{"id":"https://openalex.org/W2588820692","doi":"https://doi.org/10.1007/s00454-017-9878-7","title":"Four Soviets Walk the Dog: Improved Bounds for Computing the Fr\u00e9chet Distance","display_name":"Four Soviets Walk the Dog: Improved Bounds for Computing the Fr\u00e9chet Distance","publication_year":2017,"publication_date":"2017-02-27","ids":{"openalex":"https://openalex.org/W2588820692","doi":"https://doi.org/10.1007/s00454-017-9878-7","mag":"2588820692"},"language":"en","primary_location":{"id":"doi:10.1007/s00454-017-9878-7","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-017-9878-7","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-017-9878-7.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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete & Computational Geometry","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00454-017-9878-7.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5077490455","display_name":"Kevin Buchin","orcid":"https://orcid.org/0000-0002-3022-7877"},"institutions":[{"id":"https://openalex.org/I83019370","display_name":"Eindhoven University of Technology","ror":"https://ror.org/02c2kyt77","country_code":"NL","type":"education","lineage":["https://openalex.org/I83019370"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Kevin Buchin","raw_affiliation_strings":["Department of Mathematics and Computer Science, TU Eindhoven, PO Box 513, 5600 MB, Eindhoven, The Netherlands"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science, TU Eindhoven, PO Box 513, 5600 MB, Eindhoven, The Netherlands","institution_ids":["https://openalex.org/I83019370"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5086805770","display_name":"Maike Buchin","orcid":"https://orcid.org/0000-0002-3446-4343"},"institutions":[{"id":"https://openalex.org/I904495901","display_name":"Ruhr University Bochum","ror":"https://ror.org/04tsk2644","country_code":"DE","type":"education","lineage":["https://openalex.org/I904495901"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Maike Buchin","raw_affiliation_strings":["Mathematik, Ruhr Universit\u00e4t Bochum, 44780, Bochum, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematik, Ruhr Universit\u00e4t Bochum, 44780, Bochum, Germany","institution_ids":["https://openalex.org/I904495901"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5062614232","display_name":"Wouter Meulemans","orcid":"https://orcid.org/0000-0002-4978-3400"},"institutions":[{"id":"https://openalex.org/I83019370","display_name":"Eindhoven University of Technology","ror":"https://ror.org/02c2kyt77","country_code":"NL","type":"education","lineage":["https://openalex.org/I83019370"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Wouter Meulemans","raw_affiliation_strings":["Department of Mathematics and Computer Science, TU Eindhoven, PO Box 513, 5600 MB, Eindhoven, The Netherlands"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science, TU Eindhoven, PO Box 513, 5600 MB, Eindhoven, The Netherlands","institution_ids":["https://openalex.org/I83019370"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5090438334","display_name":"Wolfgang Mulzer","orcid":"https://orcid.org/0000-0002-1948-5840"},"institutions":[{"id":"https://openalex.org/I75951250","display_name":"Freie Universit\u00e4t Berlin","ror":"https://ror.org/046ak2485","country_code":"DE","type":"education","lineage":["https://openalex.org/I75951250"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Wolfgang Mulzer","raw_affiliation_strings":["Institut f\u00fcr Informatik, Freie Universit\u00e4t Berlin, 14195, Berlin, Germany"],"raw_orcid":"https://orcid.org/0000-0002-1948-5840","affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Informatik, Freie Universit\u00e4t Berlin, 14195, Berlin, Germany","institution_ids":["https://openalex.org/I75951250"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5090438334"],"corresponding_institution_ids":["https://openalex.org/I75951250"],"apc_list":{"value":2890,"currency":"USD","value_usd":2890},"apc_paid":{"value":2890,"currency":"USD","value_usd":2890},"fwci":5.899,"has_fulltext":true,"cited_by_count":31,"citation_normalized_percentile":{"value":0.95465509,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"58","issue":"1","first_page":"180","last_page":"216"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"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"}},"topics":[{"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/T11106","display_name":"Data Management and Algorithms","score":0.9976000189781189,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/T12923","display_name":"Digital Image Processing Techniques","score":0.9940999746322632,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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":0.6391498446464539},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6276543736457825},{"id":"https://openalex.org/keywords/binary-logarithm","display_name":"Binary logarithm","score":0.5621581673622131},{"id":"https://openalex.org/keywords/edit-distance","display_name":"Edit distance","score":0.5215016007423401},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.492501825094223},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.4809640944004059},{"id":"https://openalex.org/keywords/log-log-plot","display_name":"Log-log plot","score":0.41734617948532104},{"id":"https://openalex.org/keywords/computational-geometry","display_name":"Computational geometry","score":0.41472938656806946},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3349590003490448},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.28903061151504517}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6391498446464539},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6276543736457825},{"id":"https://openalex.org/C63553672","wikidata":"https://www.wikidata.org/wiki/Q581168","display_name":"Binary logarithm","level":2,"score":0.5621581673622131},{"id":"https://openalex.org/C44359876","wikidata":"https://www.wikidata.org/wiki/Q5338467","display_name":"Edit distance","level":2,"score":0.5215016007423401},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.492501825094223},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.4809640944004059},{"id":"https://openalex.org/C195292467","wikidata":"https://www.wikidata.org/wiki/Q2091879","display_name":"Log-log plot","level":3,"score":0.41734617948532104},{"id":"https://openalex.org/C29123130","wikidata":"https://www.wikidata.org/wiki/Q874709","display_name":"Computational geometry","level":2,"score":0.41472938656806946},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3349590003490448},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.28903061151504517}],"mesh":[],"locations_count":8,"locations":[{"id":"doi:10.1007/s00454-017-9878-7","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-017-9878-7","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-017-9878-7.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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete & Computational Geometry","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1209.4403","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1209.4403","pdf_url":"https://arxiv.org/pdf/1209.4403","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:pure.tue.nl:publications/386f7e9c-81e6-48fa-ac3a-d9d0a97b7f71","is_oa":true,"landing_page_url":"https://research.tue.nl/en/publications/386f7e9c-81e6-48fa-ac3a-d9d0a97b7f71","pdf_url":"https://pure.tue.nl/ws/files/71081973/10.1007_s00454_017_9878_7.pdf","source":{"id":"https://openalex.org/S4406922641","display_name":"TU/e Research Portal","issn_l":null,"issn":null,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Buchin, K A, Buchin, M, Meulemans, W & Mulzer, W 2017, 'Four Soviets walk the dog: improved bounds for computing the Fr\u00e9chet distance', Discrete and Computational Geometry, vol. 58, no. 1, pp. 180-216. https://doi.org/10.1007/s00454-017-9878-7","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:865514","is_oa":false,"landing_page_url":"http://library.tue.nl/csp/dare/LinkToRepository.csp?recordnumber=865514","pdf_url":null,"source":{"id":"https://openalex.org/S4406923046","display_name":"TU/e Research Portal (Eindhoven University of Technology)","issn_l":null,"issn":null,"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":"ISSN:0179-5376","raw_type":"Article / Letter to the editor"},{"id":"pmh:881701","is_oa":false,"landing_page_url":"http://library.tue.nl/csp/dare/LinkToRepository.csp?recordnumber=881701","pdf_url":null,"source":{"id":"https://openalex.org/S4406923046","display_name":"TU/e Research Portal (Eindhoven University of Technology)","issn_l":null,"issn":null,"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":"ISSN:0179-5376","raw_type":"Article / Letter to the editor"},{"id":"pmh:oai:library.tue.nl:865514","is_oa":false,"landing_page_url":"http://repository.tue.nl/865514","pdf_url":null,"source":{"id":"https://openalex.org/S4406923046","display_name":"TU/e Research Portal (Eindhoven University of Technology)","issn_l":null,"issn":null,"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":"ISSN:0179-5376","raw_type":"Article / Letter to the editor"},{"id":"pmh:oai:library.tue.nl:881701","is_oa":false,"landing_page_url":"http://repository.tue.nl/881701","pdf_url":null,"source":{"id":"https://openalex.org/S4406923046","display_name":"TU/e Research Portal (Eindhoven University of Technology)","issn_l":null,"issn":null,"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":"ISSN:0179-5376","raw_type":"Article / Letter to the editor"},{"id":"pmh:tue:oai:pure.tue.nl:publications/386f7e9c-81e6-48fa-ac3a-d9d0a97b7f71","is_oa":true,"landing_page_url":"https://research.tue.nl/nl/publications/386f7e9c-81e6-48fa-ac3a-d9d0a97b7f71","pdf_url":null,"source":{"id":"https://openalex.org/S4306401843","display_name":"Data Archiving and Networked Services (DANS)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1322597698","host_organization_name":"Royal Netherlands Academy of Arts and Sciences","host_organization_lineage":["https://openalex.org/I1322597698"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Discrete and Computational Geometry, 58(1), 180 - 216. Springer","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.1007/s00454-017-9878-7","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-017-9878-7","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-017-9878-7.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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete & Computational Geometry","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.699999988079071,"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions"}],"awards":[{"id":"https://openalex.org/G1065468951","display_name":null,"funder_award_id":"MU/3501/2","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G258765838","display_name":null,"funder_award_id":"639.022.707","funder_id":"https://openalex.org/F4320321800","funder_display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek"},{"id":"https://openalex.org/G3881026628","display_name":null,"funder_award_id":"IC0903 MOVE","funder_id":"https://openalex.org/F4320320366","funder_display_name":"European Cooperation in Science and Technology"},{"id":"https://openalex.org/G822396784","display_name":null,"funder_award_id":"MU/3501/1","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G8924767945","display_name":null,"funder_award_id":"612.001.106","funder_id":"https://openalex.org/F4320321800","funder_display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek"}],"funders":[{"id":"https://openalex.org/F4320320366","display_name":"European Cooperation in Science and Technology","ror":"https://ror.org/01bstzn19"},{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320321800","display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek","ror":"https://ror.org/04jsz6e67"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2588820692.pdf","grobid_xml":"https://content.openalex.org/works/W2588820692.grobid-xml"},"referenced_works_count":75,"referenced_works":["https://openalex.org/W15092079","https://openalex.org/W77353308","https://openalex.org/W987035227","https://openalex.org/W1497463354","https://openalex.org/W1519444547","https://openalex.org/W1527197079","https://openalex.org/W1543972922","https://openalex.org/W1544411027","https://openalex.org/W1734262574","https://openalex.org/W1864508826","https://openalex.org/W1897841194","https://openalex.org/W1967985699","https://openalex.org/W1985655539","https://openalex.org/W1986022261","https://openalex.org/W1986338919","https://openalex.org/W2005314985","https://openalex.org/W2008735761","https://openalex.org/W2009283111","https://openalex.org/W2009798194","https://openalex.org/W2010438541","https://openalex.org/W2010536454","https://openalex.org/W2020874136","https://openalex.org/W2024305877","https://openalex.org/W2028747718","https://openalex.org/W2049647076","https://openalex.org/W2060270693","https://openalex.org/W2062556295","https://openalex.org/W2064671795","https://openalex.org/W2074286662","https://openalex.org/W2082176820","https://openalex.org/W2083244827","https://openalex.org/W2083364906","https://openalex.org/W2086825382","https://openalex.org/W2091505308","https://openalex.org/W2091720561","https://openalex.org/W2091735588","https://openalex.org/W2098207812","https://openalex.org/W2100503751","https://openalex.org/W2102465478","https://openalex.org/W2108233707","https://openalex.org/W2110138621","https://openalex.org/W2113946784","https://openalex.org/W2116264435","https://openalex.org/W2121770144","https://openalex.org/W2122005371","https://openalex.org/W2122089364","https://openalex.org/W2122538444","https://openalex.org/W2123644741","https://openalex.org/W2124299914","https://openalex.org/W2128953738","https://openalex.org/W2134112278","https://openalex.org/W2135531396","https://openalex.org/W2147429200","https://openalex.org/W2150123893","https://openalex.org/W2153708898","https://openalex.org/W2157734830","https://openalex.org/W2161679356","https://openalex.org/W2162911459","https://openalex.org/W2174643652","https://openalex.org/W2256871140","https://openalex.org/W2561675875","https://openalex.org/W2568308068","https://openalex.org/W2570995828","https://openalex.org/W2597608265","https://openalex.org/W2623873233","https://openalex.org/W2746911795","https://openalex.org/W2884439552","https://openalex.org/W2911302472","https://openalex.org/W2949306052","https://openalex.org/W3022326557","https://openalex.org/W3041834803","https://openalex.org/W4213071546","https://openalex.org/W4247633649","https://openalex.org/W4285719527","https://openalex.org/W4298227433"],"related_works":["https://openalex.org/W2035522910","https://openalex.org/W2005615533","https://openalex.org/W2055932080","https://openalex.org/W4377371889","https://openalex.org/W2018076478","https://openalex.org/W1992470151","https://openalex.org/W2113623403","https://openalex.org/W1968512104","https://openalex.org/W1862126075","https://openalex.org/W78560857"],"abstract_inverted_index":{"Given":[0],"two":[1,141],"polygonal":[2,124,142],"curves":[3,143],"in":[4,34,144,156],"the":[5,23,50,62,66,69,74,89,105,109,113,137,176,209,215],"plane,":[6],"there":[7,169],"are":[8],"many":[9,36],"ways":[10],"to":[11,86,103,135,207],"define":[12],"a":[13,132,152,162,220],"notion":[14],"of":[15,68,76,112,120,123,179,199],"similarity":[16],"between":[17,140],"them.":[18],"One":[19],"popular":[20],"measure":[21],"is":[22,93],"Fr\u00e9chet":[24,63,114,138,217],"distance.":[25],"Since":[26],"it":[27],"was":[28],"proposed":[29],"by":[30,56],"Alt":[31,57,85],"and":[32,38,58,155],"Godau":[33,59],"1992,":[35],"variants":[37],"extensions":[39],"have":[40],"been":[41],"studied.":[42],"Nonetheless,":[43],"even":[44],"more":[45],"than":[46],"20":[47],"years":[48],"later,":[49],"original":[51],"$$O(n^2":[52,146],"\\log":[53,149,159],"n)$$":[54],"algorithm":[55,134,212],"for":[60,108,175,184,213],"computing":[61,214],"distance":[64,139,218],"remains":[65],"state":[67],"art":[70],"(here,":[71],"n":[72],"denotes":[73],"number":[75],"edges":[77],"on":[78,127,151,161,219],"each":[79],"curve).":[80],"This":[81],"has":[82],"led":[83],"Helmut":[84],"conjecture":[87],"that":[88,168,192],"associated":[90],"decision":[91,173,177],"problem":[92,178],"3SUM-hard.":[94],"In":[95],"recent":[96],"work,":[97,129],"Agarwal":[98],"et":[99],"al.":[100],"show":[101,167,205],"how":[102,206],"break":[104],"quadratic":[106],"barrier":[107],"discrete":[110],"version":[111],"distance,":[115],"where":[116],"one":[117],"considers":[118],"sequences":[119],"points":[121],"instead":[122],"curves.":[125],"Building":[126],"their":[128],"we":[130,166,204],"give":[131],"randomized":[133],"compute":[136],"time":[145,157],"\\sqrt{\\log":[147],"n}(\\log":[148],"n)^{3/2})$$":[150],"pointer":[153],"machine":[154],"$$O(n^2(\\log":[158],"n)^2)$$":[160],"word":[163,221],"RAM.":[164,222],"Furthermore,":[165],"exists":[170],"an":[171,195],"algebraic":[172],"tree":[174],"depth":[180],"$$O(n^{2-\\varepsilon":[181],"})$$":[182],",":[183],"some":[185],"$$\\varepsilon":[186],">":[187],"0$$":[188],".":[189],"We":[190],"believe":[191],"this":[193,200],"reveals":[194],"intriguing":[196],"new":[197],"aspect":[198],"well-studied":[201],"problem.":[202],"Finally,":[203],"obtain":[208],"first":[210],"subquadratic":[211],"weak":[216]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":8},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":3}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}