{"id":"https://openalex.org/W2149694164","doi":"https://doi.org/10.1142/s0218195907002227","title":"PARALLEL DELAUNAY REFINEMENT: ALGORITHMS AND ANALYSES","display_name":"PARALLEL DELAUNAY REFINEMENT: ALGORITHMS AND ANALYSES","publication_year":2007,"publication_date":"2007-02-01","ids":{"openalex":"https://openalex.org/W2149694164","doi":"https://doi.org/10.1142/s0218195907002227","mag":"2149694164"},"language":"en","primary_location":{"id":"doi:10.1142/s0218195907002227","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218195907002227","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/A5061644327","display_name":"Daniel A. Spielman","orcid":"https://orcid.org/0000-0002-8958-879X"},"institutions":[{"id":"https://openalex.org/I32971472","display_name":"Yale University","ror":"https://ror.org/03v76x132","country_code":"US","type":"education","lineage":["https://openalex.org/I32971472"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"DANIEL A. SPIELMAN","raw_affiliation_strings":["Department of Computer Science, Yale University, New Haven, CT 06511, USA"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Yale University, New Haven, CT 06511, USA","institution_ids":["https://openalex.org/I32971472"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102005063","display_name":"Shang\u2010Hua Teng","orcid":"https://orcid.org/0000-0001-5011-4514"},"institutions":[{"id":"https://openalex.org/I111088046","display_name":"Boston University","ror":"https://ror.org/05qwgg493","country_code":"US","type":"education","lineage":["https://openalex.org/I111088046"]},{"id":"https://openalex.org/I10734018","display_name":"Akamai (United States)","ror":"https://ror.org/03tarb191","country_code":"US","type":"company","lineage":["https://openalex.org/I10734018"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"SHANG-HUA TENG","raw_affiliation_strings":["Department of Computer Science, Boston University and Akamai Technologies, Boston, MA 02215, USA"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Boston University and Akamai Technologies, Boston, MA 02215, USA","institution_ids":["https://openalex.org/I10734018","https://openalex.org/I111088046"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5034966177","display_name":"Alper \u00dcng\u00f6r","orcid":null},"institutions":[{"id":"https://openalex.org/I33213144","display_name":"University of Florida","ror":"https://ror.org/02y3ad647","country_code":"US","type":"education","lineage":["https://openalex.org/I33213144"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"ALPER \u00dcNG\u00d6R","raw_affiliation_strings":["Department of Computer & Information Science & Engineering, University of Florida, Gainesville, FL 32605, USA"],"affiliations":[{"raw_affiliation_string":"Department of Computer & Information Science & Engineering, University of Florida, Gainesville, FL 32605, USA","institution_ids":["https://openalex.org/I33213144"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5061644327"],"corresponding_institution_ids":["https://openalex.org/I32971472"],"apc_list":null,"apc_paid":null,"fwci":5.5094,"has_fulltext":false,"cited_by_count":32,"citation_normalized_percentile":{"value":0.95157895,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"17","issue":"01","first_page":"1","last_page":"30"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9998999834060669,"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":0.9998999834060669,"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/T10586","display_name":"Robotic Path Planning Algorithms","score":0.9868000149726868,"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"}},{"id":"https://openalex.org/T11164","display_name":"Remote Sensing and LiDAR Applications","score":0.9660999774932861,"subfield":{"id":"https://openalex.org/subfields/2305","display_name":"Environmental Engineering"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/chews-second-algorithm","display_name":"Chew's second algorithm","score":0.9203364849090576},{"id":"https://openalex.org/keywords/rupperts-algorithm","display_name":"Ruppert's algorithm","score":0.8995616436004639},{"id":"https://openalex.org/keywords/delaunay-triangulation","display_name":"Delaunay triangulation","score":0.8835151195526123},{"id":"https://openalex.org/keywords/bowyer\u2013watson-algorithm","display_name":"Bowyer\u2013Watson algorithm","score":0.6913986206054688},{"id":"https://openalex.org/keywords/polygon-mesh","display_name":"Polygon mesh","score":0.6509649157524109},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.6174874305725098},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5818157196044922},{"id":"https://openalex.org/keywords/constrained-delaunay-triangulation","display_name":"Constrained Delaunay triangulation","score":0.44098031520843506},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4245501458644867},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.37525227665901184},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07674908638000488}],"concepts":[{"id":"https://openalex.org/C183342303","wikidata":"https://www.wikidata.org/wiki/Q105742691","display_name":"Chew's second algorithm","level":4,"score":0.9203364849090576},{"id":"https://openalex.org/C99886907","wikidata":"https://www.wikidata.org/wiki/Q105742691","display_name":"Ruppert's algorithm","level":4,"score":0.8995616436004639},{"id":"https://openalex.org/C68010082","wikidata":"https://www.wikidata.org/wiki/Q192445","display_name":"Delaunay triangulation","level":2,"score":0.8835151195526123},{"id":"https://openalex.org/C121198538","wikidata":"https://www.wikidata.org/wiki/Q4951461","display_name":"Bowyer\u2013Watson algorithm","level":3,"score":0.6913986206054688},{"id":"https://openalex.org/C31487907","wikidata":"https://www.wikidata.org/wiki/Q1154597","display_name":"Polygon mesh","level":2,"score":0.6509649157524109},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6174874305725098},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5818157196044922},{"id":"https://openalex.org/C128321387","wikidata":"https://www.wikidata.org/wiki/Q5164356","display_name":"Constrained Delaunay triangulation","level":3,"score":0.44098031520843506},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4245501458644867},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.37525227665901184},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07674908638000488},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218195907002227","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218195907002227","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320332222","display_name":"University of Illinois at Urbana-Champaign","ror":"https://ror.org/047426m28"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W180080237","https://openalex.org/W269812687","https://openalex.org/W574423895","https://openalex.org/W1492109951","https://openalex.org/W1601577618","https://openalex.org/W1987569615","https://openalex.org/W1995005469","https://openalex.org/W2014843742","https://openalex.org/W2025166133","https://openalex.org/W2029520714","https://openalex.org/W2100061495","https://openalex.org/W2120018535","https://openalex.org/W2121431945","https://openalex.org/W2135301926","https://openalex.org/W2137568470","https://openalex.org/W2147827640","https://openalex.org/W2164205216","https://openalex.org/W2727854388"],"related_works":["https://openalex.org/W2353304988","https://openalex.org/W2359979928","https://openalex.org/W1989161402","https://openalex.org/W2384614608","https://openalex.org/W2063329372","https://openalex.org/W2024358741","https://openalex.org/W2394349965","https://openalex.org/W2378792796","https://openalex.org/W2368931253","https://openalex.org/W2378686409"],"abstract_inverted_index":{"We":[0,66],"present":[1],"a":[2,29,54,68,88,230],"parallel":[3,22,102,137,168,198,220],"Delaunay":[4,45,82,149,169],"refinement":[5,150,170],"algorithm":[6,23,156,162,171,213,222],"for":[7],"generating":[8,185],"well-shaped":[9,225],"meshes":[10,226],"in":[11,157,163,201],"both":[12],"two":[13,158],"and":[14,84,97,160,177],"three":[15,164],"dimensions.":[16,165],"Like":[17],"its":[18],"sequential":[19,148,182],"counterparts,":[20],"the":[21,26,35,39,44,60,99,112,115,118,121,124,136,173,195,207,215,234],"iteratively":[24],"improves":[25],"quality":[27,176],"of":[28,56,62,70,90,101,114,120,139,142,197,209,227,233],"mesh":[30],"by":[31,147,154,192],"inserting":[32],"new":[33],"points,":[34,37],"Steiner":[36,48,74],"into":[38],"input":[40,116,129],"domain":[41],"while":[42],"maintaining":[43],"triangulation.":[46],"The":[47],"points":[49,75,92,143],"are":[50],"carefully":[51],"chosen":[52],"from":[53],"set":[55,89,141],"candidates":[57],"that":[58,76,86,98,135,223],"includes":[59],"circumcenters":[61],"poorly-shaped":[63],"triangular":[64],"elements.":[65],"introduce":[67],"notion":[69],"independence":[71],"among":[72,128],"possible":[73],"can":[77,93,144],"be":[78,94,145],"inserted":[79],"simultaneously":[80],"during":[81],"refinements":[83],"show":[85,134],"such":[87,152,188],"independent":[91],"constructed":[95],"efficiently":[96],"number":[100,196],"iterations":[103,199],"is":[104,111,200,214],"O(":[105,203],"log":[106,204],"2":[107],"\u0394),":[108],"where":[109],"\u0394":[110],"spread":[113],"\u2014":[117],"ratio":[119],"longest":[122],"to":[123],"shortest":[125],"pairwise":[126],"distances":[127],"features.":[130],"In":[131],"addition,":[132],"we":[133],"insertion":[138],"these":[140,181],"realized":[146],"algorithms":[151],"as":[153,180,189],"Ruppert's":[155],"dimensions":[159],"Shewchuk's":[161],"Therefore,":[166],"our":[167,210,212],"provides":[172],"same":[174],"shape":[175],"mesh-size":[178],"guarantees":[179],"algorithms.":[183],"For":[184],"quasi-uniform":[186],"meshes,":[187],"those":[190],"produced":[191],"Chew's":[193],"algorithms,":[194],"fact":[202],"\u0394).":[205],"To":[206],"best":[208,235],"knowledge,":[211],"first":[216],"provably":[217],"polylog(\u0394)":[218],"time":[219],"Delaunay-refinement":[221],"generates":[224],"size":[228],"within":[229],"constant":[231],"factor":[232],"possible.":[236]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":2}],"updated_date":"2026-03-22T08:09:32.410652","created_date":"2025-10-10T00:00:00"}