{"id":"https://openalex.org/W2754203313","doi":"https://doi.org/10.1142/s0218195917600020","title":"Navigating Weighted Regions with Scattered Skinny Tetrahedra","display_name":"Navigating Weighted Regions with Scattered Skinny Tetrahedra","publication_year":2017,"publication_date":"2017-03-01","ids":{"openalex":"https://openalex.org/W2754203313","doi":"https://doi.org/10.1142/s0218195917600020","mag":"2754203313"},"language":"en","primary_location":{"id":"doi:10.1142/s0218195917600020","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218195917600020","pdf_url":null,"source":{"id":"https://openalex.org/S25827807","display_name":"International Journal of Computational Geometry & Applications","issn_l":"0218-1959","issn":["0218-1959","1793-6357"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computational Geometry & Applications","raw_type":"journal-article"},"type":"article","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/A5070497738","display_name":"Siu-Wing Cheng","orcid":"https://orcid.org/0000-0002-3557-9935"},"institutions":[{"id":"https://openalex.org/I200769079","display_name":"Hong Kong University of Science and Technology","ror":"https://ror.org/00q4vv597","country_code":"HK","type":"education","lineage":["https://openalex.org/I200769079"]}],"countries":["HK"],"is_corresponding":true,"raw_author_name":"Siu-Wing Cheng","raw_affiliation_strings":["Department of Computer Science and Engineering, HKUST, Hong Kong"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Engineering, HKUST, Hong Kong","institution_ids":["https://openalex.org/I200769079"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5032317194","display_name":"Man-Kwun Chiu","orcid":"https://orcid.org/0000-0001-7435-1020"},"institutions":[{"id":"https://openalex.org/I184597095","display_name":"National Institute of Informatics","ror":"https://ror.org/04ksd4g47","country_code":"JP","type":"facility","lineage":["https://openalex.org/I1319490839","https://openalex.org/I184597095","https://openalex.org/I4210158934"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Man-Kwun Chiu","raw_affiliation_strings":["JST, ERATO, Kawarabayashi Large Graph Project, Japan","National Institute of Informatics (NII), Tokyo, Japan"],"affiliations":[{"raw_affiliation_string":"JST, ERATO, Kawarabayashi Large Graph Project, Japan","institution_ids":[]},{"raw_affiliation_string":"National Institute of Informatics (NII), Tokyo, Japan","institution_ids":["https://openalex.org/I184597095"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5085514835","display_name":"Jiongxin Jin","orcid":null},"institutions":[{"id":"https://openalex.org/I1291425158","display_name":"Google (United States)","ror":"https://ror.org/00njsd438","country_code":"US","type":"company","lineage":["https://openalex.org/I1291425158","https://openalex.org/I4210128969"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jiongxin Jin","raw_affiliation_strings":["Google Inc., USA"],"affiliations":[{"raw_affiliation_string":"Google Inc., USA","institution_ids":["https://openalex.org/I1291425158"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5019937157","display_name":"Antoine Vigneron","orcid":"https://orcid.org/0000-0003-3586-3431"},"institutions":[{"id":"https://openalex.org/I48566637","display_name":"Ulsan National Institute of Science and Technology","ror":"https://ror.org/017cjz748","country_code":"KR","type":"education","lineage":["https://openalex.org/I48566637"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Antoine Vigneron","raw_affiliation_strings":["School of Electrical and Computer Engineering, Ulsan National Institute of Science and Technology, Ulsan, Korea"],"affiliations":[{"raw_affiliation_string":"School of Electrical and Computer Engineering, Ulsan National Institute of Science and Technology, Ulsan, Korea","institution_ids":["https://openalex.org/I48566637"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5070497738"],"corresponding_institution_ids":["https://openalex.org/I200769079"],"apc_list":null,"apc_paid":null,"fwci":0.7126,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.77420507,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"27","issue":"01n02","first_page":"13","last_page":"32"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":1.0,"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":1.0,"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":0.9995999932289124,"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/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9966999888420105,"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/mathematics","display_name":"Mathematics","score":0.7188286185264587},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6993402242660522},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.5916962623596191},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.4731006622314453},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.4382336139678955},{"id":"https://openalex.org/keywords/tetrahedron","display_name":"Tetrahedron","score":0.42108237743377686},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.21377906203269958},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.14052274823188782},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.09434017539024353}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7188286185264587},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6993402242660522},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5916962623596191},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.4731006622314453},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.4382336139678955},{"id":"https://openalex.org/C105239961","wikidata":"https://www.wikidata.org/wiki/Q160003","display_name":"Tetrahedron","level":2,"score":0.42108237743377686},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.21377906203269958},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.14052274823188782},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09434017539024353},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1142/s0218195917600020","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218195917600020","pdf_url":null,"source":{"id":"https://openalex.org/S25827807","display_name":"International Journal of Computational Geometry & Applications","issn_l":"0218-1959","issn":["0218-1959","1793-6357"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computational Geometry & Applications","raw_type":"journal-article"},{"id":"pmh:oai:repository.hkust.edu.hk:1783.1-87568","is_oa":false,"landing_page_url":"http://repository.hkust.edu.hk/ir/Record/1783.1-87568","pdf_url":null,"source":{"id":"https://openalex.org/S4306401796","display_name":"Rare & Special e-Zone (The Hong Kong University of Science and Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I200769079","host_organization_name":"Hong Kong University of Science and Technology","host_organization_lineage":["https://openalex.org/I200769079"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},{"id":"pmh:oai:repository.ust.hk:1783.1-87568","is_oa":false,"landing_page_url":"http://www.scopus.com/record/display.url?eid=2-s2.0-85029381856&origin=inward","pdf_url":null,"source":{"id":"https://openalex.org/S4306401796","display_name":"Rare & Special e-Zone (The Hong Kong University of Science and Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I200769079","host_organization_name":"Hong Kong University of Science and Technology","host_organization_lineage":["https://openalex.org/I200769079"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"pmh:oai:scholarworks.unist.ac.kr:201301/22741","is_oa":false,"landing_page_url":"http://www.worldscientific.com/doi/abs/10.1142/S0218195917600020","pdf_url":null,"source":{"id":"https://openalex.org/S4306401118","display_name":"Scholarworks@UNIST (Ulsan National Institute of Science and Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I48566637","host_organization_name":"Ulsan National Institute of Science and Technology","host_organization_lineage":["https://openalex.org/I48566637"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"ARTICLE"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W1559701472","https://openalex.org/W1798872925","https://openalex.org/W1974056748","https://openalex.org/W1989723858","https://openalex.org/W2024693023","https://openalex.org/W2025130628","https://openalex.org/W2028769163","https://openalex.org/W2029177589","https://openalex.org/W2029668981","https://openalex.org/W2049480565","https://openalex.org/W2058510050","https://openalex.org/W2069323107","https://openalex.org/W2079124625","https://openalex.org/W2084224084","https://openalex.org/W2108567935","https://openalex.org/W2109032771","https://openalex.org/W2112346596","https://openalex.org/W2117878581","https://openalex.org/W2127076644","https://openalex.org/W2127945324","https://openalex.org/W2132432991","https://openalex.org/W2159549579","https://openalex.org/W3136732126","https://openalex.org/W4214677270"],"related_works":["https://openalex.org/W3118783749","https://openalex.org/W2002583644","https://openalex.org/W3119989344","https://openalex.org/W2025402442","https://openalex.org/W2098990162","https://openalex.org/W1987870972","https://openalex.org/W2993813190","https://openalex.org/W4286974865","https://openalex.org/W4214593871","https://openalex.org/W3199408051"],"abstract_inverted_index":{"We":[0],"propose":[1],"an":[2],"algorithm":[3,119],"for":[4],"finding":[5],"a":[6,13,92],"[Formula:":[7,18,28,38,49,58,62,70,87,94,99,105,111,123,126,130,134,142],"see":[8,19,29,39,50,59,63,71,88,95,100,106,112,124,127,131,135,143],"text]-approximate":[9],"shortest":[10],"path":[11],"through":[12],"weighted":[14],"3D":[15],"simplicial":[16],"complex":[17],"text].":[20,60,89,132,144],"The":[21],"weights":[22],"are":[23],"integers":[24],"from":[25],"the":[26,32,42,53,74,77,114,137],"range":[27],"text]":[30,40,51,64,72,96,101,107,128],"and":[31,47,129],"vertices":[33],"have":[34],"integral":[35],"coordinates.":[36],"Let":[37,61,69],"be":[41,52,65,73],"largest":[43,78],"vertex":[44],"coordinate":[45],"magnitude,":[46],"let":[48],"number":[54],"of":[55,76,81,104,117],"tetrahedra":[56,82],"in":[57,122],"some":[66],"arbitrary":[67],"constant.":[68],"size":[75],"connected":[79],"component":[80],"whose":[83],"aspect":[84],"ratios":[85],"exceed":[86],"There":[90],"exists":[91],"constant":[93],"dependent":[97],"on":[98],"but":[102],"independent":[103],"such":[108],"that":[109],"if":[110],"text],":[113,125,136],"running":[115,138],"time":[116,139],"our":[118],"is":[120],"polynomial":[121],"If":[133],"reduces":[140],"to":[141]},"counts_by_year":[{"year":2020,"cited_by_count":1}],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2025-10-10T00:00:00"}