{"id":"https://openalex.org/W2041495686","doi":"https://doi.org/10.1137/s0097539791221505","title":"An Optimal Algorithm for Computing Visibility in the Plane","display_name":"An Optimal Algorithm for Computing Visibility in the Plane","publication_year":1995,"publication_date":"1995-02-01","ids":{"openalex":"https://openalex.org/W2041495686","doi":"https://doi.org/10.1137/s0097539791221505","mag":"2041495686"},"language":"en","primary_location":{"id":"doi:10.1137/s0097539791221505","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0097539791221505","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/A5037274151","display_name":"Paul J. Heffernan","orcid":null},"institutions":[{"id":"https://openalex.org/I205783295","display_name":"Cornell University","ror":"https://ror.org/05bnh6r87","country_code":"US","type":"education","lineage":["https://openalex.org/I205783295"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Paul J. Heffernan","raw_affiliation_strings":["School of Operations Research and Industrial Engineering Engineering and Theory Center, Cornell University, Ithaca,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Operations Research and Industrial Engineering Engineering and Theory Center, Cornell University, Ithaca,","institution_ids":["https://openalex.org/I205783295"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5015247956","display_name":"Joseph S. B. Mitchell","orcid":"https://orcid.org/0000-0002-0152-2279"},"institutions":[{"id":"https://openalex.org/I205783295","display_name":"Cornell University","ror":"https://ror.org/05bnh6r87","country_code":"US","type":"education","lineage":["https://openalex.org/I205783295"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Joseph S. B. Mitchell","raw_affiliation_strings":["School of Operations Research and Industrial Engineering Engineering and Theory Center, Cornell University, Ithaca,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Operations Research and Industrial Engineering Engineering and Theory Center, Cornell University, Ithaca,","institution_ids":["https://openalex.org/I205783295"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I205783295"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":51,"citation_normalized_percentile":{"value":0.14231738,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"24","issue":"1","first_page":"184","last_page":"201"},"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":0.9976999759674072,"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/T10191","display_name":"Robotics and Sensor-Based Localization","score":0.9800999760627747,"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/disjoint-sets","display_name":"Disjoint sets","score":0.8170784115791321},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7461903095245361},{"id":"https://openalex.org/keywords/convex-hull","display_name":"Convex hull","score":0.6712826490402222},{"id":"https://openalex.org/keywords/simple-polygon","display_name":"Simple polygon","score":0.6489635705947876},{"id":"https://openalex.org/keywords/visibility","display_name":"Visibility","score":0.5943613648414612},{"id":"https://openalex.org/keywords/binary-logarithm","display_name":"Binary logarithm","score":0.579643726348877},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5225979089736938},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5130742788314819},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.49027636647224426},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4715321660041809},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.4618017077445984},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.4608577787876129},{"id":"https://openalex.org/keywords/polygon","display_name":"Polygon (computer graphics)","score":0.4606803059577942},{"id":"https://openalex.org/keywords/computational-geometry","display_name":"Computational geometry","score":0.4379903972148895},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.42880675196647644},{"id":"https://openalex.org/keywords/visibility-polygon","display_name":"Visibility polygon","score":0.41671156883239746},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.32388174533843994},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.27862679958343506},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.06636252999305725}],"concepts":[{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.8170784115791321},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7461903095245361},{"id":"https://openalex.org/C206194317","wikidata":"https://www.wikidata.org/wiki/Q1138624","display_name":"Convex hull","level":3,"score":0.6712826490402222},{"id":"https://openalex.org/C197949415","wikidata":"https://www.wikidata.org/wiki/Q782746","display_name":"Simple polygon","level":3,"score":0.6489635705947876},{"id":"https://openalex.org/C123403432","wikidata":"https://www.wikidata.org/wiki/Q654068","display_name":"Visibility","level":2,"score":0.5943613648414612},{"id":"https://openalex.org/C63553672","wikidata":"https://www.wikidata.org/wiki/Q581168","display_name":"Binary logarithm","level":2,"score":0.579643726348877},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5225979089736938},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5130742788314819},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.49027636647224426},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4715321660041809},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.4618017077445984},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.4608577787876129},{"id":"https://openalex.org/C190694206","wikidata":"https://www.wikidata.org/wiki/Q3276654","display_name":"Polygon (computer graphics)","level":3,"score":0.4606803059577942},{"id":"https://openalex.org/C29123130","wikidata":"https://www.wikidata.org/wiki/Q874709","display_name":"Computational geometry","level":2,"score":0.4379903972148895},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.42880675196647644},{"id":"https://openalex.org/C1449246","wikidata":"https://www.wikidata.org/wiki/Q7936080","display_name":"Visibility polygon","level":4,"score":0.41671156883239746},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.32388174533843994},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.27862679958343506},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06636252999305725},{"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/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","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/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s0097539791221505","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0097539791221505","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W1971842242","https://openalex.org/W1986014106","https://openalex.org/W1989150421","https://openalex.org/W2019236084","https://openalex.org/W2028747718","https://openalex.org/W2030848465","https://openalex.org/W2033775003","https://openalex.org/W2085041675","https://openalex.org/W2094658339","https://openalex.org/W2106413026","https://openalex.org/W2126876121","https://openalex.org/W2132026455","https://openalex.org/W3011379640"],"related_works":["https://openalex.org/W53644101","https://openalex.org/W2011353791","https://openalex.org/W4296464845","https://openalex.org/W1973688271","https://openalex.org/W2136884464","https://openalex.org/W2155364694","https://openalex.org/W2139414590","https://openalex.org/W3180769701","https://openalex.org/W2136318972","https://openalex.org/W2132031696"],"abstract_inverted_index":{"The":[0,27],"authors":[1],"give":[2],"an":[3,59],"algorithm":[4,28,57,66],"to":[5],"compute":[6],"the":[7,44,56,69],"visibility":[8],"polygon":[9],"from":[10],"a":[11,14,22],"point":[12],"among":[13],"set":[15],"of":[16,24,48,55,72],"h":[17,40,62,73],"pairwise-disjoint":[18],"polygonal":[19],"obstacles":[20],"with":[21],"total":[23],"n":[25],"vertices.":[26],"uses":[29],"$O(n)$":[30],"space":[31],"and":[32],"runs":[33],"in":[34],"optimal":[35],"time":[36,65],"$\\Theta":[37],"(n":[38],"+":[39,61],"\\log":[41,50,63],"h)$,":[42],"improving":[43],"previous":[45],"upper":[46],"bound":[47],"$O(n":[49,60],"n)$.":[51],"A":[52],"direct":[53],"consequence":[54],"is":[58],"h)$":[64],"for":[67],"computing":[68],"convex":[70],"hull":[71],"disjoint":[74],"simple":[75],"polygons.":[76]},"counts_by_year":[{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":7}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}