{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,29]],"date-time":"2025-05-29T16:43:30Z","timestamp":1748537010780,"version":"3.28.0"},"reference-count":30,"publisher":"IEEE Comput. Soc","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"DOI":"10.1109\/sfcs.2002.1181979","type":"proceedings-article","created":{"date-parts":[[2003,6,26]],"date-time":"2003-06-26T11:35:00Z","timestamp":1056627300000},"page":"551-560","source":"Crossref","is-referenced-by-count":6,"title":["Dimension reduction in the \/spl lscr\/\/sub 1\/ norm"],"prefix":"10.1109","author":[{"given":"M.","family":"Charikar","sequence":"first","affiliation":[]},{"given":"A.","family":"Sahai","sequence":"additional","affiliation":[]}],"member":"263","reference":[{"key":"ref30","first-page":"363","article-title":"Embedding subspaces of $L_{1}$ into $\\ell_{1}^{n}$","volume":"108","author":"talagrand","year":"1990","journal-title":"Proc Amer Math Soc"},{"doi-asserted-by":"publisher","key":"ref10","DOI":"10.1007\/978-3-642-04295-9"},{"doi-asserted-by":"publisher","key":"ref11","DOI":"10.1016\/0095-8956(88)90043-3"},{"doi-asserted-by":"publisher","key":"ref12","DOI":"10.1007\/s004540010020"},{"key":"ref13","first-page":"399","article-title":"Cuts, Trees and $l_{1}$-Embeddings of Graphs","author":"gupta","year":"1999","journal-title":"Proc 40th FOCS"},{"key":"ref14","first-page":"371","article-title":"Dimensionality reduction techniques for proximity problems","author":"indyk","year":"2000","journal-title":"Proc 9th SODA"},{"doi-asserted-by":"publisher","key":"ref15","DOI":"10.1109\/SFCS.2000.892082"},{"key":"ref16","first-page":"10","article-title":"Algorithmic applications of low-distortion embeddings","author":"indyk","year":"2001","journal-title":"Proc 42nd FOCS"},{"doi-asserted-by":"publisher","key":"ref17","DOI":"10.1145\/276698.276876"},{"key":"ref18","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1090\/conm\/026\/737400","article-title":"Extensions of Lipschitz mapping into Hilbert space","volume":"26","author":"johnson","year":"1984","journal-title":"Contemporary Mathematics"},{"doi-asserted-by":"publisher","key":"ref19","DOI":"10.1137\/S0097539798347177"},{"doi-asserted-by":"publisher","key":"ref28","DOI":"10.1145\/509907.509963"},{"key":"ref4","first-page":"103","volume":"79","author":"arias-de reyna","year":"1992","journal-title":"Finite metric spaces needing high dimension for lipschitz embeddings in banach spaces Israel Journal of Mathematics"},{"doi-asserted-by":"publisher","key":"ref27","DOI":"10.1109\/SFCS.2000.892123"},{"doi-asserted-by":"publisher","key":"ref3","DOI":"10.1006\/jcss.1997.1545"},{"key":"ref6","first-page":"46","volume":"52","author":"bourgain","year":"1985","journal-title":"On Lipschitz embedding of finite metric spaces in Hilbert space Israel Journal of Mathematics"},{"key":"ref29","first-page":"159","article-title":"More on embedding subspaces of $L_{{p}}$ in $\\ell_{r}^{n}$","volume":"61","author":"schechtman","year":"1987","journal-title":"Compositio Math"},{"doi-asserted-by":"publisher","key":"ref5","DOI":"10.1016\/S0195-6698(13)80131-X"},{"doi-asserted-by":"publisher","key":"ref8","DOI":"10.1109\/SFFCS.1999.814639"},{"doi-asserted-by":"publisher","key":"ref7","DOI":"10.1023\/A:1004907919611"},{"year":"0","author":"alon","journal-title":"Problems and Results in Extremal Combinatorics Part I manuscript","key":"ref2"},{"year":"1999","author":"dasgupta","journal-title":"An elementary proof of the Johnson-Lindenstrauss lemma Technical Report TR-99&#x2013;06","key":"ref9"},{"doi-asserted-by":"publisher","key":"ref1","DOI":"10.1145\/375551.375608"},{"key":"ref20","article-title":"Finite Metric Spaces - Combinatorics, Geometry and Algorithms","author":"linial","year":"0","journal-title":"Proc International Congress of Mathematicians 2002"},{"doi-asserted-by":"publisher","key":"ref22","DOI":"10.1007\/BF02773475"},{"doi-asserted-by":"publisher","key":"ref21","DOI":"10.1007\/BF01200757"},{"doi-asserted-by":"publisher","key":"ref24","DOI":"10.1007\/BF02761110"},{"key":"ref23","first-page":"589","article-title":"Note on bi-Lipschitz embeddings into low-dimensional Euclidean spaces","volume":"31","author":"matousek","year":"1990","journal-title":"Comment Math Univ Carolinae"},{"key":"ref26","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4613-0039-7_15","article-title":"Embedding finite metric spaces into Euclidean spaces, chapter in Lectures on discrete geometry","volume":"212","author":"matousek","year":"2002","journal-title":"Graduate Texts in Mathematics"},{"doi-asserted-by":"publisher","key":"ref25","DOI":"10.1007\/BF02785579"}],"event":{"acronym":"SFCS-02","name":"43rd Annual IEEE Symposium on Foundations of Computer Science","location":"Vancouver, BC, Canada"},"container-title":["The 43rd Annual IEEE Symposium on Foundations of Computer Science, 2002. Proceedings."],"original-title":[],"link":[{"URL":"http:\/\/xplorestaging.ieee.org\/ielx5\/8411\/26517\/01181979.pdf?arnumber=1181979","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2017,6,15]],"date-time":"2017-06-15T18:46:26Z","timestamp":1497552386000},"score":1,"resource":{"primary":{"URL":"http:\/\/ieeexplore.ieee.org\/document\/1181979\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[null]]},"references-count":30,"URL":"https:\/\/doi.org\/10.1109\/sfcs.2002.1181979","relation":{},"subject":[]}}