{"id":"https://openalex.org/W1520510766","doi":"https://doi.org/10.1109/sfcs.2003.1238224","title":"On the impossibility of dimension reduction in /spl lscr//sub 1/","display_name":"On the impossibility of dimension reduction in /spl lscr//sub 1/","publication_year":2004,"publication_date":"2004-03-02","ids":{"openalex":"https://openalex.org/W1520510766","doi":"https://doi.org/10.1109/sfcs.2003.1238224","mag":"1520510766"},"language":"en","primary_location":{"id":"doi:10.1109/sfcs.2003.1238224","is_oa":false,"landing_page_url":"https://doi.org/10.1109/sfcs.2003.1238224","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"44th Annual IEEE Symposium on Foundations of Computer Science, 2003. Proceedings.","raw_type":"proceedings-article"},"type":"conference-paper","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5025420692","display_name":"Bo Brinkman","orcid":"https://orcid.org/0000-0003-2951-2141"},"institutions":[{"id":"https://openalex.org/I20089843","display_name":"Princeton University","ror":"https://ror.org/00hx57361","country_code":"US","type":"education","lineage":["https://openalex.org/I20089843"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"B. Brinkman","raw_affiliation_strings":["Princeton University, Princeton, NJ, USA","Princeton Univ, NJ, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Princeton University, Princeton, NJ, USA","institution_ids":["https://openalex.org/I20089843"]},{"raw_affiliation_string":"Princeton Univ, NJ, USA","institution_ids":["https://openalex.org/I20089843"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5071016611","display_name":"Moses Charikar","orcid":"https://orcid.org/0000-0003-0807-3389"},"institutions":[{"id":"https://openalex.org/I20089843","display_name":"Princeton University","ror":"https://ror.org/00hx57361","country_code":"US","type":"education","lineage":["https://openalex.org/I20089843"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"M. Charikar","raw_affiliation_strings":["Princeton University, Princeton, NJ, USA","Princeton Univ, NJ, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Princeton University, Princeton, NJ, USA","institution_ids":["https://openalex.org/I20089843"]},{"raw_affiliation_string":"Princeton Univ, NJ, USA","institution_ids":["https://openalex.org/I20089843"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I20089843"],"apc_list":null,"apc_paid":null,"fwci":1.3496,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.78136201,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"514","last_page":"523"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9977999925613403,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6508854031562805},{"id":"https://openalex.org/keywords/embedding","display_name":"Embedding","score":0.6466513276100159},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5547705888748169},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.5305590629577637},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4480215311050415},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1264139711856842}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6508854031562805},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.6466513276100159},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5547705888748169},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.5305590629577637},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4480215311050415},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1264139711856842},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/sfcs.2003.1238224","is_oa":false,"landing_page_url":"https://doi.org/10.1109/sfcs.2003.1238224","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"44th Annual IEEE Symposium on Foundations of Computer Science, 2003. Proceedings.","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W48861618","https://openalex.org/W1516726196","https://openalex.org/W1943182387","https://openalex.org/W1956647075","https://openalex.org/W2004322147","https://openalex.org/W2012383576","https://openalex.org/W2027697499","https://openalex.org/W2046056514","https://openalex.org/W2053171205","https://openalex.org/W2063491776","https://openalex.org/W2065195508","https://openalex.org/W2068221647","https://openalex.org/W2080745194","https://openalex.org/W2088101210","https://openalex.org/W2096746450","https://openalex.org/W2122929038","https://openalex.org/W2147717514","https://openalex.org/W2158907148","https://openalex.org/W2273002128","https://openalex.org/W2951166730","https://openalex.org/W2979473749","https://openalex.org/W2983923309","https://openalex.org/W4249560439","https://openalex.org/W6661743294","https://openalex.org/W6764178384"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2013985456","https://openalex.org/W2951564084","https://openalex.org/W4302984940","https://openalex.org/W2776807270","https://openalex.org/W2392685819"],"abstract_inverted_index":{"The":[0],"Johnson-Lindenstrauss":[1,110],"Lemma":[2,111],"shows":[3],"that":[4,31,88,103,177],"any":[5,89,120],"n":[6,81],"points":[7,82,131],"in":[8,52,71,83,116,171],"Euclidean":[9],"space":[10],"(with":[11],"distances":[12],"measured":[13],"by":[14,37],"the":[15,109,130,178],"/spl":[16,42,53,72,84,93,97,113,125,133,139,193],"lscr//sub":[17,54,73,85,114,134,194],"2/":[18],"norm)":[19],"may":[20],"be":[21,185],"mapped":[22],"down":[23],"to":[24],"O((log":[25],"n)//spl":[26],"epsiv//sup":[27],"2/)":[28],"dimensions":[29],"such":[30,47,87],"no":[32,106],"pairwise":[33],"distance":[34],"is":[35,50,105],"distorted":[36],"more":[38],"than":[39],"a":[40],"(1+":[41],"epsiv/)":[43],"factor.":[44],"Determining":[45],"whether":[46],"dimension":[48,69],"reduction":[49,70],"possible":[51],"1/":[55,86,135],"has":[56],"been":[57],"an":[58,77],"intriguing":[59],"open":[60],"question.":[61],"We":[62,75,162,175],"show":[63],"strong":[64],"lower":[65,153],"bounds":[66],"for":[67,112,155,187],"general":[68],"1/.":[74,195],"give":[76],"explicit":[78],"family":[79],"of":[80,108,159,166,190],"embedding":[90,118,129],"with":[91,119,136],"distortion":[92,122,141],"delta/":[94],"requires":[95,123,142],"n/sup":[96,124,143],"Omega/(1//spl":[98],"delta/2)/":[99],"dimensions.":[100,127,148],"This":[101],"proves":[102],"there":[104],"analog":[107],"1/;":[115],"fact":[117],"constant":[121],"Omega/(1)/":[126],"Further,":[128],"into":[132,192],"1":[137],"+":[138],"epsiv/":[140],"1/2":[144],"-O(/spl":[145],"epsiv/log(1//spl":[146],"epsiv/))/":[147],"Our":[149],"proof":[150],"establishes":[151],"this":[152],"bound":[154],"shortest":[156],"path":[157],"metrics":[158],"series-parallel":[160],"graphs.":[161],"make":[163],"extensive":[164],"use":[165],"linear":[167],"programming":[168],"and":[169,180],"duality":[170],"devising":[172],"our":[173],"bounds.":[174],"expect":[176],"tools":[179],"techniques":[181],"we":[182],"develop":[183],"will":[184],"useful":[186],"future":[188],"investigations":[189],"embeddings":[191]},"counts_by_year":[{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-10T00:00:00"}
