{"id":"https://openalex.org/W2038607380","doi":"https://doi.org/10.1007/s00454-003-2872-2","title":"Metric Embeddings?Beyond One-Dimensional Distortion","display_name":"Metric Embeddings?Beyond One-Dimensional Distortion","publication_year":2004,"publication_date":"2004-02-01","ids":{"openalex":"https://openalex.org/W2038607380","doi":"https://doi.org/10.1007/s00454-003-2872-2","mag":"2038607380"},"language":"en","primary_location":{"id":"doi:10.1007/s00454-003-2872-2","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-003-2872-2","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-003-2872-2.pdf","source":{"id":"https://openalex.org/S103671469","display_name":"Discrete & Computational Geometry","issn_l":"0179-5376","issn":["0179-5376","1432-0444"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete and Computational Geometry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://link.springer.com/content/pdf/10.1007/s00454-003-2872-2.pdf","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":[{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]},{"id":"https://openalex.org/I1297971548","display_name":"International Computer Science Institute","ror":"https://ror.org/01ewh7m12","country_code":"US","type":"nonprofit","lineage":["https://openalex.org/I1297971548"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Robert Krauthgamer","raw_affiliation_strings":["International Computer Science Institute and Computer Science Division, University of California, Berkeley, CA 94720, USA"],"affiliations":[{"raw_affiliation_string":"International Computer Science Institute and Computer Science Division, University of California, Berkeley, CA 94720, USA","institution_ids":["https://openalex.org/I1297971548","https://openalex.org/I95457486"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5050009387","display_name":"Nathan Linial","orcid":null},"institutions":[{"id":"https://openalex.org/I197251160","display_name":"Hebrew University of Jerusalem","ror":"https://ror.org/03qxff017","country_code":"IL","type":"education","lineage":["https://openalex.org/I197251160"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Nathan Linial","raw_affiliation_strings":["School of Computer Science and Engineering, The Hebrew \nUniversity of Jerusalem, Jerusalem 91904, Israel","School of Computer Science and Engineering, The Hebrew University of Jerusalem, Jerusalem 91904, Israel;"],"affiliations":[{"raw_affiliation_string":"School of Computer Science and Engineering, The Hebrew \nUniversity of Jerusalem, Jerusalem 91904, Israel","institution_ids":["https://openalex.org/I197251160"]},{"raw_affiliation_string":"School of Computer Science and Engineering, The Hebrew University of Jerusalem, Jerusalem 91904, Israel;","institution_ids":["https://openalex.org/I197251160"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5043150610","display_name":"Avner Magen","orcid":null},"institutions":[{"id":"https://openalex.org/I185261750","display_name":"University of Toronto","ror":"https://ror.org/03dbr7087","country_code":"CA","type":"education","lineage":["https://openalex.org/I185261750"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Avner Magen","raw_affiliation_strings":["Department of Computer Science, University of Toronto, Toronto, Ontario, Canada M5S 3G4","Department of Computer Science, University of Toronto, Toronto, Ontario, Canada M5S 3G4#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Toronto, Toronto, Ontario, Canada M5S 3G4","institution_ids":["https://openalex.org/I185261750"]},{"raw_affiliation_string":"Department of Computer Science, University of Toronto, Toronto, Ontario, Canada M5S 3G4#TAB#","institution_ids":["https://openalex.org/I185261750"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5037378898"],"corresponding_institution_ids":["https://openalex.org/I1297971548","https://openalex.org/I95457486"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":1.7286,"has_fulltext":true,"cited_by_count":12,"citation_normalized_percentile":{"value":0.84008621,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"31","issue":"3","first_page":"339","last_page":"356"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","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/T10374","display_name":"Advanced Graph Theory Research","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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9998000264167786,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9997000098228455,"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/pairwise-comparison","display_name":"Pairwise comparison","score":0.8393704891204834},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7260503768920898},{"id":"https://openalex.org/keywords/embedding","display_name":"Embedding","score":0.7241924405097961},{"id":"https://openalex.org/keywords/distortion","display_name":"Distortion (music)","score":0.6663292646408081},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.5982347130775452},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5721310377120972},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5464119911193848},{"id":"https://openalex.org/keywords/metric-space","display_name":"Metric space","score":0.5390689969062805},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3501468300819397},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.16689324378967285},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.10056540369987488},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.05946993827819824}],"concepts":[{"id":"https://openalex.org/C184898388","wikidata":"https://www.wikidata.org/wiki/Q1435712","display_name":"Pairwise comparison","level":2,"score":0.8393704891204834},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7260503768920898},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.7241924405097961},{"id":"https://openalex.org/C126780896","wikidata":"https://www.wikidata.org/wiki/Q899871","display_name":"Distortion (music)","level":4,"score":0.6663292646408081},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.5982347130775452},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5721310377120972},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5464119911193848},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.5390689969062805},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3501468300819397},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.16689324378967285},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.10056540369987488},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.05946993827819824},{"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/C194257627","wikidata":"https://www.wikidata.org/wiki/Q211554","display_name":"Amplifier","level":3,"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/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/s00454-003-2872-2","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-003-2872-2","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-003-2872-2.pdf","source":{"id":"https://openalex.org/S103671469","display_name":"Discrete & Computational Geometry","issn_l":"0179-5376","issn":["0179-5376","1432-0444"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete and Computational Geometry","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.21.8310","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.21.8310","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.huji.ac.il/~nati/PAPERS/volume.ps.gz","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.3.7767","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.3.7767","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://leibniz.cs.huji.ac.il/tr/acc/2003/HUJI-CSE-LTR-2003-53_volume.ps.gz","raw_type":"text"},{"id":"pmh:oai:berkeley.edu:13030-hb0z09n9cz","is_oa":false,"landing_page_url":"http://techreports.lib.berkeley.edu/accessPages/CSD-02-1181.html","pdf_url":null,"source":{"id":"https://openalex.org/S7407050879","display_name":"UC Berkeley","issn_l":null,"issn":[],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"technical reports"}],"best_oa_location":{"id":"doi:10.1007/s00454-003-2872-2","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-003-2872-2","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-003-2872-2.pdf","source":{"id":"https://openalex.org/S103671469","display_name":"Discrete & Computational Geometry","issn_l":"0179-5376","issn":["0179-5376","1432-0444"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete and Computational Geometry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2049968996","display_name":"A Proposal for Research on Markov Chains, Approximate Counting and Finite Metric Spaces","funder_award_id":"9820951","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G3617495587","display_name":"ITR/SY: Discrete Models & Algorithms in the Sciences","funder_award_id":"0121555","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8001024703","display_name":null,"funder_award_id":"CCR-0121555","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320321950","display_name":"Hebrew University of Jerusalem","ror":"https://ror.org/03qxff017"},{"id":"https://openalex.org/F4320332180","display_name":"Defense Advanced Research Projects Agency","ror":"https://ror.org/02caytj08"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2038607380.pdf","grobid_xml":"https://content.openalex.org/works/W2038607380.grobid-xml"},"referenced_works_count":20,"referenced_works":["https://openalex.org/W192109880","https://openalex.org/W1530239281","https://openalex.org/W1578390689","https://openalex.org/W1621295142","https://openalex.org/W1978020111","https://openalex.org/W1981853164","https://openalex.org/W1984569679","https://openalex.org/W2001231944","https://openalex.org/W2004322147","https://openalex.org/W2017271493","https://openalex.org/W2047378159","https://openalex.org/W2063491776","https://openalex.org/W2066864620","https://openalex.org/W2080608361","https://openalex.org/W2096746450","https://openalex.org/W2141793995","https://openalex.org/W2167816765","https://openalex.org/W2176446742","https://openalex.org/W2295428206","https://openalex.org/W2951166730"],"related_works":["https://openalex.org/W2773696207","https://openalex.org/W4294491141","https://openalex.org/W1483352855","https://openalex.org/W2163459114","https://openalex.org/W2007806267","https://openalex.org/W2905013296","https://openalex.org/W4295332041","https://openalex.org/W2038607380","https://openalex.org/W1585282976","https://openalex.org/W2952186229"],"abstract_inverted_index":null,"counts_by_year":[{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}