{"id":"https://openalex.org/W2132339863","doi":"https://doi.org/10.1007/bf01840360","title":"Linear-time algorithms for visibility and shortest path problems inside triangulated simple polygons","display_name":"Linear-time algorithms for visibility and shortest path problems inside triangulated simple polygons","publication_year":1987,"publication_date":"1987-11-01","ids":{"openalex":"https://openalex.org/W2132339863","doi":"https://doi.org/10.1007/bf01840360","mag":"2132339863"},"language":"en","primary_location":{"id":"doi:10.1007/bf01840360","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf01840360","pdf_url":null,"source":{"id":"https://openalex.org/S89324355","display_name":"Algorithmica","issn_l":"0178-4617","issn":["0178-4617","1432-0541"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithmica","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/A5065368881","display_name":"Leonidas Guibas","orcid":"https://orcid.org/0000-0002-8315-4886"},"institutions":[{"id":"https://openalex.org/I173498003","display_name":"Palo Alto Research Center","ror":"https://ror.org/0529fxt39","country_code":"US","type":"facility","lineage":["https://openalex.org/I173498003","https://openalex.org/I4210132870"]},{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Leonidas Guibas","raw_affiliation_strings":["Computer Science Department, Stanford University, 94305, Stanford, CA, USA","DEC/SRC, 130 Lytton Avenue, 94301, Palo Alto, CA, USA"],"affiliations":[{"raw_affiliation_string":"Computer Science Department, Stanford University, 94305, Stanford, CA, USA","institution_ids":["https://openalex.org/I97018004"]},{"raw_affiliation_string":"DEC/SRC, 130 Lytton Avenue, 94301, Palo Alto, CA, USA","institution_ids":["https://openalex.org/I173498003"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5038416046","display_name":"John Hershberger","orcid":null},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"John Hershberger","raw_affiliation_strings":["Computer Science Department, Stanford University, 94305, Stanford, CA, USA"],"affiliations":[{"raw_affiliation_string":"Computer Science Department, Stanford University, 94305, Stanford, CA, USA","institution_ids":["https://openalex.org/I97018004"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5028941620","display_name":"Daniel Leven","orcid":null},"institutions":[{"id":"https://openalex.org/I16391192","display_name":"Tel Aviv University","ror":"https://ror.org/04mhzgx49","country_code":"IL","type":"education","lineage":["https://openalex.org/I16391192"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Daniel Leven","raw_affiliation_strings":["School of Mathematical Sciences, Tel-Aviv University, 69978, Tel Aviv, Israel"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Tel-Aviv University, 69978, Tel Aviv, Israel","institution_ids":["https://openalex.org/I16391192"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5055296785","display_name":"Micha Sharir","orcid":"https://orcid.org/0000-0002-2541-3763"},"institutions":[{"id":"https://openalex.org/I16391192","display_name":"Tel Aviv University","ror":"https://ror.org/04mhzgx49","country_code":"IL","type":"education","lineage":["https://openalex.org/I16391192"]},{"id":"https://openalex.org/I57206974","display_name":"New York University","ror":"https://ror.org/0190ak572","country_code":"US","type":"education","lineage":["https://openalex.org/I57206974"]},{"id":"https://openalex.org/I36672615","display_name":"Courant Institute of Mathematical Sciences","ror":"https://ror.org/037tm7f56","country_code":"US","type":"education","lineage":["https://openalex.org/I36672615","https://openalex.org/I57206974"]}],"countries":["IL","US"],"is_corresponding":false,"raw_author_name":"Micha Sharir","raw_affiliation_strings":["Courant Institute of Mathematical Sciences, New York University, 10012, New York, NY, USA","School of Mathematical Sciences, Tel-Aviv University, 69978, Tel Aviv, Israel"],"affiliations":[{"raw_affiliation_string":"Courant Institute of Mathematical Sciences, New York University, 10012, New York, NY, USA","institution_ids":["https://openalex.org/I36672615","https://openalex.org/I57206974"]},{"raw_affiliation_string":"School of Mathematical Sciences, Tel-Aviv University, 69978, Tel Aviv, Israel","institution_ids":["https://openalex.org/I16391192"]}]},{"author_position":"last","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"]},{"id":"https://openalex.org/I1283103587","display_name":"AT&T (United States)","ror":"https://ror.org/02bbd5539","country_code":"US","type":"company","lineage":["https://openalex.org/I1283103587"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Robert E. Tarjan","raw_affiliation_strings":["AT&T Bell Laboratories, 07974, Murray Hill, NJ, USA","Department of Computer Science, Princeton University, 08544, Princeton, NJ, USA"],"affiliations":[{"raw_affiliation_string":"AT&T Bell Laboratories, 07974, Murray Hill, NJ, USA","institution_ids":["https://openalex.org/I1283103587"]},{"raw_affiliation_string":"Department of Computer Science, Princeton University, 08544, Princeton, NJ, USA","institution_ids":["https://openalex.org/I20089843"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5065368881"],"corresponding_institution_ids":["https://openalex.org/I173498003","https://openalex.org/I97018004"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":13.9219,"has_fulltext":false,"cited_by_count":508,"citation_normalized_percentile":{"value":0.99527745,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":100},"biblio":{"volume":"2","issue":"1-4","first_page":"209","last_page":"233"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9991999864578247,"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":0.9991999864578247,"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":0.9818000197410583,"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/T12288","display_name":"Optimization and Search Problems","score":0.9750000238418579,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/shortest-path-problem","display_name":"Shortest path problem","score":0.7799192667007446},{"id":"https://openalex.org/keywords/visibility","display_name":"Visibility","score":0.6889192461967468},{"id":"https://openalex.org/keywords/triangulation","display_name":"Triangulation","score":0.6573545932769775},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.5659248232841492},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.5427899360656738},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4755920171737671},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.47058430314064026},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.46910080313682556},{"id":"https://openalex.org/keywords/visibility-graph","display_name":"Visibility graph","score":0.44848358631134033},{"id":"https://openalex.org/keywords/path","display_name":"Path (computing)","score":0.43716001510620117},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4345768094062805},{"id":"https://openalex.org/keywords/simple-polygon","display_name":"Simple polygon","score":0.4340527057647705},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.4271906614303589},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.15796303749084473},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.13059425354003906},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.06213498115539551}],"concepts":[{"id":"https://openalex.org/C22590252","wikidata":"https://www.wikidata.org/wiki/Q1058754","display_name":"Shortest path problem","level":3,"score":0.7799192667007446},{"id":"https://openalex.org/C123403432","wikidata":"https://www.wikidata.org/wiki/Q654068","display_name":"Visibility","level":2,"score":0.6889192461967468},{"id":"https://openalex.org/C135981907","wikidata":"https://www.wikidata.org/wiki/Q188056","display_name":"Triangulation","level":2,"score":0.6573545932769775},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.5659248232841492},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.5427899360656738},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4755920171737671},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.47058430314064026},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.46910080313682556},{"id":"https://openalex.org/C173362246","wikidata":"https://www.wikidata.org/wiki/Q8216024","display_name":"Visibility graph","level":3,"score":0.44848358631134033},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.43716001510620117},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4345768094062805},{"id":"https://openalex.org/C197949415","wikidata":"https://www.wikidata.org/wiki/Q782746","display_name":"Simple polygon","level":3,"score":0.4340527057647705},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.4271906614303589},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.15796303749084473},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.13059425354003906},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06213498115539551},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/bf01840360","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf01840360","pdf_url":null,"source":{"id":"https://openalex.org/S89324355","display_name":"Algorithmica","issn_l":"0178-4617","issn":["0178-4617","1432-0541"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithmica","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W24696750","https://openalex.org/W1513400187","https://openalex.org/W1825136300","https://openalex.org/W1964869106","https://openalex.org/W1980707954","https://openalex.org/W1983487792","https://openalex.org/W1993217815","https://openalex.org/W2001513095","https://openalex.org/W2009530930","https://openalex.org/W2019236084","https://openalex.org/W2032159439","https://openalex.org/W2033775003","https://openalex.org/W2037007500","https://openalex.org/W2038280788","https://openalex.org/W2045783875","https://openalex.org/W2056531186","https://openalex.org/W2058872551","https://openalex.org/W2069750902","https://openalex.org/W2069941763","https://openalex.org/W2073058919","https://openalex.org/W2077180154","https://openalex.org/W2086797345","https://openalex.org/W2097429092","https://openalex.org/W2126876121","https://openalex.org/W2130055503","https://openalex.org/W2443862921","https://openalex.org/W2475478067","https://openalex.org/W2911302472","https://openalex.org/W3148461011","https://openalex.org/W4206442385"],"related_works":["https://openalex.org/W2359682335","https://openalex.org/W2208683552","https://openalex.org/W2108250208","https://openalex.org/W2910504761","https://openalex.org/W2109416368","https://openalex.org/W1508258340","https://openalex.org/W1970737314","https://openalex.org/W2352073446","https://openalex.org/W1587445384","https://openalex.org/W2073145634"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":7},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":8},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":12},{"year":2019,"cited_by_count":22},{"year":2018,"cited_by_count":8},{"year":2017,"cited_by_count":10},{"year":2016,"cited_by_count":11},{"year":2015,"cited_by_count":20},{"year":2014,"cited_by_count":14},{"year":2013,"cited_by_count":23},{"year":2012,"cited_by_count":16}],"updated_date":"2026-04-07T14:57:38.498316","created_date":"2025-10-10T00:00:00"}