{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,3]],"date-time":"2022-04-03T17:40:29Z","timestamp":1649007629665},"reference-count":0,"publisher":"World Scientific Pub Co Pte Lt","issue":"06","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Comput. Geom. Appl."],"published-print":{"date-parts":[[1997,12]]},"abstract":"<jats:p> Given a family of pairwise disjoint convex sets S in the plane, a set [Formula: see text] is separated from a subset X \u2286 S if there exists a line l such that [Formula: see text] lies on one side of l and the sets in X lie on the other side. In this paper, we establish two combinatorial bounds related to the separation problem for families of n pairwise disjoint translates of a convex set in the plane: 1) there exists a line which separates one translate from at least [Formula: see text] translates, for some constant [Formula: see text] that depends only on the shape of the translates and 2) there is a function [Formula: see text], defined only by the shape of [Formula: see text], such that there exists a line with orientation \u0398 or [Formula: see text] which separates one translate from at least [Formula: see text] translates, for any orientation \u0398. We also present an O(n log (n + k) + k) time algorithm for finding a translate which can be separated from the maximum number of translates amongst families of n pairwise disjoint translates of convex k-gons in the plane. <\/jats:p>","DOI":"10.1142\/s021819599700034x","type":"journal-article","created":{"date-parts":[[2003,10,16]],"date-time":"2003-10-16T10:47:26Z","timestamp":1066301246000},"page":"551-562","source":"Crossref","is-referenced-by-count":0,"title":["Separating Translates in the Plane: Combinatorial Bounds and an Algorithm"],"prefix":"10.1142","volume":"07","author":[{"given":"Jurek","family":"Czyzowicz","sequence":"first","affiliation":[{"name":"D\u00e9p. d'informatique,  Universit\u00e9 du Qu\u00e9bec \u00e0 Hull, C.P. 1250, Succ. B, Hull, Canada, J8X 3X7, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hazel","family":"Everett","sequence":"additional","affiliation":[{"name":"D\u00e9p. d'informatique, Universit\u00e9 du Qu\u00e9bec \u00e0 Montr\u00e9al, C.P. 8888, Succ. Centre-Ville, Montr\u00e9al, Canada, H3C 3P8, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jean-Marc","family":"Robert","sequence":"additional","affiliation":[{"name":"D\u00e9p. d'informatique et de math\u00e9matique, Universit\u00e9 du Qu\u00e9bec \u00e0 Chicoutimi, 555 boul. de I'Universit\u00e9, Chicoutimi, Canada, G7H 2B1, Canada"}],"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\/S021819599700034X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T00:31:47Z","timestamp":1565137907000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S021819599700034X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1997,12]]},"references-count":0,"journal-issue":{"issue":"06","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[1997,12]]}},"alternative-id":["10.1142\/S021819599700034X"],"URL":"https:\/\/doi.org\/10.1142\/s021819599700034x","relation":{},"ISSN":["0218-1959","1793-6357"],"issn-type":[{"value":"0218-1959","type":"print"},{"value":"1793-6357","type":"electronic"}],"subject":[],"published":{"date-parts":[[1997,12]]}}}