{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,4]],"date-time":"2022-04-04T09:39:31Z","timestamp":1649065171943},"reference-count":0,"publisher":"World Scientific Pub Co Pte Lt","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Comput. Geom. Appl."],"published-print":{"date-parts":[[1993,6]]},"abstract":"<jats:p> We consider the problem of separating a set of d-dimensional non-overlapping isothetic hyperrectangles by means of one cutting isothetic hyperplane. If the cutting hyperplane crosses one hyperrectangle this is split into two non-overlapping hyperrectangles. We show that it always exists a cutting hyperplane that separates n given hyperrectangles into two sets each containing no more than [\u03b1<jats:sub>d<\/jats:sub> \u00b7 n] hyperrectangles, where \u03b1<jats:sub>d<\/jats:sub>=(2d\u22121)\/2d. Also, we show that there are instances for which it is not possible to do better. <\/jats:p><jats:p> An optimal O(d \u00b7 n) time and space algorithm for finding this cutting hyperplane is presented. <\/jats:p><jats:p> An upper bound to the number of intersected hyperrectangles is also given, thus proving a separator theorem for hyperrectangles. <\/jats:p>","DOI":"10.1142\/s0218195993000105","type":"journal-article","created":{"date-parts":[[2004,11,23]],"date-time":"2004-11-23T03:29:30Z","timestamp":1101180570000},"page":"155-165","source":"Crossref","is-referenced-by-count":3,"title":["SEPARATING SETS OF HYPERRECTANGLES"],"prefix":"10.1142","volume":"03","author":[{"given":"FABRIZIO","family":"D\u2019AMORE","sequence":"first","affiliation":[{"name":"Dipartimento di Informatica e Sistemistica, Universit\u00e0 di Roma \u201cLa Sapienza\u201d, via Salaria 113, I-00198 Roma, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"PAOLO GIULIO","family":"FRANCIOSA","sequence":"additional","affiliation":[{"name":"Dipartimento di Informatica e Sistemistica, Universit\u00e0 di Roma \u201cLa Sapienza\u201d, via. Salaria 113, I-00198 Roma, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"container-title":["International Journal of Computational Geometry &amp; Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218195993000105","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T23:57:41Z","timestamp":1565135861000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218195993000105"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1993,6]]},"references-count":0,"journal-issue":{"issue":"02","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[1993,6]]}},"alternative-id":["10.1142\/S0218195993000105"],"URL":"https:\/\/doi.org\/10.1142\/s0218195993000105","relation":{},"ISSN":["0218-1959","1793-6357"],"issn-type":[{"value":"0218-1959","type":"print"},{"value":"1793-6357","type":"electronic"}],"subject":[],"published":{"date-parts":[[1993,6]]}}}