{"id":"https://openalex.org/W2070380571","doi":"https://doi.org/10.1145/1998196.1998216","title":"Disjoint compatible geometric matchings","display_name":"Disjoint compatible geometric matchings","publication_year":2011,"publication_date":"2011-06-13","ids":{"openalex":"https://openalex.org/W2070380571","doi":"https://doi.org/10.1145/1998196.1998216","mag":"2070380571"},"language":"en","primary_location":{"id":"doi:10.1145/1998196.1998216","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1998196.1998216","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the twenty-seventh annual symposium on Computational geometry","raw_type":"proceedings-article"},"type":"conference-paper","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/A5088920007","display_name":"Mashhood Ishaque","orcid":null},"institutions":[{"id":"https://openalex.org/I121934306","display_name":"Tufts University","ror":"https://ror.org/05wvpxv85","country_code":"US","type":"education","lineage":["https://openalex.org/I121934306"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Mashhood Ishaque","raw_affiliation_strings":["Tufts University, Medford, MA, USA","Tufts University, Medford, MA, USA#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Tufts University, Medford, MA, USA","institution_ids":["https://openalex.org/I121934306"]},{"raw_affiliation_string":"Tufts University, Medford, MA, USA#TAB#","institution_ids":["https://openalex.org/I121934306"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5069555175","display_name":"Diane L. Souvaine","orcid":null},"institutions":[{"id":"https://openalex.org/I121934306","display_name":"Tufts University","ror":"https://ror.org/05wvpxv85","country_code":"US","type":"education","lineage":["https://openalex.org/I121934306"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Diane L. Souvaine","raw_affiliation_strings":["Tufts University, Medford, MA, USA","Tufts University, Medford, MA, USA#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Tufts University, Medford, MA, USA","institution_ids":["https://openalex.org/I121934306"]},{"raw_affiliation_string":"Tufts University, Medford, MA, USA#TAB#","institution_ids":["https://openalex.org/I121934306"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5030799674","display_name":"Csaba D. T\u00f3th","orcid":"https://orcid.org/0000-0002-8769-3190"},"institutions":[{"id":"https://openalex.org/I168635309","display_name":"University of Calgary","ror":"https://ror.org/03yjb2x39","country_code":"CA","type":"education","lineage":["https://openalex.org/I168635309"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Csaba D. Toth","raw_affiliation_strings":["University of Calgary, Calgary, AB, Canada","University of Calgary; Calgary; AB; Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Calgary, Calgary, AB, Canada","institution_ids":["https://openalex.org/I168635309"]},{"raw_affiliation_string":"University of Calgary; Calgary; AB; Canada","institution_ids":["https://openalex.org/I168635309"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"125","last_page":"134"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9998999834060669,"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":0.9998999834060669,"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/T11830","display_name":"Point processes and geometric inequalities","score":0.9986000061035156,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9915000200271606,"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/disjoint-sets","display_name":"Disjoint sets","score":0.8981038928031921},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.787114143371582},{"id":"https://openalex.org/keywords/subdivision","display_name":"Subdivision","score":0.5784172415733337},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5360064506530762},{"id":"https://openalex.org/keywords/pairwise-comparison","display_name":"Pairwise comparison","score":0.4423516094684601},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.4411185383796692},{"id":"https://openalex.org/keywords/line-segment","display_name":"Line segment","score":0.4316202402114868},{"id":"https://openalex.org/keywords/dual-graph","display_name":"Dual graph","score":0.4234403371810913},{"id":"https://openalex.org/keywords/matching","display_name":"Matching (statistics)","score":0.4233455955982208},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4164869785308838},{"id":"https://openalex.org/keywords/general-position","display_name":"General position","score":0.41507619619369507},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.32096076011657715},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.30650514364242554},{"id":"https://openalex.org/keywords/planar-graph","display_name":"Planar graph","score":0.21503230929374695},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.12634339928627014}],"concepts":[{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.8981038928031921},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.787114143371582},{"id":"https://openalex.org/C143392562","wikidata":"https://www.wikidata.org/wiki/Q449111","display_name":"Subdivision","level":2,"score":0.5784172415733337},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5360064506530762},{"id":"https://openalex.org/C184898388","wikidata":"https://www.wikidata.org/wiki/Q1435712","display_name":"Pairwise comparison","level":2,"score":0.4423516094684601},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.4411185383796692},{"id":"https://openalex.org/C182124507","wikidata":"https://www.wikidata.org/wiki/Q166154","display_name":"Line segment","level":2,"score":0.4316202402114868},{"id":"https://openalex.org/C169827030","wikidata":"https://www.wikidata.org/wiki/Q2294516","display_name":"Dual graph","level":4,"score":0.4234403371810913},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.4233455955982208},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4164869785308838},{"id":"https://openalex.org/C150397156","wikidata":"https://www.wikidata.org/wiki/Q591310","display_name":"General position","level":2,"score":0.41507619619369507},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.32096076011657715},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.30650514364242554},{"id":"https://openalex.org/C101837359","wikidata":"https://www.wikidata.org/wiki/Q547823","display_name":"Planar graph","level":3,"score":0.21503230929374695},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.12634339928627014},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C95457728","wikidata":"https://www.wikidata.org/wiki/Q309","display_name":"History","level":0,"score":0.0},{"id":"https://openalex.org/C166957645","wikidata":"https://www.wikidata.org/wiki/Q23498","display_name":"Archaeology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/1998196.1998216","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1998196.1998216","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the twenty-seventh annual symposium on Computational geometry","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W35252975","https://openalex.org/W79131202","https://openalex.org/W1509846055","https://openalex.org/W1817632074","https://openalex.org/W1860878659","https://openalex.org/W1968583908","https://openalex.org/W1972083652","https://openalex.org/W1972830235","https://openalex.org/W1984188921","https://openalex.org/W1992743664","https://openalex.org/W2020148103","https://openalex.org/W2042706982","https://openalex.org/W2046450589","https://openalex.org/W2057259762","https://openalex.org/W2058858486","https://openalex.org/W2065196403","https://openalex.org/W2075384617","https://openalex.org/W2085179971","https://openalex.org/W2094658339","https://openalex.org/W2109083408","https://openalex.org/W2116031575","https://openalex.org/W2119790501","https://openalex.org/W2138849026","https://openalex.org/W2161968825","https://openalex.org/W2163448076","https://openalex.org/W3023768696","https://openalex.org/W3024372063"],"related_works":["https://openalex.org/W2980534072","https://openalex.org/W3103266813","https://openalex.org/W2019903130","https://openalex.org/W2011903683","https://openalex.org/W2127420314","https://openalex.org/W1519914687","https://openalex.org/W2157671279","https://openalex.org/W2182952931","https://openalex.org/W122487145","https://openalex.org/W2004787924"],"abstract_inverted_index":{"We":[0],"prove":[1],"that":[2,27,80],"for":[3],"every":[4],"even":[5],"set":[6,22],"of":[7,23,64,84],"$n$":[8],"pairwise":[9,32],"disjoint":[10,33,70],"line":[11,71],"segments":[12,25,30,72],"in":[13,16,36,41,57],"the":[14,28,37,42,44,65,81,85],"plane":[15],"general":[17],"position,":[18],"there":[19],"is":[20,60],"another":[21],"n":[24,69],"such":[26,79],"2n":[29],"form":[31],"simple":[34],"polygons":[35],"plane.":[38],"This":[39],"settles":[40],"affirmative":[43],"Disjoint":[45],"Compatible":[46],"Matching":[47],"Conjecture":[48],"by":[49],"Aichholzer":[50],"et":[51],"al.":[52],"[ABD08].":[53],"The":[54],"key":[55],"tool":[56],"our":[58],"proof":[59],"a":[61],"novel":[62],"subdivision":[63,86],"free":[66],"space":[67],"around":[68],"into":[73],"at":[74],"most":[75],"n+1":[76],"convex":[77],"cells":[78],"dual":[82],"graph":[83],"contains":[87],"two":[88],"edge-disjoint":[89],"spanning":[90],"trees.":[91]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":3}],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2025-10-10T00:00:00"}
