{"id":"https://openalex.org/W1971842242","doi":"https://doi.org/10.1137/0217010","title":"An $O(n\\log \\log n)$-Time Algorithm for Triangulating a Simple Polygon","display_name":"An $O(n\\log \\log n)$-Time Algorithm for Triangulating a Simple Polygon","publication_year":1988,"publication_date":"1988-02-01","ids":{"openalex":"https://openalex.org/W1971842242","doi":"https://doi.org/10.1137/0217010","mag":"1971842242"},"language":"en","primary_location":{"id":"doi:10.1137/0217010","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0217010","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","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/A5051027549","display_name":"Robert E. Tarjan","orcid":"https://orcid.org/0000-0001-7505-5768"},"institutions":[{"id":"https://openalex.org/I20089843","display_name":"Princeton University","ror":"https://ror.org/00hx57361","country_code":"US","type":"education","lineage":["https://openalex.org/I20089843"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Robert E. Tarjan","raw_affiliation_strings":["Princeton Univ., Princeton , NJ"],"affiliations":[{"raw_affiliation_string":"Princeton Univ., Princeton , NJ","institution_ids":["https://openalex.org/I20089843"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5083959816","display_name":"Christopher J. Van Wyk","orcid":null},"institutions":[{"id":"https://openalex.org/I20089843","display_name":"Princeton University","ror":"https://ror.org/00hx57361","country_code":"US","type":"education","lineage":["https://openalex.org/I20089843"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Christopher J. Van Wyk","raw_affiliation_strings":["Princeton Univ., Princeton , NJ"],"affiliations":[{"raw_affiliation_string":"Princeton Univ., Princeton , NJ","institution_ids":["https://openalex.org/I20089843"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5051027549"],"corresponding_institution_ids":["https://openalex.org/I20089843"],"apc_list":null,"apc_paid":null,"fwci":15.4044,"has_fulltext":false,"cited_by_count":158,"citation_normalized_percentile":{"value":0.99044205,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"17","issue":"1","first_page":"143","last_page":"178"},"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/T12288","display_name":"Optimization and Search Problems","score":0.9941999912261963,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T10191","display_name":"Robotics and Sensor-Based Localization","score":0.9902999997138977,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/simple-polygon","display_name":"Simple polygon","score":0.8482341766357422},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7458806037902832},{"id":"https://openalex.org/keywords/polygon-covering","display_name":"Polygon covering","score":0.6913237571716309},{"id":"https://openalex.org/keywords/diagonal","display_name":"Diagonal","score":0.6391412615776062},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.59839928150177},{"id":"https://openalex.org/keywords/polygon","display_name":"Polygon (computer graphics)","score":0.5919692516326904},{"id":"https://openalex.org/keywords/partition","display_name":"Partition (number theory)","score":0.5710446834564209},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.5404589772224426},{"id":"https://openalex.org/keywords/computational-geometry","display_name":"Computational geometry","score":0.5329611897468567},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.5288708806037903},{"id":"https://openalex.org/keywords/binary-logarithm","display_name":"Binary logarithm","score":0.5269489884376526},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.49797558784484863},{"id":"https://openalex.org/keywords/triangulation","display_name":"Triangulation","score":0.4942760467529297},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.49271872639656067},{"id":"https://openalex.org/keywords/simple-algorithm","display_name":"SIMPLE algorithm","score":0.43053311109542847},{"id":"https://openalex.org/keywords/sorting","display_name":"Sorting","score":0.4176177382469177},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.3783408999443054},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.24009066820144653},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.16015130281448364},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.11130854487419128}],"concepts":[{"id":"https://openalex.org/C197949415","wikidata":"https://www.wikidata.org/wiki/Q782746","display_name":"Simple polygon","level":3,"score":0.8482341766357422},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7458806037902832},{"id":"https://openalex.org/C187778580","wikidata":"https://www.wikidata.org/wiki/Q18389289","display_name":"Polygon covering","level":3,"score":0.6913237571716309},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.6391412615776062},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.59839928150177},{"id":"https://openalex.org/C190694206","wikidata":"https://www.wikidata.org/wiki/Q3276654","display_name":"Polygon (computer graphics)","level":3,"score":0.5919692516326904},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.5710446834564209},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.5404589772224426},{"id":"https://openalex.org/C29123130","wikidata":"https://www.wikidata.org/wiki/Q874709","display_name":"Computational geometry","level":2,"score":0.5329611897468567},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.5288708806037903},{"id":"https://openalex.org/C63553672","wikidata":"https://www.wikidata.org/wiki/Q581168","display_name":"Binary logarithm","level":2,"score":0.5269489884376526},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.49797558784484863},{"id":"https://openalex.org/C135981907","wikidata":"https://www.wikidata.org/wiki/Q188056","display_name":"Triangulation","level":2,"score":0.4942760467529297},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.49271872639656067},{"id":"https://openalex.org/C97542219","wikidata":"https://www.wikidata.org/wiki/Q497863","display_name":"SIMPLE algorithm","level":2,"score":0.43053311109542847},{"id":"https://openalex.org/C111696304","wikidata":"https://www.wikidata.org/wiki/Q2303697","display_name":"Sorting","level":2,"score":0.4176177382469177},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.3783408999443054},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.24009066820144653},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.16015130281448364},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.11130854487419128},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C126042441","wikidata":"https://www.wikidata.org/wiki/Q1324888","display_name":"Frame (networking)","level":2,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","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},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/0217010","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0217010","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.186.5949","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.186.5949","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.princeton.edu/courses/archive/fall05/cos528/handouts/time%20algorithm%20for%20triangulating.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W6840519","https://openalex.org/W1513400187","https://openalex.org/W1570973162","https://openalex.org/W1801747540","https://openalex.org/W1967635159","https://openalex.org/W1983487792","https://openalex.org/W1987927249","https://openalex.org/W2009530930","https://openalex.org/W2010483698","https://openalex.org/W2015553450","https://openalex.org/W2023182928","https://openalex.org/W2030261330","https://openalex.org/W2037007500","https://openalex.org/W2041437464","https://openalex.org/W2051831392","https://openalex.org/W2068027817","https://openalex.org/W2069750902","https://openalex.org/W2073058919","https://openalex.org/W2077180154","https://openalex.org/W2085041675","https://openalex.org/W2088864905","https://openalex.org/W2130055503","https://openalex.org/W2132026455","https://openalex.org/W2132339863","https://openalex.org/W2169271351","https://openalex.org/W2475478067"],"related_works":["https://openalex.org/W2608536130","https://openalex.org/W1975883249","https://openalex.org/W1963624385","https://openalex.org/W255996094","https://openalex.org/W1521167118","https://openalex.org/W2167623422","https://openalex.org/W60842993","https://openalex.org/W2139606248","https://openalex.org/W2047178754","https://openalex.org/W2088816968"],"abstract_inverted_index":{"Given":[0],"a":[1,68],"simple":[2],"n-vertex":[3],"polygon,":[4],"the":[5,11,14,40],"triangulation":[6,50],"problem":[7],"is":[8,51,70],"to":[9],"partition":[10],"interior":[12],"of":[13,44],"polygon":[15,69],"into":[16],"$n":[17,23],"-":[18,24],"2$":[19],"triangles":[20],"by":[21],"adding":[22],"3$":[25],"nonintersecting":[26],"diagonals.":[27],"We":[28],"propose":[29],"an":[30],"$O(n\\log":[31,45],"\\log":[32],"n)$-time":[33],"algorithm":[34],"for":[35,59],"this":[36],"problem,":[37],"improving":[38],"on":[39],"previously":[41],"best":[42],"bound":[43],"n)$":[46],"and":[47],"showing":[48],"that":[49],"not":[52],"as":[53,55],"hard":[54],"sorting.":[56],"Improved":[57],"algorithms":[58],"several":[60],"other":[61],"computational":[62],"geometry":[63],"problems,":[64],"including":[65],"testing":[66],"whether":[67],"simple,":[71],"follow":[72],"from":[73],"our":[74],"result.":[75]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":4},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":6},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}