{"id":"https://openalex.org/W2122161604","doi":"https://doi.org/10.1142/s0218195906002002","title":"GUARDING ART GALLERIES BY GUARDING WITNESSES","display_name":"GUARDING ART GALLERIES BY GUARDING WITNESSES","publication_year":2006,"publication_date":"2006-04-27","ids":{"openalex":"https://openalex.org/W2122161604","doi":"https://doi.org/10.1142/s0218195906002002","mag":"2122161604"},"language":"en","primary_location":{"id":"doi:10.1142/s0218195906002002","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218195906002002","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":true,"oa_status":"green","oa_url":"https://dspace.library.uu.nl/handle/1874/19007","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5112563629","display_name":"Kyung-Yong Chwa","orcid":null},"institutions":[{"id":"https://openalex.org/I157485424","display_name":"Korea Advanced Institute of Science and Technology","ror":"https://ror.org/05apxxy63","country_code":"KR","type":"education","lineage":["https://openalex.org/I157485424"]}],"countries":["KR"],"is_corresponding":true,"raw_author_name":"KYUNG-YONG CHWA","raw_affiliation_strings":["Department of Computer Science, KAIST, 373-1 Guseong-dong Yuseong-gu, Daejeon, 305-701, Korea","Department of Computer Science, KAIST, 373-1 Guseong-dong, Yuseong-gu, Daejeon 305-701, Korea"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, KAIST, 373-1 Guseong-dong Yuseong-gu, Daejeon, 305-701, Korea","institution_ids":["https://openalex.org/I157485424"]},{"raw_affiliation_string":"Department of Computer Science, KAIST, 373-1 Guseong-dong, Yuseong-gu, Daejeon 305-701, Korea","institution_ids":["https://openalex.org/I157485424"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5026877149","display_name":"Byung-Cheol Jo","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"BYUNG-CHEOL JO","raw_affiliation_strings":["Taff System, Co. Ltd., Seoul, Korea"],"affiliations":[{"raw_affiliation_string":"Taff System, Co. Ltd., Seoul, Korea","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5003621581","display_name":"Christian Knauer","orcid":null},"institutions":[{"id":"https://openalex.org/I75951250","display_name":"Freie Universit\u00e4t Berlin","ror":"https://ror.org/046ak2485","country_code":"DE","type":"education","lineage":["https://openalex.org/I75951250"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"CHRISTIAN KNAUER","raw_affiliation_strings":["Institut f\u00fcr Informatik, Freie Universit\u00e4t Berlin, Takustra\u00dfe 9, D-14195 Berlin, Germany"],"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Informatik, Freie Universit\u00e4t Berlin, Takustra\u00dfe 9, D-14195 Berlin, Germany","institution_ids":["https://openalex.org/I75951250"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5046375175","display_name":"Esther Moet","orcid":null},"institutions":[{"id":"https://openalex.org/I193662353","display_name":"Utrecht University","ror":"https://ror.org/04pp8hn57","country_code":"NL","type":"education","lineage":["https://openalex.org/I193662353"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"ESTHER MOET","raw_affiliation_strings":["Department of Information & Computing Sciences, Universiteit Utrecht, P. O. Box 80.089, 3508 TB Utrecht, The Netherlands"],"affiliations":[{"raw_affiliation_string":"Department of Information & Computing Sciences, Universiteit Utrecht, P. O. Box 80.089, 3508 TB Utrecht, The Netherlands","institution_ids":["https://openalex.org/I193662353"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5000419856","display_name":"Ren\u00e9 van Oostrum","orcid":"https://orcid.org/0009-0006-5734-4201"},"institutions":[{"id":"https://openalex.org/I193662353","display_name":"Utrecht University","ror":"https://ror.org/04pp8hn57","country_code":"NL","type":"education","lineage":["https://openalex.org/I193662353"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"REN\u00c9 VAN OOSTRUM","raw_affiliation_strings":["Department of Information & Computing Sciences, Universiteit Utrecht, P. O. Box 80.089, 3508 TB Utrecht, The Netherlands"],"affiliations":[{"raw_affiliation_string":"Department of Information & Computing Sciences, Universiteit Utrecht, P. O. Box 80.089, 3508 TB Utrecht, The Netherlands","institution_ids":["https://openalex.org/I193662353"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5042351684","display_name":"Chan-Su Shin","orcid":"https://orcid.org/0000-0003-3073-6863"},"institutions":[{"id":"https://openalex.org/I83436808","display_name":"Hankuk University of Foreign Studies","ror":"https://ror.org/051q2m369","country_code":"KR","type":"education","lineage":["https://openalex.org/I83436808"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"CHAN-SU SHIN","raw_affiliation_strings":["School of Electronics and Information Engineering, Hankuk University of Foreign Studies, Yongin, Korea"],"affiliations":[{"raw_affiliation_string":"School of Electronics and Information Engineering, Hankuk University of Foreign Studies, Yongin, Korea","institution_ids":["https://openalex.org/I83436808"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5112563629"],"corresponding_institution_ids":["https://openalex.org/I157485424"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":14,"citation_normalized_percentile":{"value":0.14740965,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"16","issue":"02n03","first_page":"205","last_page":"226"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9840999841690063,"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":0.953499972820282,"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/witness","display_name":"Witness","score":0.8896876573562622},{"id":"https://openalex.org/keywords/guard","display_name":"Guard (computer science)","score":0.7085496187210083},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6182547807693481},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6092453598976135},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5520534515380859},{"id":"https://openalex.org/keywords/polygon","display_name":"Polygon (computer graphics)","score":0.4892423152923584},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.4785483479499817},{"id":"https://openalex.org/keywords/finite-set","display_name":"Finite set","score":0.41706418991088867},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3808646500110626},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.21511587500572205},{"id":"https://openalex.org/keywords/law","display_name":"Law","score":0.17718061804771423},{"id":"https://openalex.org/keywords/political-science","display_name":"Political science","score":0.06657862663269043}],"concepts":[{"id":"https://openalex.org/C2776900844","wikidata":"https://www.wikidata.org/wiki/Q8028383","display_name":"Witness","level":2,"score":0.8896876573562622},{"id":"https://openalex.org/C141141315","wikidata":"https://www.wikidata.org/wiki/Q2379942","display_name":"Guard (computer science)","level":2,"score":0.7085496187210083},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6182547807693481},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6092453598976135},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5520534515380859},{"id":"https://openalex.org/C190694206","wikidata":"https://www.wikidata.org/wiki/Q3276654","display_name":"Polygon (computer graphics)","level":3,"score":0.4892423152923584},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.4785483479499817},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.41706418991088867},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3808646500110626},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.21511587500572205},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.17718061804771423},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.06657862663269043},{"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/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/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1142/s0218195906002002","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218195906002002","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:uu:oai:dspace.library.uu.nl:1874/19007","is_oa":true,"landing_page_url":"https://dspace.library.uu.nl/handle/1874/19007","pdf_url":null,"source":{"id":"https://openalex.org/S4306401843","display_name":"Data Archiving and Networked Services (DANS)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1322597698","host_organization_name":"Royal Netherlands Academy of Arts and Sciences","host_organization_lineage":["https://openalex.org/I1322597698"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Special Issue: Selected Papers from the 15th Annual International Symposium on Algorithm and Computation (ISAAC'04), 205","raw_type":"info:eu-repo/semantics/bookpart"}],"best_oa_location":{"id":"pmh:uu:oai:dspace.library.uu.nl:1874/19007","is_oa":true,"landing_page_url":"https://dspace.library.uu.nl/handle/1874/19007","pdf_url":null,"source":{"id":"https://openalex.org/S4306401843","display_name":"Data Archiving and Networked Services (DANS)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1322597698","host_organization_name":"Royal Netherlands Academy of Arts and Sciences","host_organization_lineage":["https://openalex.org/I1322597698"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Special Issue: Selected Papers from the 15th Annual International Symposium on Algorithm and Computation (ISAAC'04), 205","raw_type":"info:eu-repo/semantics/bookpart"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W1874694348","https://openalex.org/W1973307935","https://openalex.org/W1998909289","https://openalex.org/W2003711098","https://openalex.org/W2030848465","https://openalex.org/W2032159439","https://openalex.org/W2087422927","https://openalex.org/W2122845873","https://openalex.org/W2502636724","https://openalex.org/W2609210027"],"related_works":["https://openalex.org/W2890518300","https://openalex.org/W2366687089","https://openalex.org/W588843504","https://openalex.org/W2382947717","https://openalex.org/W4302574074","https://openalex.org/W2892143878","https://openalex.org/W2360970878","https://openalex.org/W2370332886","https://openalex.org/W3042074040","https://openalex.org/W2804118840"],"abstract_inverted_index":{"Let":[0],"P":[1,21,101,134],"be":[2,15,78],"a":[3,10,16,44,49,95,110,130,138],"polygon,":[4],"possibly":[5],"with":[6],"holes.":[7],"We":[8,89,123],"define":[9],"witness":[11,46,52,60,82,98,131],"set":[12,17,28,53,99,111,132,141],"W":[13],"to":[14,93,114,135],"of":[18,64,73,86],"points":[19,144],"in":[20,61,83,102,145],"such":[22,109],"that":[23,36,128],"if":[24,108],"any":[25,59],"(prospective)":[26,139],"guard":[27,140],"G":[29,37],"guards":[30,38],"W,":[31],"then":[32,55],"it":[33,56],"is":[34],"guaranteed":[35],"P.":[39,146],"Not":[40],"all":[41,66,143],"polygons":[42],"admit":[43],"finite":[45,50],"set.":[47],"If":[48],"minimal":[51],"exists,":[54,112],"cannot":[57],"contain":[58],"the":[62,71,84,116,119],"interior":[63,85],"P,":[65,74],"witnesses":[67],"must":[68],"lie":[69],"on":[70],"boundary":[72],"and":[75],"there":[76],"can":[77],"at":[79],"most":[80],"one":[81],"every":[87],"edge.":[88],"give":[90],"an":[91],"algorithm":[92],"compute":[94],"minimum":[96],"size":[97],"for":[100,133],"O(n":[103],"2":[104],"log":[105],"n)":[106],"time,":[107],"or":[113],"report":[115],"non-existence":[117],"within":[118],"same":[120],"time":[121],"bounds.":[122],"also":[124],"outline":[125],"two":[126],"algorithms":[127],"use":[129],"test":[136],"whether":[137],"sees":[142]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}