{"id":"https://openalex.org/W7163921183","doi":"https://doi.org/10.4230/lipics.swat.2026.36","title":"Exact Subquadratic Algorithm for Many-To-Many Matching on Planar Point Sets with Integer Coordinates","display_name":"Exact Subquadratic Algorithm for Many-To-Many Matching on Planar Point Sets with Integer Coordinates","publication_year":2026,"publication_date":"2026-01-01","ids":{"openalex":"https://openalex.org/W7163921183","doi":"https://doi.org/10.4230/lipics.swat.2026.36"},"language":"en","primary_location":{"id":"pmh:oai:drops-oai.dagstuhl.de:26072","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2026.36","pdf_url":"https://drops.dagstuhl.de/storage/00lipics/lipics-vol370-swat2026/LIPIcs.SWAT.2026.36/LIPIcs.SWAT.2026.36.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":null,"raw_type":"publishedVersion"},"type":"article","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://drops.dagstuhl.de/storage/00lipics/lipics-vol370-swat2026/LIPIcs.SWAT.2026.36/LIPIcs.SWAT.2026.36.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5134196802","display_name":"Seongbin Park","orcid":null},"institutions":[{"id":"https://openalex.org/I123900574","display_name":"Pohang University of Science and Technology","ror":"https://ror.org/04xysgw12","country_code":"KR","type":"education","lineage":["https://openalex.org/I123900574"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Park, Seongbin","raw_affiliation_strings":["Department of Computer Science and Engineering, POSTECH, Pohang, Republic of Korea"],"raw_orcid":"https://orcid.org/0009-0000-9018-5798","affiliations":[{"raw_affiliation_string":"Department of Computer Science and Engineering, POSTECH, Pohang, Republic of Korea","institution_ids":["https://openalex.org/I123900574"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5138121040","display_name":"Eunjin Oh","orcid":"https://orcid.org/0000-0003-0798-2580"},"institutions":[{"id":"https://openalex.org/I123900574","display_name":"Pohang University of Science and Technology","ror":"https://ror.org/04xysgw12","country_code":"KR","type":"education","lineage":["https://openalex.org/I123900574"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Oh, Eunjin","raw_affiliation_strings":["Department of Computer Science and Engineering, POSTECH, Pohang, Republic of Korea"],"raw_orcid":"https://orcid.org/0000-0003-0798-2580","affiliations":[{"raw_affiliation_string":"Department of Computer Science and Engineering, POSTECH, Pohang, Republic of Korea","institution_ids":["https://openalex.org/I123900574"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.94597494,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.1673000007867813,"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":0.1673000007867813,"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":0.15729999542236328,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.1501999944448471,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/disjoint-sets","display_name":"Disjoint sets","score":0.7328000068664551},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.6725999712944031},{"id":"https://openalex.org/keywords/matching","display_name":"Matching (statistics)","score":0.6261000037193298},{"id":"https://openalex.org/keywords/planar","display_name":"Planar","score":0.5687999725341797},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5203999876976013},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.5120999813079834},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.46799999475479126},{"id":"https://openalex.org/keywords/point-set-registration","display_name":"Point set registration","score":0.3817000091075897}],"concepts":[{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.7328000068664551},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7224000096321106},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.6725999712944031},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6477000117301941},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.6261000037193298},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.5687999725341797},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5203999876976013},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.5120999813079834},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5109999775886536},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4839000105857849},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.46799999475479126},{"id":"https://openalex.org/C200336642","wikidata":"https://www.wikidata.org/wiki/Q15058706","display_name":"Point set registration","level":3,"score":0.3817000091075897},{"id":"https://openalex.org/C61455927","wikidata":"https://www.wikidata.org/wiki/Q1030529","display_name":"Blossom algorithm","level":3,"score":0.3720000088214874},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.3628999888896942},{"id":"https://openalex.org/C162307627","wikidata":"https://www.wikidata.org/wiki/Q204833","display_name":"Enhanced Data Rates for GSM Evolution","level":2,"score":0.3343999981880188},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.3222000002861023},{"id":"https://openalex.org/C120174047","wikidata":"https://www.wikidata.org/wiki/Q847073","display_name":"Euclidean distance","level":2,"score":0.29760000109672546},{"id":"https://openalex.org/C72545166","wikidata":"https://www.wikidata.org/wiki/Q10866593","display_name":"3-dimensional matching","level":4,"score":0.29249998927116394},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.2921000123023987},{"id":"https://openalex.org/C56086750","wikidata":"https://www.wikidata.org/wiki/Q6042592","display_name":"Integer programming","level":2,"score":0.2685999870300293},{"id":"https://openalex.org/C520416788","wikidata":"https://www.wikidata.org/wiki/Q5419229","display_name":"Exact solutions in general relativity","level":2,"score":0.2624000012874603}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:drops-oai.dagstuhl.de:26072","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2026.36","pdf_url":"https://drops.dagstuhl.de/storage/00lipics/lipics-vol370-swat2026/LIPIcs.SWAT.2026.36/LIPIcs.SWAT.2026.36.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":null,"raw_type":"publishedVersion"},{"id":"doi:10.4230/lipics.swat.2026.36","is_oa":true,"landing_page_url":"https://doi.org/10.4230/lipics.swat.2026.36","pdf_url":null,"source":{"id":"https://openalex.org/S7407052059","display_name":"Dagstuhl Research Online Publication Server","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":""}],"best_oa_location":{"id":"pmh:oai:drops-oai.dagstuhl.de:26072","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2026.36","pdf_url":"https://drops.dagstuhl.de/storage/00lipics/lipics-vol370-swat2026/LIPIcs.SWAT.2026.36/LIPIcs.SWAT.2026.36.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":null,"raw_type":"publishedVersion"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7163921183.pdf","grobid_xml":"https://content.openalex.org/works/W7163921183.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"In":[0,58],"this":[1,103],"paper,":[2],"we":[3],"study":[4],"the":[5,27,52,59,70,72,76,98,105],"many-to-many":[6,77,112],"matching":[7,78,113],"problem":[8,79],"on":[9],"planar":[10,111],"point":[11,43,67,93],"sets":[12,19,68,94],"with":[13,23],"integer":[14,116],"coordinates:":[15],"Given":[16],"two":[17],"disjoint":[18],"R,B":[20],"\u2282":[21],"[\u0394]\u00b2":[22],"|R|+|B|":[24],"=":[25],"n,":[26],"goal":[28],"is":[29,44,56,104],"to":[30,46],"select":[31],"a":[32],"set":[33],"of":[34,100],"edges":[35],"between":[36],"R":[37,63],"and":[38,51,64],"B":[39,65],"so":[40],"that":[41,62],"every":[42],"incident":[45],"at":[47],"least":[48],"one":[49],"edge":[50],"total":[53],"Euclidean":[54],"length":[55],"minimized.":[57],"general":[60],"case":[61],"are":[66],"in":[69,95],"plane,":[71],"best-known":[73],"algorithm":[74,91,109],"for":[75,92,110],"takes":[80],"O\u0303(n\u00b2)":[81],"time.":[82],"We":[83],"present":[84],"an":[85],"exact":[86,108],"O\u0303(n^{1.5}":[87],"log":[88],"\u0394)":[89],"time":[90],"[\u0394]\u00b2.":[96],"To":[97],"best":[99],"our":[101],"knowledge,":[102],"first":[106],"subquadratic":[107],"under":[114],"bounded":[115],"coordinates.":[117]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2026-06-09T00:00:00"}