{"id":"https://openalex.org/W2091399525","doi":"https://doi.org/10.1137/060660126","title":"Improved Lower Bounds for Embeddings into $L_1$","display_name":"Improved Lower Bounds for Embeddings into $L_1$","publication_year":2009,"publication_date":"2009-01-01","ids":{"openalex":"https://openalex.org/W2091399525","doi":"https://doi.org/10.1137/060660126","mag":"2091399525"},"language":"en","primary_location":{"id":"doi:10.1137/060660126","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060660126","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","raw_type":"journal-article"},"type":"article","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/A5037378898","display_name":"Robert Krauthgamer","orcid":"https://orcid.org/0009-0003-8154-3735"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Robert Krauthgamer","raw_affiliation_strings":["robert.krauthgamer@weizmann.ac.il#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"robert.krauthgamer@weizmann.ac.il#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5010842984","display_name":"Yuval Rabani","orcid":"https://orcid.org/0000-0001-7772-2544"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yuval Rabani","raw_affiliation_strings":["rabani@cs.technion.ac.il#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"rabani@cs.technion.ac.il#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.4302,"has_fulltext":false,"cited_by_count":39,"citation_normalized_percentile":{"value":0.88728049,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"38","issue":"6","first_page":"2487","last_page":"2498"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9998000264167786,"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":0.9998000264167786,"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/T12288","display_name":"Optimization and Search Problems","score":0.98089998960495,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T10237","display_name":"Cryptography and Data Security","score":0.9724000096321106,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/semidefinite-programming","display_name":"Semidefinite programming","score":0.7561147809028625},{"id":"https://openalex.org/keywords/embedding","display_name":"Embedding","score":0.7519996166229248},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.6714305877685547},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6401908993721008},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.6009169816970825},{"id":"https://openalex.org/keywords/metric-space","display_name":"Metric space","score":0.5715428590774536},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.5437535047531128},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5108591914176941},{"id":"https://openalex.org/keywords/distortion","display_name":"Distortion (music)","score":0.48474690318107605},{"id":"https://openalex.org/keywords/omega","display_name":"Omega","score":0.46993526816368103},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.45553019642829895},{"id":"https://openalex.org/keywords/edit-distance","display_name":"Edit distance","score":0.4193374514579773},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.23730674386024475},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.19591596722602844},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.1420224905014038},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.0769868791103363},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07121023535728455}],"concepts":[{"id":"https://openalex.org/C101901036","wikidata":"https://www.wikidata.org/wiki/Q2269096","display_name":"Semidefinite programming","level":2,"score":0.7561147809028625},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.7519996166229248},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.6714305877685547},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6401908993721008},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.6009169816970825},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.5715428590774536},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.5437535047531128},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5108591914176941},{"id":"https://openalex.org/C126780896","wikidata":"https://www.wikidata.org/wiki/Q899871","display_name":"Distortion (music)","level":4,"score":0.48474690318107605},{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.46993526816368103},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.45553019642829895},{"id":"https://openalex.org/C44359876","wikidata":"https://www.wikidata.org/wiki/Q5338467","display_name":"Edit distance","level":2,"score":0.4193374514579773},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.23730674386024475},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.19591596722602844},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.1420224905014038},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0769868791103363},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07121023535728455},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","level":1,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"id":"https://openalex.org/C2776257435","wikidata":"https://www.wikidata.org/wiki/Q1576430","display_name":"Bandwidth (computing)","level":2,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C194257627","wikidata":"https://www.wikidata.org/wiki/Q211554","display_name":"Amplifier","level":3,"score":0.0},{"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:10.1137/060660126","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060660126","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W1529556207","https://openalex.org/W1986296546","https://openalex.org/W2005090831","https://openalex.org/W2063491776","https://openalex.org/W2074231493","https://openalex.org/W2088101210","https://openalex.org/W2107881198","https://openalex.org/W2119338820","https://openalex.org/W2150148016","https://openalex.org/W2161719898","https://openalex.org/W2176446742"],"related_works":["https://openalex.org/W238609530","https://openalex.org/W3044917232","https://openalex.org/W1498160656","https://openalex.org/W2119149496","https://openalex.org/W2055693471","https://openalex.org/W2139858675","https://openalex.org/W2952580779","https://openalex.org/W1537327044","https://openalex.org/W4295101776","https://openalex.org/W2734192830"],"abstract_inverted_index":{"We":[0,119],"improve":[1],"upon":[2,67],"recent":[3,71,143],"lower":[4,49,72,146],"bounds":[5],"on":[6,51,108,128,165],"the":[7,47,52,70,92,103,124,160],"minimum":[8],"distortion":[9,38,134],"of":[10,32,39,55,74,94,102,110,135,159,167],"embedding":[11,123],"certain":[12],"finite":[13],"metric":[14,30,127],"spaces":[15],"into":[16,98,130],"$L_1$.":[17],"In":[18],"particular,":[19],"we":[20],"show":[21,121],"that":[22,35,122],"for":[23,42,61,88],"every":[24],"$n\\ge1$,":[25],"there":[26],"is":[27],"an":[28,44],"n-point":[29],"space":[31],"negative":[33,95],"type":[34,96],"requires":[36,132],"a":[37,56,133,141],"$\\Omega(\\log\\log":[40],"n)$":[41],"such":[43],"embedding,":[45],"implying":[46],"same":[48],"bound":[50,73,147],"integrality":[53,86],"gap":[54,87],"well-known":[57],"semidefinite":[58],"programming":[59],"relaxation":[60],"sparsest":[62],"cut.":[63],"This":[64,138],"result":[65,139],"builds":[66],"and":[68,80,91,150],"improves":[69,140],"$(\\log\\log":[75],"n)^{1/6-o(1)}$":[76],"due":[77],"to":[78],"Khot":[79,149],"Vishnoi":[81],"[The":[82],"unique":[83],"games":[84],"conjecture,":[85],"cut":[89],"problems":[90],"embeddability":[93],"metrics":[97],"$l_1$,":[99],"in":[100,157],"Proceedings":[101,158],"46th":[104,161],"Annual":[105,162],"IEEE":[106,163],"Symposium":[107,164],"Foundations":[109,166],"Computer":[111,168],"Science,":[112,169],"IEEE,":[113,170],"Piscataway,":[114,171],"NJ,":[115,172],"2005,":[116,173],"pp.":[117,174],"53\u201362].":[118],"also":[120],"edit":[125],"distance":[126],"$\\{0,1\\}^n$":[129],"$L_1$":[131],"$\\Omega(\\log":[136],"n)$.":[137],"very":[142],"$(\\log":[144],"n)^{1/2-o(1)}$":[145],"by":[148],"Naor":[151],"[Nonembeddability":[152],"theorems":[153],"via":[154],"Fourier":[155],"analysis,":[156],"101\u2013112].":[175]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":6},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}