{"id":"https://openalex.org/W7080542863","doi":"https://doi.org/10.20382/jocg.v16i2a7","title":"Effective computation of the Heegaard genus of 3-manifolds","display_name":"Effective computation of the Heegaard genus of 3-manifolds","publication_year":2025,"publication_date":"2025-07-21","ids":{"openalex":"https://openalex.org/W7080542863","doi":"https://doi.org/10.20382/jocg.v16i2a7"},"language":"en","primary_location":{"id":"pmh:oai:ojs.library.carleton.ca:article/5533","is_oa":true,"landing_page_url":"https://jocg.org/index.php/jocg/article/view/5533","pdf_url":null,"source":{"id":"https://openalex.org/S4306400962","display_name":"Journal of Computational Geometry (Carleton University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I67031392","host_organization_name":"Carleton University","host_organization_lineage":["https://openalex.org/I67031392"],"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":"10.20382/jocg.v16i2","raw_type":"info:eu-repo/semantics/publishedVersion"},"type":"article","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://jocg.org/index.php/jocg/article/view/5533","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Thompson, Finn","orcid":"https://orcid.org/0000-0003-3241-8332"},"institutions":[{"id":"https://openalex.org/I165143802","display_name":"University of Queensland","ror":"https://ror.org/00rqy9422","country_code":"AU","type":"education","lineage":["https://openalex.org/I165143802"]}],"countries":["AU"],"is_corresponding":true,"raw_author_name":"Thompson, Finn","raw_affiliation_strings":["The University of Queensland"],"affiliations":[{"raw_affiliation_string":"The University of Queensland","institution_ids":["https://openalex.org/I165143802"]}]},{"author_position":"last","author":{"id":null,"display_name":"Burton, Benjamin","orcid":"https://orcid.org/0000-0002-3478-3301"},"institutions":[{"id":"https://openalex.org/I165143802","display_name":"University of Queensland","ror":"https://ror.org/00rqy9422","country_code":"AU","type":"education","lineage":["https://openalex.org/I165143802"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Burton, Benjamin","raw_affiliation_strings":["The University of Queensland"],"affiliations":[{"raw_affiliation_string":"The University of Queensland","institution_ids":["https://openalex.org/I165143802"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I165143802"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.50770474,"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":true,"primary_topic":{"id":"https://openalex.org/T12157","display_name":"Geochemistry and Geologic Mapping","score":0.4165000021457672,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T12157","display_name":"Geochemistry and Geologic Mapping","score":0.4165000021457672,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T13177","display_name":"Geological and Geophysical Studies","score":0.03880000114440918,"subfield":{"id":"https://openalex.org/subfields/1907","display_name":"Geology"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T13067","display_name":"Geological Modeling and Analysis","score":0.025599999353289604,"subfield":{"id":"https://openalex.org/subfields/1906","display_name":"Geochemistry and Petrology"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.670799970626831},{"id":"https://openalex.org/keywords/heuristics","display_name":"Heuristics","score":0.6365000009536743},{"id":"https://openalex.org/keywords/triangulation","display_name":"Triangulation","score":0.5547000169754028},{"id":"https://openalex.org/keywords/normal-surface","display_name":"Normal surface","score":0.48570001125335693},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.46239998936653137},{"id":"https://openalex.org/keywords/surface","display_name":"Surface (topology)","score":0.4578000009059906},{"id":"https://openalex.org/keywords/genus","display_name":"Genus","score":0.45419999957084656}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7182000279426575},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.670799970626831},{"id":"https://openalex.org/C127705205","wikidata":"https://www.wikidata.org/wiki/Q5748245","display_name":"Heuristics","level":2,"score":0.6365000009536743},{"id":"https://openalex.org/C135981907","wikidata":"https://www.wikidata.org/wiki/Q188056","display_name":"Triangulation","level":2,"score":0.5547000169754028},{"id":"https://openalex.org/C182173840","wikidata":"https://www.wikidata.org/wiki/Q3977889","display_name":"Normal surface","level":3,"score":0.48570001125335693},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.46810001134872437},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.46239998936653137},{"id":"https://openalex.org/C2776799497","wikidata":"https://www.wikidata.org/wiki/Q484298","display_name":"Surface (topology)","level":2,"score":0.4578000009059906},{"id":"https://openalex.org/C157369684","wikidata":"https://www.wikidata.org/wiki/Q34740","display_name":"Genus","level":2,"score":0.45419999957084656},{"id":"https://openalex.org/C76956144","wikidata":"https://www.wikidata.org/wiki/Q5697916","display_name":"Heegaard splitting","level":3,"score":0.421999990940094},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.40619999170303345},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.38909998536109924},{"id":"https://openalex.org/C3017489831","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Running time","level":2,"score":0.3353999853134155},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.3319999873638153},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.319599986076355},{"id":"https://openalex.org/C29123130","wikidata":"https://www.wikidata.org/wiki/Q874709","display_name":"Computational geometry","level":2,"score":0.28450000286102295},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.2736999988555908},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.26820001006126404}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:ojs.library.carleton.ca:article/5533","is_oa":true,"landing_page_url":"https://jocg.org/index.php/jocg/article/view/5533","pdf_url":null,"source":{"id":"https://openalex.org/S4306400962","display_name":"Journal of Computational Geometry (Carleton University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I67031392","host_organization_name":"Carleton University","host_organization_lineage":["https://openalex.org/I67031392"],"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":"10.20382/jocg.v16i2","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"doi:10.20382/jocg.v16i2a7","is_oa":true,"landing_page_url":"https://doi.org/10.20382/jocg.v16i2a7","pdf_url":null,"source":{"id":"https://openalex.org/S4306400962","display_name":"Journal of Computational Geometry (Carleton University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I67031392","host_organization_name":"Carleton University","host_organization_lineage":["https://openalex.org/I67031392"],"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:ojs.library.carleton.ca:article/5533","is_oa":true,"landing_page_url":"https://jocg.org/index.php/jocg/article/view/5533","pdf_url":null,"source":{"id":"https://openalex.org/S4306400962","display_name":"Journal of Computational Geometry (Carleton University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I67031392","host_organization_name":"Carleton University","host_organization_lineage":["https://openalex.org/I67031392"],"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":"10.20382/jocg.v16i2","raw_type":"info:eu-repo/semantics/publishedVersion"},"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":{"The":[0,110],"Heegaard":[1,12,151,199],"genus":[2,13,179],"is":[3,18,112,120],"a":[4,15,69,81,104,167],"fundamental":[5],"invariant":[6],"of":[7,14,49,73,84,106,136,150,170,184],"3-manifolds.":[8],"However,":[9],"computing":[10],"the":[11,50,86,118,133,140,148,178,187,198],"triangulated":[16],"3-manifold":[17],"NP-hard,":[19],"and":[20,35,64,117,157],"while":[21],"algorithms":[22,40,156],"exist,":[23],"little":[24],"work":[25],"has":[26],"been":[27],"done":[28],"in":[29,139,162],"making":[30],"such":[31],"an":[32,47],"algorithm":[33],"efficient":[34],"practical":[36],"for":[37,60,103,180],"implementation.":[38,65],"Current":[39],"use":[41],"almost":[42,76,94,107,127],"normal":[43,52,77,95,108,128,137],"surfaces,":[44,78],"which":[45,56],"are":[46],"extension":[48],"algorithm-friendly":[51],"surface":[53],"theory":[54],"but":[55],"add":[57],"considerable":[58],"complexity":[59],"both":[61],"running":[62],"time":[63],"Here":[66],"we":[67,79,154,175],"take":[68],"different":[70],"approach:":[71],"instead":[72],"working":[74],"with":[75],"give":[80],"general":[82],"method":[83],"modifying":[85],"input":[87],"triangulation":[88],"that":[89,121,124,159],"allows":[90],"us":[91],"to":[92,99,132,147,166],"avoid":[93],"surfaces":[96,123,138],"entirely,":[97],"similar":[98],"existing":[100],"techniques":[101],"used":[102],"subset":[105],"surfaces.":[109],"cost":[111],"just":[113],"four":[114],"new":[115,141],"tetrahedra,":[116],"benefit":[119],"important":[122],"were":[125],"once":[126],"can":[129],"be":[130],"moved":[131],"simpler":[134],"setting":[135],"triangulation.":[142],"We":[143],"apply":[144],"this":[145],"technique":[146],"computation":[149],"genus,":[152],"where":[153],"develop":[155],"heuristics":[158],"prove":[160],"successful":[161],"practice":[163],"when":[164],"applied":[165],"data":[168],"set":[169],"11,031":[171],"closed":[172],"hyperbolic":[173],"3-manifolds:":[174],"precisely":[176],"determine":[177],"at":[181],"least":[182],"8,854":[183],"these.":[185],"In":[186],"remaining":[188],"2,177":[189],"triangulations,":[190],"our":[191],"methods":[192],"provide":[193],"tight":[194],"upper":[195],"bounds":[196],"on":[197],"genus.":[200]},"counts_by_year":[],"updated_date":"2025-11-06T06:51:31.235846","created_date":"2025-10-10T00:00:00"}