{"id":"https://openalex.org/W2004067661","doi":"https://doi.org/10.1137/070712080","title":"Local Global Tradeoffs in Metric Embeddings","display_name":"Local Global Tradeoffs in Metric Embeddings","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W2004067661","doi":"https://doi.org/10.1137/070712080","mag":"2004067661"},"language":"en","primary_location":{"id":"doi:10.1137/070712080","is_oa":false,"landing_page_url":"https://doi.org/10.1137/070712080","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/A5071016611","display_name":"Moses Charikar","orcid":"https://orcid.org/0000-0003-0807-3389"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Moses Charikar","raw_affiliation_strings":["moses@cs.princeton.edu#TAB#"],"affiliations":[{"raw_affiliation_string":"moses@cs.princeton.edu#TAB#","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5033681881","display_name":"Konstantin Makarychev","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Konstantin Makarychev","raw_affiliation_strings":["konstantin@us.ibm.com#TAB#"],"affiliations":[{"raw_affiliation_string":"konstantin@us.ibm.com#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5068045392","display_name":"Yury Makarychev","orcid":"https://orcid.org/0000-0003-3114-3947"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yury Makarychev","raw_affiliation_strings":["yurym@microsoft.com#TAB#"],"affiliations":[{"raw_affiliation_string":"yurym@microsoft.com#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5071016611"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.6833,"has_fulltext":false,"cited_by_count":18,"citation_normalized_percentile":{"value":0.70146716,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"39","issue":"6","first_page":"2487","last_page":"2512"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9991999864578247,"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":0.9991999864578247,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9976000189781189,"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":0.9757999777793884,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.7896201610565186},{"id":"https://openalex.org/keywords/omega","display_name":"Omega","score":0.7553536891937256},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7539554238319397},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.7416329383850098},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.710404098033905},{"id":"https://openalex.org/keywords/metric-space","display_name":"Metric space","score":0.6533697247505188},{"id":"https://openalex.org/keywords/binary-logarithm","display_name":"Binary logarithm","score":0.5875091552734375},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.521906852722168},{"id":"https://openalex.org/keywords/lift","display_name":"Lift (data mining)","score":0.5099483728408813},{"id":"https://openalex.org/keywords/distortion","display_name":"Distortion (music)","score":0.4902198910713196},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4670397639274597},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.4270508587360382},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3754779100418091},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.13582852482795715},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1337040364742279},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.08106866478919983}],"concepts":[{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.7896201610565186},{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.7553536891937256},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7539554238319397},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.7416329383850098},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.710404098033905},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.6533697247505188},{"id":"https://openalex.org/C63553672","wikidata":"https://www.wikidata.org/wiki/Q581168","display_name":"Binary logarithm","level":2,"score":0.5875091552734375},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.521906852722168},{"id":"https://openalex.org/C139002025","wikidata":"https://www.wikidata.org/wiki/Q3001212","display_name":"Lift (data mining)","level":2,"score":0.5099483728408813},{"id":"https://openalex.org/C126780896","wikidata":"https://www.wikidata.org/wiki/Q899871","display_name":"Distortion (music)","level":4,"score":0.4902198910713196},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4670397639274597},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4270508587360382},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3754779100418091},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.13582852482795715},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1337040364742279},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.08106866478919983},{"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C46362747","wikidata":"https://www.wikidata.org/wiki/Q173431","display_name":"CMOS","level":2,"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C49040817","wikidata":"https://www.wikidata.org/wiki/Q193091","display_name":"Optoelectronics","level":1,"score":0.0},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1137/070712080","is_oa":false,"landing_page_url":"https://doi.org/10.1137/070712080","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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.129.842","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.129.842","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.princeton.edu/~kmakaryc/pdf/LocalGlobal.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.169.8013","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.169.8013","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://ttic.uchicago.edu/%7Eyury/papers/LocalGlobal.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.363.9207","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.363.9207","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.princeton.edu/~moses/papers/LocalGlobal.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.430.1716","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.430.1716","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://eccc.hpi-web.de/report/2007/108/download/","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.92.522","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.92.522","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.princeton.edu/~ymakaryc/papers/LocalGlobal.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.4099999964237213,"id":"https://metadata.un.org/sdg/8","display_name":"Decent work and economic growth"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W1587123489","https://openalex.org/W1966053554","https://openalex.org/W1981853164","https://openalex.org/W2017271493","https://openalex.org/W2036959865","https://openalex.org/W2049143039","https://openalex.org/W2063491776","https://openalex.org/W2066864620","https://openalex.org/W2106264302","https://openalex.org/W2107881198","https://openalex.org/W2176446742","https://openalex.org/W4248108185"],"related_works":["https://openalex.org/W238609530","https://openalex.org/W2734192830","https://openalex.org/W3016395638","https://openalex.org/W1636163329","https://openalex.org/W4292947165","https://openalex.org/W3045121788","https://openalex.org/W3201655533","https://openalex.org/W3134442314","https://openalex.org/W3127082728","https://openalex.org/W2067936666"],"abstract_inverted_index":{"Suppose":[0],"that":[1,63,80],"every":[2],"k":[3],"points":[4],"in":[5],"a":[6,37,76,96,106,127],"n":[7],"point":[8],"metric":[9],"space":[10,31],"X":[11,32,64],"are":[12],"D-distortion":[13],"embeddable":[14],"into":[15,33,68],"$\\ell_1$.":[16,34],"We":[17],"give":[18,75,95,105],"upper":[19],"and":[20,41,101],"lower":[21,77,97,107],"bounds":[22,115],"on":[23,118],"the":[24,29,46,119],"distortion":[25,71],"required":[26],"to":[27],"embed":[28],"entire":[30],"This":[35],"is":[36,42,83,87],"natural":[38],"mathematical":[39],"question":[40],"also":[43],"motivated":[44],"by":[45,51],"study":[47,128],"of":[48,99,109,121,129],"relaxations":[49],"obtained":[50],"lift-and-project":[52],"methods":[53],"for":[54,102],"graph":[55],"partitioning":[56],"problems.":[57],"In":[58],"this":[59,81],"setting,":[60],"we":[61,74,94,104],"show":[62],"can":[65],"be":[66],"embedded":[67],"$\\ell_1$":[69],"with":[70],"$O(D\\times\\log(n/k))$.":[72],"Moreover,":[73],"bound":[78,98,108],"showing":[79],"result":[82],"tight":[84],"if":[85],"D":[86],"bounded":[88],"away":[89],"from":[90],"1.":[91],"For":[92],"$D=1+\\delta$":[93],"$\\Omega(\\log(n/k)/\\log(1/\\delta))$;":[100],"$D=1$,":[103],"$\\Omega(\\log":[110],"n/(\\log":[111],"k+\\log\\log":[112],"n))$.":[113],"Our":[114],"significantly":[116],"improve":[117],"results":[120],"Arora":[122],"et":[123],"al.":[124],"who":[125],"initiated":[126],"these":[130],"questions.":[131]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":2},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}