{"id":"https://openalex.org/W7156824040","doi":"https://doi.org/10.48550/arxiv.2604.23330","title":"Bowties and Hourglasses: Intersections of Double-Wedges (or Stabbing and Avoiding Line Segments)","display_name":"Bowties and Hourglasses: Intersections of Double-Wedges (or Stabbing and Avoiding Line Segments)","publication_year":2026,"publication_date":"2026-04-25","ids":{"openalex":"https://openalex.org/W7156824040","doi":"https://doi.org/10.48550/arxiv.2604.23330"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2604.23330","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.23330","pdf_url":null,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2604.23330","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5053720453","display_name":"Daniel Bertschinger","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Bertschinger, Daniel","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5035031209","display_name":"Henry F\u00f6rster","orcid":"https://orcid.org/0000-0002-1441-4189"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"F\u00f6rster, Henry","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5091269394","display_name":"Fabian Klute","orcid":"https://orcid.org/0000-0002-7791-3604"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Klute, Fabian","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5134639984","display_name":"Irene Parada","orcid":"https://orcid.org/0000-0003-3147-0083"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Parada, Irene","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5134751491","display_name":"Patrick Schnider","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Schnider, Patrick","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5134753595","display_name":"Birgit Vogtenhuber","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Vogtenhuber, Birgit","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5053720453"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.3846000134944916,"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"}},"topics":[{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.3846000134944916,"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"}},{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.3416000008583069,"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/T13664","display_name":"Genome Rearrangement Algorithms","score":0.04729999974370003,"subfield":{"id":"https://openalex.org/subfields/1311","display_name":"Genetics"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/intersection","display_name":"Intersection (aeronautics)","score":0.9200000166893005},{"id":"https://openalex.org/keywords/complement","display_name":"Complement (music)","score":0.725600004196167},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.6735000014305115},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.6340000033378601},{"id":"https://openalex.org/keywords/line","display_name":"Line (geometry)","score":0.5898000001907349},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5716000199317932}],"concepts":[{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.9200000166893005},{"id":"https://openalex.org/C112313634","wikidata":"https://www.wikidata.org/wiki/Q7886648","display_name":"Complement (music)","level":5,"score":0.725600004196167},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.6735000014305115},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.6340000033378601},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6187000274658203},{"id":"https://openalex.org/C198352243","wikidata":"https://www.wikidata.org/wiki/Q37105","display_name":"Line (geometry)","level":2,"score":0.5898000001907349},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5716000199317932},{"id":"https://openalex.org/C182124507","wikidata":"https://www.wikidata.org/wiki/Q166154","display_name":"Line segment","level":2,"score":0.5378000140190125},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5030999779701233},{"id":"https://openalex.org/C2992444157","wikidata":"https://www.wikidata.org/wiki/Q775079","display_name":"Single point","level":3,"score":0.4311000108718872},{"id":"https://openalex.org/C2776502983","wikidata":"https://www.wikidata.org/wiki/Q690182","display_name":"Contrast (vision)","level":2,"score":0.35409998893737793},{"id":"https://openalex.org/C75432250","wikidata":"https://www.wikidata.org/wiki/Q29654355","display_name":"Real line","level":2,"score":0.32089999318122864},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3190999925136566},{"id":"https://openalex.org/C103368685","wikidata":"https://www.wikidata.org/wiki/Q638846","display_name":"Intersection number","level":3,"score":0.28369998931884766},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.27219998836517334},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2709999978542328}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2604.23330","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.23330","pdf_url":null,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2604.23330","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.23330","pdf_url":null,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0,9,102],"study":[1],"the":[2,47,58,65,84,97,100,109,137],"common":[3],"intersection":[4,66,110,138,157],"of":[5,7,41,67,79,92,99,111,116,127,139],"arrangements":[6,11,40,126,141],"double-wedges.":[8],"consider":[10],"where":[12],"double-wedges":[13,69,113],"may":[14,114],"be":[15],"either":[16],"bowties":[17],"(which":[18,27],"do":[19],"not":[20],"contain":[21,28],"a":[22,29,62,73,77,89,155],"vertical":[23,30],"line)":[24],"or":[25],"hourglasses":[26],"line),":[31],"in":[32,50,64,105,159],"contrast":[33],"to":[34,54,72,83,96],"earlier":[35],"studies":[36],"that":[37,75,104,151,165],"focused":[38],"on":[39],"only":[42],"bowties.":[43],"This":[44],"generalization":[45],"changes":[46],"setting":[48],"drastically,":[49],"particular,":[51],"with":[52,142],"respect":[53],"all":[55,68],"arguments":[56],"involving":[57],"point-line":[59],"duality.":[60],"Namely,":[61],"point":[63,158],"is":[70],"equivalent":[71],"line":[74],"stabs":[76],"set":[78,91],"segments":[80,93,128],"$\\mathcal{S}$":[81],"(corresponding":[82,95],"bowties)":[85],"while":[86],"it":[87],"avoids":[88],"different":[90],"$\\mathcal{A}$":[94],"complement":[98],"hourglasses).":[101],"show":[103],"this":[106],"general":[107],"setting,":[108],"$n$":[112],"consist":[115],"$\u03a9(n^2)$":[117],"interior-disjoint":[118],"regions.":[119],"Further,":[120],"we":[121,132,148,152],"discuss":[122],"Gallai-type":[123],"results":[124],"for":[125,135],"and":[129,131],"anti-segments,":[130],"provide":[133],"algorithms":[134],"computing":[136],"such":[140],"worst-case":[143],"optimal":[144,161],"running":[145,162],"time.":[146],"Finally,":[147],"also":[149],"prove":[150],"can":[153],"find":[154],"single":[156],"almost":[160],"time,":[163],"assuming":[164],"3SUM":[166],"admits":[167],"no":[168],"truly":[169],"subquadratic-time":[170],"algorithm.":[171]},"counts_by_year":[],"updated_date":"2026-04-29T06:16:36.941037","created_date":"2026-04-29T00:00:00"}