{"id":"https://openalex.org/W4392617076","doi":"https://doi.org/10.20382/jocg.v16i2a10","title":"Fine-Grained Complexity of Earth Mover's Distance under Translation","display_name":"Fine-Grained Complexity of Earth Mover's Distance under Translation","publication_year":2024,"publication_date":"2024-01-01","ids":{"openalex":"https://openalex.org/W4392617076","doi":"https://doi.org/10.20382/jocg.v16i2a10"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2403.04356","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2403.04356","pdf_url":"https://arxiv.org/pdf/2403.04356","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"","raw_type":"text"},"type":"preprint","indexed_in":["arxiv","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2403.04356","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5044394587","display_name":"Karl Bringmann","orcid":"https://orcid.org/0000-0003-1356-5177"},"institutions":[{"id":"https://openalex.org/I4210109712","display_name":"Max Planck Institute for Informatics","ror":"https://ror.org/01w19ak89","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210109712"]},{"id":"https://openalex.org/I91712215","display_name":"Saarland University","ror":"https://ror.org/01jdpyv68","country_code":"DE","type":"education","lineage":["https://openalex.org/I91712215"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Bringmann, Karl","raw_affiliation_strings":["Saarland University and Max Planck Institute for Informatics"],"raw_orcid":"https://orcid.org/0000-0003-1356-5177","affiliations":[{"raw_affiliation_string":"Saarland University and Max Planck Institute for Informatics","institution_ids":["https://openalex.org/I4210109712","https://openalex.org/I91712215"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5032979919","display_name":"Frank Staals","orcid":null},"institutions":[{"id":"https://openalex.org/I193662353","display_name":"Utrecht University","ror":"https://ror.org/04pp8hn57","country_code":"NL","type":"education","lineage":["https://openalex.org/I193662353"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Staals, Frank","raw_affiliation_strings":["Utrecht University"],"raw_orcid":"https://orcid.org/0009-0004-8522-1351","affiliations":[{"raw_affiliation_string":"Utrecht University","institution_ids":["https://openalex.org/I193662353"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5055238529","display_name":"Karol W\u0119grzycki","orcid":"https://orcid.org/0000-0001-9746-5733"},"institutions":[{"id":"https://openalex.org/I4210109712","display_name":"Max Planck Institute for Informatics","ror":"https://ror.org/01w19ak89","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210109712"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"W\u0119grzycki, Karol","raw_affiliation_strings":["Max Planck Institute for Informatics"],"raw_orcid":"https://orcid.org/0000-0001-9746-5733","affiliations":[{"raw_affiliation_string":"Max Planck Institute for Informatics","institution_ids":["https://openalex.org/I4210109712"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5028724460","display_name":"Geert van Wordragen","orcid":"https://orcid.org/0000-0002-2650-638X"},"institutions":[{"id":"https://openalex.org/I9927081","display_name":"Aalto University","ror":"https://ror.org/020hwjq30","country_code":"FI","type":"education","lineage":["https://openalex.org/I9927081"]}],"countries":["FI"],"is_corresponding":false,"raw_author_name":"van Wordragen, Geert","raw_affiliation_strings":["Aalto University"],"raw_orcid":"https://orcid.org/0000-0002-2650-638X","affiliations":[{"raw_affiliation_string":"Aalto University","institution_ids":["https://openalex.org/I9927081"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T14470","display_name":"Advanced Data Processing Techniques","score":0.8863000273704529,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T14470","display_name":"Advanced Data Processing Techniques","score":0.8863000273704529,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10586","display_name":"Robotic Path Planning Algorithms","score":0.881600022315979,"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"}},{"id":"https://openalex.org/T14025","display_name":"Educational Technology and Assessment","score":0.8483999967575073,"subfield":{"id":"https://openalex.org/subfields/1710","display_name":"Information Systems"},"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/translation","display_name":"Translation (biology)","score":0.6786198616027832},{"id":"https://openalex.org/keywords/earth-movers-distance","display_name":"Earth mover's distance","score":0.6088677644729614},{"id":"https://openalex.org/keywords/earth","display_name":"Earth (classical element)","score":0.5712780356407166},{"id":"https://openalex.org/keywords/first-mover-advantage","display_name":"First-mover advantage","score":0.5015661716461182},{"id":"https://openalex.org/keywords/astrobiology","display_name":"Astrobiology","score":0.3512578308582306},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.32244372367858887},{"id":"https://openalex.org/keywords/business","display_name":"Business","score":0.22742459177970886},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2265283763408661},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.21885013580322266},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.13978052139282227},{"id":"https://openalex.org/keywords/industrial-organization","display_name":"Industrial organization","score":0.1316421627998352},{"id":"https://openalex.org/keywords/astronomy","display_name":"Astronomy","score":0.10082069039344788}],"concepts":[{"id":"https://openalex.org/C149364088","wikidata":"https://www.wikidata.org/wiki/Q185917","display_name":"Translation (biology)","level":4,"score":0.6786198616027832},{"id":"https://openalex.org/C82668687","wikidata":"https://www.wikidata.org/wiki/Q3046456","display_name":"Earth mover's distance","level":2,"score":0.6088677644729614},{"id":"https://openalex.org/C26148502","wikidata":"https://www.wikidata.org/wiki/Q2488752","display_name":"Earth (classical element)","level":2,"score":0.5712780356407166},{"id":"https://openalex.org/C196276664","wikidata":"https://www.wikidata.org/wiki/Q121716","display_name":"First-mover advantage","level":2,"score":0.5015661716461182},{"id":"https://openalex.org/C87355193","wikidata":"https://www.wikidata.org/wiki/Q411","display_name":"Astrobiology","level":1,"score":0.3512578308582306},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.32244372367858887},{"id":"https://openalex.org/C144133560","wikidata":"https://www.wikidata.org/wiki/Q4830453","display_name":"Business","level":0,"score":0.22742459177970886},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2265283763408661},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.21885013580322266},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.13978052139282227},{"id":"https://openalex.org/C40700","wikidata":"https://www.wikidata.org/wiki/Q1411783","display_name":"Industrial organization","level":1,"score":0.1316421627998352},{"id":"https://openalex.org/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","level":1,"score":0.10082069039344788},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C105580179","wikidata":"https://www.wikidata.org/wiki/Q188928","display_name":"Messenger RNA","level":3,"score":0.0}],"mesh":[],"locations_count":9,"locations":[{"id":"pmh:oai:arXiv.org:2403.04356","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2403.04356","pdf_url":"https://arxiv.org/pdf/2403.04356","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"","raw_type":"text"},{"id":"pmh:oai:drops-oai.dagstuhl.de:19970","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2024.25","pdf_url":"https://drops.dagstuhl.de/storage/00lipics/lipics-vol293-socg2024/LIPIcs.SoCG.2024.25/LIPIcs.SoCG.2024.25.pdf","source":{"id":"https://openalex.org/S4377196569","display_name":"DROPS (Schloss Dagstuhl \u2013 Leibniz Center for Informatics)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2799853480","host_organization_name":"Schloss Dagstuhl \u2013 Leibniz Center for Informatics","host_organization_lineage":["https://openalex.org/I2799853480"],"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":"","raw_type":"InProceedings"},{"id":"pmh:oai:aaltodoc.aalto.fi:123456789/129016","is_oa":true,"landing_page_url":"https://research.aalto.fi/en/publications/0ca4c3b4-9f42-47fd-8541-bdd4d80f10af","pdf_url":null,"source":{"id":"https://openalex.org/S4306401662","display_name":"Aaltodoc (Aalto University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I9927081","host_organization_name":"Aalto University","host_organization_lineage":["https://openalex.org/I9927081"],"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":null,"raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:doaj.org/article:bbe6073e1bbd49b8b6f3b45e92421275","is_oa":true,"landing_page_url":"https://doaj.org/article/bbe6073e1bbd49b8b6f3b45e92421275","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","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-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Computational Geometry, Vol 16, Iss 2 (2025)","raw_type":"article"},{"id":"pmh:oai:dspace.library.uu.nl:1874/479634","is_oa":true,"landing_page_url":"https://dspace.library.uu.nl/handle/1874/479634","pdf_url":null,"source":{"id":"https://openalex.org/S4306401649","display_name":"Utrecht University Repository (Utrecht University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I193662353","host_organization_name":"Utrecht University","host_organization_lineage":["https://openalex.org/I193662353"],"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":null,"raw_type":"Article"},{"id":"pmh:oai:dspace.library.uu.nl:1874/482309","is_oa":true,"landing_page_url":"https://dspace.library.uu.nl/handle/1874/482309","pdf_url":null,"source":{"id":"https://openalex.org/S4306401649","display_name":"Utrecht University Repository (Utrecht University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I193662353","host_organization_name":"Utrecht University","host_organization_lineage":["https://openalex.org/I193662353"],"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":null,"raw_type":"Part of book"},{"id":"doi:10.48550/arxiv.2403.04356","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2403.04356","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"},{"id":"doi:10.20382/jocg.v16i2a10","is_oa":true,"landing_page_url":"https://doi.org/10.20382/jocg.v16i2a10","pdf_url":null,"source":{"id":"https://openalex.org/S4306400962","display_name":"Journal of Computational Geometry (Carleton University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I67031392","host_organization_name":"Carleton University","host_organization_lineage":["https://openalex.org/I67031392"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"JournalArticle"},{"id":"doi:10.4230/lipics.socg.2024.25","is_oa":true,"landing_page_url":"https://doi.org/10.4230/lipics.socg.2024.25","pdf_url":null,"source":null,"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"ConferencePaper"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2403.04356","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2403.04356","pdf_url":"https://arxiv.org/pdf/2403.04356","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2608529560","display_name":null,"funder_award_id":"850979","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G7842005466","display_name":null,"funder_award_id":"Horizon 2020","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"}],"funders":[{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2125221595","https://openalex.org/W1637585205","https://openalex.org/W3027684452","https://openalex.org/W3087128175","https://openalex.org/W3156371387","https://openalex.org/W2327420602","https://openalex.org/W201712113","https://openalex.org/W2015573458","https://openalex.org/W2069209154","https://openalex.org/W1547647895"],"abstract_inverted_index":{"The":[0,30],"Earth":[1,31,45],"Mover's":[2,32,46],"Distance":[3,33,47],"is":[4,37,70,108],"a":[5,23,38,75],"popular":[6],"similarity":[7],"measure":[8],"in":[9,57,88],"several":[10],"branches":[11],"of":[12,22,51],"computer":[13],"science.":[14],"It":[15,42],"measures":[16],"the":[17,44,82,96,121],"minimum":[18],"total":[19],"edge":[20],"length":[21],"perfect":[24],"matching":[25,76],"between":[26],"two":[27],"point":[28,53],"sets.":[29],"under":[34],"Translation":[35],"($\\mathrm{EMDuT}$)":[36],"translation-invariant":[39],"version":[40],"thereof.":[41],"minimizes":[43],"over":[48],"all":[49],"translations":[50],"one":[52],"set.":[54],"For":[55,86],"$\\mathrm{EMDuT}$":[56,87],"$\\mathbb{R}^1$,":[58],"we":[59,90],"present":[60,91],"an":[61,92,112],"$\\tilde{\\mathcal{O}}(n^2)$-time":[62],"algorithm.":[63],"We":[64,101],"also":[65],"show":[66,102],"that":[67,103],"this":[68,104],"algorithm":[69,94,114],"nearly":[71],"optimal":[72],"by":[73],"presenting":[74],"conditional":[77],"lower":[78],"bound":[79],"based":[80],"on":[81,106],"Orthogonal":[83],"Vectors":[84],"Hypothesis.":[85],"$\\mathbb{R}^d$,":[89],"$\\tilde{\\mathcal{O}}(n^{2d+2})$-time":[93],"for":[95,115,135],"$L_1$":[97,116],"and":[98],"$L_\\infty$":[99,118],"metric.":[100],"dependence":[105],"$d$":[107],"asymptotically":[109],"tight,":[110],"as":[111],"$n^{o(d)}$-time":[113],"or":[117],"would":[119],"contradict":[120],"Exponential":[122],"Time":[123],"Hypothesis":[124],"(ETH).":[125],"Prior":[126],"to":[127],"our":[128],"work,":[129],"only":[130],"approximation":[131],"algorithms":[132],"were":[133],"known":[134],"these":[136],"problems.":[137]},"counts_by_year":[],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2024-03-09T00:00:00"}