{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,12,29]],"date-time":"2022-12-29T21:08:52Z","timestamp":1672348132033},"reference-count":5,"publisher":"World Scientific Pub Co Pte Lt","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Comput. Geom. Appl."],"published-print":{"date-parts":[[1999,6]]},"abstract":"<jats:p> In the p-piercing problem, a set [Formula: see text] of nd-dimensional objects is given, and one has to compute a piercing set for [Formula: see text] of size p, if such a set exists. We consider several instances of the 3-piercing problem that admit linear or almost linear solutions: (i)\u00a0If [Formula: see text] consists of axis-parallel boxes in \u211b<jats:sup>d<\/jats:sup>, then a piercing triplet for [Formula: see text] can be found (if such a triplet exists) in O(n log \u00a0n) time, for 3 \u2264 d \u2264 5, and in [Formula: see text] time, for d \u2265 6. Based on the solutions for 3 \u2264 d \u2264 5, efficient solutions are obtained to the corresponding 3-center problem \u2014 Given a set [Formula: see text] of n points of \u211b<jats:sup>d<\/jats:sup>, compute the smallest edge length \u03bb such that [Formula: see text] can be covered by the union of three axis-parallel cubes of edge length \u03bb. (ii)\u00a0If [Formula: see text] consists of homothetic triangles in the plane, or of 4-oriented trapezoids in the plane, then a piercing triplet can be found in O(n log \u00a0n) time. <\/jats:p>","DOI":"10.1142\/s0218195999000170","type":"journal-article","created":{"date-parts":[[2003,5,22]],"date-time":"2003-05-22T02:35:01Z","timestamp":1053570901000},"page":"249-259","source":"Crossref","is-referenced-by-count":3,"title":["3-PIERCING OF d-DIMENSIONAL BOXES AND HOMOTHETIC TRIANGLES"],"prefix":"10.1142","volume":"09","author":[{"given":"EYAL","family":"ASSA","sequence":"first","affiliation":[{"name":"School of Mathematical Sciences, Tel Aviv University, Tel-Aviv\u00a069978, Israel"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"MATTHEW J.","family":"KATZ","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computer Science, Ben-Gurion University of the Negev, Beer-Sheva\u00a084105, Israel"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"p_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02579232"},{"key":"p_3","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0000(82)90048-4"},{"key":"p_4","doi-asserted-by":"publisher","DOI":"10.1016\/0196-6774(83)90035-4"},{"key":"p_5","doi-asserted-by":"publisher","DOI":"10.1137\/0213002"},{"key":"p_8","doi-asserted-by":"publisher","DOI":"10.1137\/0213014"}],"container-title":["International Journal of Computational Geometry &amp; Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218195999000170","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T11:37:48Z","timestamp":1565177868000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218195999000170"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1999,6]]},"references-count":5,"journal-issue":{"issue":"03","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[1999,6]]}},"alternative-id":["10.1142\/S0218195999000170"],"URL":"https:\/\/doi.org\/10.1142\/s0218195999000170","relation":{},"ISSN":["0218-1959","1793-6357"],"issn-type":[{"value":"0218-1959","type":"print"},{"value":"1793-6357","type":"electronic"}],"subject":[],"published":{"date-parts":[[1999,6]]}}}