{"id":"https://openalex.org/W4221143047","doi":"https://doi.org/10.1145/3585535","title":"Chains, Koch Chains, and Point Sets with Many Triangulations","display_name":"Chains, Koch Chains, and Point Sets with Many Triangulations","publication_year":2023,"publication_date":"2023-02-27","ids":{"openalex":"https://openalex.org/W4221143047","doi":"https://doi.org/10.1145/3585535"},"language":"en","primary_location":{"id":"doi:10.1145/3585535","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3585535","pdf_url":null,"source":{"id":"https://openalex.org/S118992489","display_name":"Journal of the ACM","issn_l":"0004-5411","issn":["0004-5411","1557-735X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of the ACM","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://hdl.handle.net/20.500.11850/559973","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5021826063","display_name":"Daniel Rutschmann","orcid":"https://orcid.org/0009-0005-6838-2628"},"institutions":[{"id":"https://openalex.org/I35440088","display_name":"ETH Zurich","ror":"https://ror.org/05a28rw58","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088"]}],"countries":["CH"],"is_corresponding":true,"raw_author_name":"Daniel Rutschmann","raw_affiliation_strings":["Department of Computer Science, ETH Zurich, Switzerland"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, ETH Zurich, Switzerland","institution_ids":["https://openalex.org/I35440088"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5067718972","display_name":"Manuel Wettstein","orcid":"https://orcid.org/0000-0002-5360-265X"},"institutions":[{"id":"https://openalex.org/I35440088","display_name":"ETH Zurich","ror":"https://ror.org/05a28rw58","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Manuel Wettstein","raw_affiliation_strings":["Department of Computer Science, ETH Zurich, Switzerland"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, ETH Zurich, Switzerland","institution_ids":["https://openalex.org/I35440088"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5021826063"],"corresponding_institution_ids":["https://openalex.org/I35440088"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.03249581,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"70","issue":"3","first_page":"1","last_page":"26"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.38679999113082886,"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":0.38679999113082886,"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":0.18780000507831573,"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/T10304","display_name":"Geometric and Algebraic Topology","score":0.08020000159740448,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/chain","display_name":"Chain (unit)","score":0.7354015707969666},{"id":"https://openalex.org/keywords/omega","display_name":"Omega","score":0.6800287961959839},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.670471727848053},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.5848383903503418},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5217065215110779},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.4973941147327423},{"id":"https://openalex.org/keywords/enhanced-data-rates-for-gsm-evolution","display_name":"Enhanced Data Rates for GSM Evolution","score":0.47861427068710327},{"id":"https://openalex.org/keywords/planar","display_name":"Planar","score":0.43606942892074585},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.41975781321525574},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.24568140506744385},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2037157118320465},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.17190465331077576}],"concepts":[{"id":"https://openalex.org/C199185054","wikidata":"https://www.wikidata.org/wiki/Q552299","display_name":"Chain (unit)","level":2,"score":0.7354015707969666},{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.6800287961959839},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.670471727848053},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.5848383903503418},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5217065215110779},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.4973941147327423},{"id":"https://openalex.org/C162307627","wikidata":"https://www.wikidata.org/wiki/Q204833","display_name":"Enhanced Data Rates for GSM Evolution","level":2,"score":0.47861427068710327},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.43606942892074585},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.41975781321525574},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.24568140506744385},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2037157118320465},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.17190465331077576},{"id":"https://openalex.org/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","level":1,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0}],"mesh":[],"locations_count":7,"locations":[{"id":"doi:10.1145/3585535","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3585535","pdf_url":null,"source":{"id":"https://openalex.org/S118992489","display_name":"Journal of the ACM","issn_l":"0004-5411","issn":["0004-5411","1557-735X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of the ACM","raw_type":"journal-article"},{"id":"pmh:oai:research-collection.ethz.ch:20.500.11850/559973","is_oa":true,"landing_page_url":"http://hdl.handle.net/20.500.11850/559973","pdf_url":null,"source":{"id":"https://openalex.org/S4306402302","display_name":"Repository for Publications and Research Data (ETH Zurich)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I35440088","host_organization_name":"ETH Zurich","host_organization_lineage":["https://openalex.org/I35440088"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"38th International Symposium on Computational Geometry","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:arXiv.org:2203.07584","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2203.07584","pdf_url":"https://arxiv.org/pdf/2203.07584","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":"","raw_type":"text"},{"id":"pmh:oai:drops-oai.dagstuhl.de:16067","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2022.59","pdf_url":"https://drops.dagstuhl.de/storage/00lipics/lipics-vol224-socg2022/LIPIcs.SoCG.2022.59/LIPIcs.SoCG.2022.59.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":"doi:10.48550/arxiv.2203.07584","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2203.07584","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"},{"id":"doi:10.3929/ethz-b-000559973","is_oa":true,"landing_page_url":"https://doi.org/10.3929/ethz-b-000559973","pdf_url":null,"source":{"id":"https://openalex.org/S7407051236","display_name":"ETH Z\u00fcrich Research Collection","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"},{"id":"doi:10.4230/lipics.socg.2022.59","is_oa":true,"landing_page_url":"https://doi.org/10.4230/lipics.socg.2022.59","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:research-collection.ethz.ch:20.500.11850/559973","is_oa":true,"landing_page_url":"http://hdl.handle.net/20.500.11850/559973","pdf_url":null,"source":{"id":"https://openalex.org/S4306402302","display_name":"Repository for Publications and Research Data (ETH Zurich)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I35440088","host_organization_name":"ETH Zurich","host_organization_lineage":["https://openalex.org/I35440088"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"38th International Symposium on Computational Geometry","raw_type":"info:eu-repo/semantics/publishedVersion"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W13988344","https://openalex.org/W146417191","https://openalex.org/W2000008376","https://openalex.org/W2004367845","https://openalex.org/W2030996579","https://openalex.org/W2057690024","https://openalex.org/W2082230637","https://openalex.org/W2089078292","https://openalex.org/W2090529709","https://openalex.org/W2110861431","https://openalex.org/W2114928211","https://openalex.org/W2163448076","https://openalex.org/W2963569915","https://openalex.org/W4244525603","https://openalex.org/W6674306307"],"related_works":["https://openalex.org/W170076","https://openalex.org/W35654066","https://openalex.org/W25928676","https://openalex.org/W77436421","https://openalex.org/W24725585","https://openalex.org/W16985043","https://openalex.org/W13311758","https://openalex.org/W22283","https://openalex.org/W30551310","https://openalex.org/W22200857"],"abstract_inverted_index":{"We":[0,59],"introduce":[1],"the":[2,16,24,43,71,79,105,117],"abstract":[3],"notion":[4],"of":[5,12,42,46,54,57,111,120,122],"a":[6,10,51,101],"chain,":[7],"which":[8,68],"is":[9,31,48,89,100],"sequence":[11],"n":[13,96,114],"points":[14,30],"in":[15],"plane,":[17],"ordered":[18],"by":[19],"x":[20],"-coordinates,":[21],"so":[22],"that":[23],"edge":[25],"between":[26],"any":[27],"two":[28],"consecutive":[29],"unavoidable":[32],"as":[33,35],"far":[34],"triangulations":[36,121],"are":[37],"concerned.":[38],"A":[39,82],"general":[40,52],"theory":[41],"structural":[44],"properties":[45],"chains":[47,88],"developed,":[49],"alongside":[50],"understanding":[53],"their":[55],"number":[56,119],"triangulations.":[58,98],"also":[60],"describe":[61],"an":[62],"intriguing":[63],"new":[64],"and":[65,107],"concrete":[66],"configuration,":[67],"we":[69],"call":[70],"Koch":[72,80,87],"chain":[73],"due":[74],"to":[75,78,92],"its":[76],"similarities":[77],"curve.":[81],"specific":[83],"construction":[84],"based":[85],"on":[86],"then":[90],"shown":[91],"have":[93],"\u03a9":[94,112],"(9.08":[95],")":[97,115],"This":[99],"significant":[102],"improvement":[103],"over":[104],"previous":[106],"long-standing":[108],"lower":[109],"bound":[110],"(8.65":[113],"for":[116],"maximum":[118],"planar":[123],"point":[124],"sets.":[125]},"counts_by_year":[],"updated_date":"2026-03-03T08:47:05.690250","created_date":"2022-04-03T00:00:00"}
