{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,3]],"date-time":"2026-03-03T05:34:43Z","timestamp":1772516083504,"version":"3.50.1"},"reference-count":23,"publisher":"Elsevier BV","issue":"1","license":[{"start":{"date-parts":[[2003,8,1]],"date-time":"2003-08-01T00:00:00Z","timestamp":1059696000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2013,7,17]],"date-time":"2013-07-17T00:00:00Z","timestamp":1374019200000},"content-version":"vor","delay-in-days":3638,"URL":"https:\/\/www.elsevier.com\/open-access\/userlicense\/1.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computational Geometry"],"published-print":{"date-parts":[[2003,8]]},"DOI":"10.1016\/s0925-7721(02)00173-6","type":"journal-article","created":{"date-parts":[[2003,4,7]],"date-time":"2003-04-07T17:19:33Z","timestamp":1049735973000},"page":"69-79","source":"Crossref","is-referenced-by-count":20,"title":["Algorithms for bivariate medians and a Fermat\u2013Torricelli problem for lines"],"prefix":"10.1016","volume":"26","author":[{"given":"Greg","family":"Aloupis","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Stefan","family":"Langerman","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Michael","family":"Soss","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Godfried","family":"Toussaint","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"78","reference":[{"key":"10.1016\/S0925-7721(02)00173-6_BIB001","unstructured":"G. Aloupis, On computing geometric estimators of location, M. Sc. Thesis, McGill University, 2001"},{"key":"10.1016\/S0925-7721(02)00173-6_BIB002","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1016\/S0167-9473(02)00032-4","article-title":"Lower bounds for computing statistical depth","volume":"40","author":"Aloupis","year":"2002","journal-title":"Computational Statistics and Data Analysis"},{"key":"10.1016\/S0925-7721(02)00173-6_BIB003","unstructured":"G. Aloupis, M. Soss, G. Toussaint, On the computation of the bivariate median and a Fermat\u2013Torricelli problem, Technical Report SOCS-01.2, School of Computer Science, McGill University, February 2001"},{"key":"10.1016\/S0925-7721(02)00173-6_BIB004","doi-asserted-by":"crossref","first-page":"24","DOI":"10.2307\/3621470","article-title":"The Fermat\u2013Torricelli points of n lines","volume":"84","author":"Barbara","year":"2000","journal-title":"Math. Gazette"},{"key":"10.1016\/S0925-7721(02)00173-6_BIB005","doi-asserted-by":"crossref","first-page":"38","DOI":"10.1007\/PL00000991","article-title":"A note on the Fermat\u2013Torricelli point of a d-simplex","volume":"70","author":"Dalla","year":"2001","journal-title":"J. Geom."},{"key":"10.1016\/S0925-7721(02)00173-6_BIB006","unstructured":"P. de Fermat, Abhandlungen \u00fcber maxima und minima, in: M. Miller (Ed.), Ostwalds Klassiker der exacten Wissenschaften, p. 238"},{"key":"10.1016\/S0925-7721(02)00173-6_BIB007","series-title":"Algorithms in Combinatorial Geometry","author":"Edelsbrunner","year":"1987"},{"key":"10.1016\/S0925-7721(02)00173-6_BIB008","doi-asserted-by":"crossref","first-page":"165","DOI":"10.1016\/0022-0000(89)90038-X","article-title":"Topologically sweeping an arrangement","volume":"38","author":"Edelsbrunner","year":"1989","journal-title":"J. Comput. System Sci."},{"key":"10.1016\/S0925-7721(02)00173-6_BIB009","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1016\/0012-365X(92)90658-3","article-title":"Geometric medians","volume":"108","author":"Gill","year":"1992","journal-title":"Discrete Math."},{"issue":"8","key":"10.1016\/S0925-7721(02)00173-6_BIB010","doi-asserted-by":"crossref","first-page":"732","DOI":"10.2307\/2588990","article-title":"On generalizations of conics and on a generalization of the Fermat\u2013Torricelli problem","volume":"105","author":"Gro\u00df","year":"1998","journal-title":"Amer. Math. Monthly"},{"key":"10.1016\/S0925-7721(02)00173-6_BIB011","doi-asserted-by":"crossref","first-page":"319","DOI":"10.1016\/0020-0190(90)90217-L","article-title":"On a triangle counting problem","volume":"33","author":"Khuller","year":"1989","journal-title":"Inform. Process. Lett."},{"key":"10.1016\/S0925-7721(02)00173-6_BIB012","first-page":"55","article-title":"Geometric aspects of the generalized Fermat\u2013Torricelli problem","volume":"6","author":"Kupitz","year":"1997","journal-title":"Intuitive Geometry, Bolyai Society Math. Studies"},{"key":"10.1016\/S0925-7721(02)00173-6_BIB013","series-title":"Japan Conference on Discrete and Computational Geometry","article-title":"Computing a maximal depth point in the plane","author":"Langerman","year":"2000"},{"key":"10.1016\/S0925-7721(02)00173-6_BIB014","doi-asserted-by":"crossref","unstructured":"S. Langerman, W. Steiger, Optimization in arrangements, Technical Report SOCS-02.7, School of Computer Science, McGill University, 2002. To appear at the 20th International Symposium on Theoretical Aspects of Computer Science (STACS 2003)","DOI":"10.1007\/3-540-36494-3_6"},{"key":"10.1016\/S0925-7721(02)00173-6_BIB015","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1016\/0020-0190(85)90015-8","article-title":"The power of geometric duality revisited","volume":"21","author":"Lee","year":"1985","journal-title":"Inform. Process. Lett."},{"key":"10.1016\/S0925-7721(02)00173-6_BIB016","doi-asserted-by":"crossref","first-page":"405","DOI":"10.1214\/aos\/1176347507","article-title":"On a notion of data depth based upon random simplices","volume":"18","author":"Liu","year":"1990","journal-title":"Ann. Statist."},{"issue":"3","key":"10.1016\/S0925-7721(02)00173-6_BIB017","doi-asserted-by":"crossref","first-page":"783","DOI":"10.1214\/aos\/1018031260","article-title":"Multivariate analysis of data depth: descriptive statistics, graphics and inference","volume":"27","author":"Liu","year":"1999","journal-title":"Ann. Statist."},{"key":"10.1016\/S0925-7721(02)00173-6_BIB018","series-title":"Opere di Evangelista Torricelli, Vol. 1","year":"1919"},{"key":"10.1016\/S0925-7721(02)00173-6_BIB019","doi-asserted-by":"crossref","first-page":"611","DOI":"10.2307\/2348099","article-title":"Algorithm AS 277: The Oja bivariate median","volume":"41","author":"Niinimaa","year":"1992","journal-title":"Appl. Statist."},{"key":"10.1016\/S0925-7721(02)00173-6_BIB020","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1016\/0167-7152(90)90050-H","article-title":"The finite-sample breakdown point of the Oja bivariate median and of the corresponding half-samples version","volume":"10","author":"Niinimaa","year":"1990","journal-title":"Statist. Probab. Lett."},{"key":"10.1016\/S0925-7721(02)00173-6_BIB021","doi-asserted-by":"crossref","first-page":"327","DOI":"10.1016\/0167-7152(83)90054-8","article-title":"Descriptive statistics for multivariate distributions","volume":"1","author":"Oja","year":"1983","journal-title":"Statist. Probab. Lett."},{"key":"10.1016\/S0925-7721(02)00173-6_BIB022","doi-asserted-by":"crossref","first-page":"516","DOI":"10.2307\/2986073","article-title":"Bivariate location depth","volume":"45","author":"Rousseeuw","year":"1996","journal-title":"Appl. Statist."},{"key":"10.1016\/S0925-7721(02)00173-6_BIB023","doi-asserted-by":"crossref","first-page":"263","DOI":"10.2307\/1403809","article-title":"A survey of multidimensional medians","volume":"58","author":"Small","year":"1990","journal-title":"Internat. Statist. Rev."}],"container-title":["Computational Geometry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0925772102001736?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0925772102001736?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2021,6,6]],"date-time":"2021-06-06T04:52:21Z","timestamp":1622955141000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0925772102001736"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,8]]},"references-count":23,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2003,8]]}},"alternative-id":["S0925772102001736"],"URL":"https:\/\/doi.org\/10.1016\/s0925-7721(02)00173-6","relation":{},"ISSN":["0925-7721"],"issn-type":[{"value":"0925-7721","type":"print"}],"subject":[],"published":{"date-parts":[[2003,8]]}}}