n<\/jats:sub> a(r<jats:sub>i<\/jats:sub>) + 0.10103a<jats:sub>max<\/jats:sub> and a<jats:sub>max<\/jats:sub> \u2264 3( min {h(R), w(R)})<jats:sup>2<\/jats:sup> hold for a a<jats:sub>max<\/jats:sub> = max <jats:sub>1\u2264i\u2264n<\/jats:sub> a(r<jats:sub>i<\/jats:sub>), then these n soft rectangles can be packed inside R so that the apect ratio of each rectangle r<jats:sub>i<\/jats:sub> is at most 3. <\/jats:p>","DOI":"10.1142\/s0129054106004327","type":"journal-article","created":{"date-parts":[[2006,9,18]],"date-time":"2006-09-18T12:04:43Z","timestamp":1158581083000},"page":"1165-1178","source":"Crossref","is-referenced-by-count":7,"title":["PACKING SOFT RECTANGLES"],"prefix":"10.1142","volume":"17","author":[{"given":"HIROSHI","family":"NAGAMOCHI","sequence":"first","affiliation":[{"name":"Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto 606-8501, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1287\/ijoc.1040.0103"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1137\/0604039"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1109\/71.963416"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1007\/s00453-002-0962-9"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-0963-8"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2004.1272729"},{"key":"rf9","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"362","DOI":"10.1007\/978-3-540-27810-8_31","volume":"3111","author":"Jansen K.","year":"2004"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1023\/A:1005263703808"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1287\/moor.25.4.645.12118"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1137\/0217077"},{"key":"rf15","doi-asserted-by":"crossref","first-page":"103","DOI":"10.4064\/cm-17-1-103-110","volume":"17","author":"Moon J. W.","journal-title":"Colloq. Math."},{"key":"rf16","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"280","DOI":"10.1007\/978-3-540-24587-2_30","volume":"2906","author":"Nagamochi H.","year":"2003"},{"key":"rf17","doi-asserted-by":"publisher","DOI":"10.1109\/43.920707"}],"container-title":["International Journal of Foundations of Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0129054106004327","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T00:40:45Z","timestamp":1565138445000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0129054106004327"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,10]]},"references-count":13,"journal-issue":{"issue":"05","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2006,10]]}},"alternative-id":["10.1142\/S0129054106004327"],"URL":"https:\/\/doi.org\/10.1142\/s0129054106004327","relation":{},"ISSN":["0129-0541","1793-6373"],"issn-type":[{"value":"0129-0541","type":"print"},{"value":"1793-6373","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006,10]]}}}