{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,17]],"date-time":"2026-02-17T15:40:35Z","timestamp":1771342835537,"version":"3.50.1"},"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> Let S be a set of n points in \u211d<jats:sup>d<\/jats:sup>, and let each point p of S have a positive weight w(p). We consider the problem of computing a ray R emanating from the origin (resp. a line l through the origin) such that min <jats:sub>p \u2208 s<\/jats:sub> w(p) \u00b7 d(p,R) ( resp. min <jats:sub>p \u2208 S<\/jats:sub> w(p) \u00b7 d(p,l)) is maximal. If all weights are one, this corresponds to computing a silo emanating from the origin ( resp. a cylinder whose axis contains the origin) that does not contain any point of S and whose radius is maximal. For d = 2, we show how to solve these problems in O(n log n) time, which is optimal in the algebraic computation tree model. For d = 3, we give algorithms that are based on the parametric search technique and run in O(n log <jats:sup>4<\/jats:sup> n) time. The previous best known algorithms for these three-dimensional problems had almost quadratic running time. In the final part of the paper, we consider some related problems. <\/jats:p>","DOI":"10.1142\/s0218195997000351","type":"journal-article","created":{"date-parts":[[2003,10,16]],"date-time":"2003-10-16T06:47:26Z","timestamp":1066286846000},"page":"563-580","source":"Crossref","is-referenced-by-count":8,"title":["Computing a Largest Empty Anchored Cylinder, and Related Problems"],"prefix":"10.1142","volume":"07","author":[{"given":"Frank","family":"Follert","sequence":"first","affiliation":[{"name":"Universit\u00e4at des Saarlandes, Fachbereich 14, Informatik, Lehrstuhl Prof. Hotz, D-66041 Saarbr\u00fccken, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Elmar","family":"Sch\u00f6mer","sequence":"additional","affiliation":[{"name":"Universit\u00e4at des Saarlandes, Fachbereich 14, Informatik, Lehrstuhl Prof. Hotz, D-66041 Saarbr\u00fccken, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"J\u00fcrgen","family":"Sellen","sequence":"additional","affiliation":[{"name":"Universit\u00e4at des Saarlandes, Fachbereich 14, Informatik, Lehrstuhl Prof. Hotz, D-66041 Saarbr\u00fccken, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Michiel","family":"Smid","sequence":"additional","affiliation":[{"name":"Max-Planck-Institut f\u00fcr Informatik, D-66123 Saarbr\u00fccken, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Christian","family":"Thiel","sequence":"additional","affiliation":[{"name":"Max-Planck-Institut f\u00fcr Informatik, D-66123 Saarbr\u00fccken, Germany"}],"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\/S0218195997000351","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T20:31:47Z","timestamp":1565123507000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218195997000351"}},"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\/S0218195997000351"],"URL":"https:\/\/doi.org\/10.1142\/s0218195997000351","relation":{},"ISSN":["0218-1959","1793-6357"],"issn-type":[{"value":"0218-1959","type":"print"},{"value":"1793-6357","type":"electronic"}],"subject":[],"published":{"date-parts":[[1997,12]]}}}