{"id":"https://openalex.org/W4280600746","doi":"https://doi.org/10.57717/cgt.v2i2.27","title":"A Bound for Delaunay Flip Algorithms on Flat Tori","display_name":"A Bound for Delaunay Flip Algorithms on Flat Tori","publication_year":2022,"publication_date":"2022-11-15","ids":{"openalex":"https://openalex.org/W4280600746","doi":"https://doi.org/10.57717/cgt.v2i2.27"},"language":"en","primary_location":{"id":"pmh:oai:HAL:hal-03666488v1","is_oa":true,"landing_page_url":"https://hal.inria.fr/hal-03666488","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"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":"https://hal.inria.fr/hal-03666488","raw_type":"info:eu-repo/semantics/report"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://hal.inria.fr/hal-03666488","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5043283903","display_name":"L. Dubois","orcid":"https://orcid.org/0000-0003-0878-1270"},"institutions":[{"id":"https://openalex.org/I4210099593","display_name":"Computer Algorithms for Medicine","ror":"https://ror.org/00zky6d38","country_code":"AT","type":"facility","lineage":["https://openalex.org/I4210099593"]},{"id":"https://openalex.org/I4210154111","display_name":"Universit\u00e9 Gustave Eiffel","ror":"https://ror.org/03x42jk29","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210154111"]},{"id":"https://openalex.org/I4210152518","display_name":"Laboratoire d'Informatique Gaspard-Monge","ror":"https://ror.org/04t50yk91","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I142631665","https://openalex.org/I4210145102","https://openalex.org/I4210152518","https://openalex.org/I4210154111","https://openalex.org/I4210159245"]}],"countries":["AT","FR"],"is_corresponding":true,"raw_author_name":"Dubois, Lo\u00efc","raw_affiliation_strings":["LIGM, CNRS, Universit\u00e9 Gustave Eiffel, F-77454 Marne-la-Vall\u00e9e","Laboratoire d'Informatique Gaspard-Monge","Geometric Algorithms and Models Beyond the Linear and Euclidean realm"],"affiliations":[{"raw_affiliation_string":"LIGM, CNRS, Universit\u00e9 Gustave Eiffel, F-77454 Marne-la-Vall\u00e9e","institution_ids":["https://openalex.org/I4210154111"]},{"raw_affiliation_string":"Laboratoire d'Informatique Gaspard-Monge","institution_ids":["https://openalex.org/I4210152518"]},{"raw_affiliation_string":"Geometric Algorithms and Models Beyond the Linear and Euclidean realm","institution_ids":["https://openalex.org/I4210099593"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5043283903"],"corresponding_institution_ids":["https://openalex.org/I4210099593","https://openalex.org/I4210154111","https://openalex.org/I4210152518"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.08318514,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9922000169754028,"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":0.9922000169754028,"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/T11106","display_name":"Data Management and Algorithms","score":0.957099974155426,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/T10586","display_name":"Robotic Path Planning Algorithms","score":0.9550999999046326,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/delaunay-triangulation","display_name":"Delaunay triangulation","score":0.8475148677825928},{"id":"https://openalex.org/keywords/torus","display_name":"Torus","score":0.6042447686195374},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5740011930465698},{"id":"https://openalex.org/keywords/flip","display_name":"Flip","score":0.46300745010375977},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4057060182094574},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.373955100774765},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.35515570640563965},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3177822232246399},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.3074808716773987}],"concepts":[{"id":"https://openalex.org/C68010082","wikidata":"https://www.wikidata.org/wiki/Q192445","display_name":"Delaunay triangulation","level":2,"score":0.8475148677825928},{"id":"https://openalex.org/C9767117","wikidata":"https://www.wikidata.org/wiki/Q12510","display_name":"Torus","level":2,"score":0.6042447686195374},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5740011930465698},{"id":"https://openalex.org/C2776591724","wikidata":"https://www.wikidata.org/wiki/Q5459651","display_name":"Flip","level":3,"score":0.46300745010375977},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4057060182094574},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.373955100774765},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.35515570640563965},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3177822232246399},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.3074808716773987},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"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/C190283241","wikidata":"https://www.wikidata.org/wiki/Q14599311","display_name":"Apoptosis","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"pmh:oai:HAL:hal-03666488v1","is_oa":true,"landing_page_url":"https://hal.inria.fr/hal-03666488","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"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":"https://hal.inria.fr/hal-03666488","raw_type":"info:eu-repo/semantics/report"},{"id":"pmh:oai:HAL:hal-03666488v3","is_oa":true,"landing_page_url":"https://inria.hal.science/hal-03666488","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"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":"CCCG 2022 - 34th Canadian Conference on Computational Geometry, Aug 2022, Toronto, Canada","raw_type":"Conference papers"},{"id":"doi:10.57717/cgt.v2i2.27","is_oa":true,"landing_page_url":"https://doi.org/10.57717/cgt.v2i2.27","pdf_url":null,"source":{"id":"https://openalex.org/S7407053285","display_name":"Computing in Geometry and Topology","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":"article-journal"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-03666488v1","is_oa":true,"landing_page_url":"https://hal.inria.fr/hal-03666488","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"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":"https://hal.inria.fr/hal-03666488","raw_type":"info:eu-repo/semantics/report"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2359979928","https://openalex.org/W2368353614","https://openalex.org/W2390369954","https://openalex.org/W1529719486","https://openalex.org/W2373917503","https://openalex.org/W2906423005","https://openalex.org/W4232052003","https://openalex.org/W2385297469","https://openalex.org/W2001914902","https://openalex.org/W2353399380"],"abstract_inverted_index":{"We":[0,29],"are":[1],"interested":[2],"in":[3,77,82],"triangulations":[4],"of":[5,18,34,47,50,56,58,85,92],"flat":[6,66],"tori.":[7],"A":[8],"Delaunay":[9,13,27,35],"flip":[10],"algorithm":[11],"performs":[12],"flips":[14,36],"on":[15,64,71],"the":[16,44,54,65,72,80,83,86,94,99],"edges":[17],"an":[19,48],"input":[20,87],"triangulation":[21,88],"T":[22],"until":[23],"it":[24],"reaches":[25],"a":[26],"triangulation.":[28],"prove":[30],"that":[31],"no":[32],"sequence":[33],"is":[37,43,53,89,96,102],"longer":[38],"than":[39],"C\u0393\u00b7n2\u00b7\u039b(T)":[40],"where":[41],"\u039b(T)":[42],"maximum":[45],"length":[46],"edge":[49],"T,":[51,59],"n":[52],"number":[55],"vertices":[57],"and":[60,98],"C\u0393":[61],"depends":[62],"only":[63],"torus.":[67],"The":[68],"bound":[69,74,95],"improves":[70],"upper":[73],"previously":[75],"known":[76],"three":[78],"ways:":[79],"dependency":[81],"\"quality\"":[84],"linear":[90],"instead":[91],"quadratic,":[93],"tight,":[97],"\"quality":[100],"parameter\"":[101],"simpler.":[103]},"counts_by_year":[],"updated_date":"2025-11-06T06:51:31.235846","created_date":"2025-10-10T00:00:00"}
