{"id":"https://openalex.org/W2105729287","doi":"https://doi.org/10.1142/s0218195910003207","title":"DILATION-OPTIMAL EDGE DELETION IN POLYGONAL CYCLES","display_name":"DILATION-OPTIMAL EDGE DELETION IN POLYGONAL CYCLES","publication_year":2010,"publication_date":"2010-02-01","ids":{"openalex":"https://openalex.org/W2105729287","doi":"https://doi.org/10.1142/s0218195910003207","mag":"2105729287"},"language":"en","primary_location":{"id":"doi:10.1142/s0218195910003207","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218195910003207","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 &amp; 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/A5054175777","display_name":"Hee-Kap Ahn","orcid":"https://orcid.org/0000-0001-7177-1679"},"institutions":[{"id":"https://openalex.org/I123900574","display_name":"Pohang University of Science and Technology","ror":"https://ror.org/04xysgw12","country_code":"KR","type":"education","lineage":["https://openalex.org/I123900574"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"HEE-KAP AHN","raw_affiliation_strings":["Department of Computer Science and Engineering, Pohang University of Science and Technology, Pohang, 790-784, Korea"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Engineering, Pohang University of Science and Technology, Pohang, 790-784, Korea","institution_ids":["https://openalex.org/I123900574"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5048590083","display_name":"Mohammad Farshi","orcid":"https://orcid.org/0000-0002-1986-2722"},"institutions":[{"id":"https://openalex.org/I112536369","display_name":"Yazd University","ror":"https://ror.org/02x99ac45","country_code":"IR","type":"education","lineage":["https://openalex.org/I112536369"]},{"id":"https://openalex.org/I67031392","display_name":"Carleton University","ror":"https://ror.org/02qtvee93","country_code":"CA","type":"education","lineage":["https://openalex.org/I67031392"]}],"countries":["CA","IR"],"is_corresponding":false,"raw_author_name":"MOHAMMAD FARSHI","raw_affiliation_strings":["Department of Computer Science, Yazd University, P.O. Box. 89195-741, Yazd, Iran","School of Computer Science, Carleton University, Ottawa, Ontario, K1S 5B6, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Yazd University, P.O. Box. 89195-741, Yazd, Iran","institution_ids":["https://openalex.org/I112536369"]},{"raw_affiliation_string":"School of Computer Science, Carleton University, Ottawa, Ontario, K1S 5B6, Canada","institution_ids":["https://openalex.org/I67031392"]}]},{"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\u201314195 Berlin, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Informatik, Freie Universit\u00e4t Berlin, Takustra\u00dfe 9, D\u201314195 Berlin, Germany","institution_ids":["https://openalex.org/I75951250"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5108374265","display_name":"Michiel Smid","orcid":null},"institutions":[{"id":"https://openalex.org/I67031392","display_name":"Carleton University","ror":"https://ror.org/02qtvee93","country_code":"CA","type":"education","lineage":["https://openalex.org/I67031392"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"MICHIEL SMID","raw_affiliation_strings":["School of Computer Science, Carleton University, Ottawa, Ontario, K1S 5B6, Canada","School of Computer Science, Carleton University, Ottawa, Ontario. K1S 5B6, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computer Science, Carleton University, Ottawa, Ontario, K1S 5B6, Canada","institution_ids":["https://openalex.org/I67031392"]},{"raw_affiliation_string":"School of Computer Science, Carleton University, Ottawa, Ontario. K1S 5B6, Canada","institution_ids":["https://openalex.org/I67031392"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100454881","display_name":"Yajun Wang","orcid":"https://orcid.org/0000-0002-0165-0561"},"institutions":[{"id":"https://openalex.org/I4210113369","display_name":"Microsoft Research Asia (China)","ror":"https://ror.org/0300m5276","country_code":"CN","type":"company","lineage":["https://openalex.org/I1290206253","https://openalex.org/I4210113369"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"YAJUN WANG","raw_affiliation_strings":["Microsoft Research Asia, Beijing, China","Microsoft research Asia, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Microsoft Research Asia, Beijing, China","institution_ids":["https://openalex.org/I4210113369"]},{"raw_affiliation_string":"Microsoft research Asia, Beijing, China","institution_ids":["https://openalex.org/I4210113369"]}]}],"institutions":[],"countries_distinct_count":5,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.15105824,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"20","issue":"01","first_page":"69","last_page":"87"},"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9872000217437744,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T12176","display_name":"Optimization and Packing Problems","score":0.9865999817848206,"subfield":{"id":"https://openalex.org/subfields/2209","display_name":"Industrial and Manufacturing 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/dilation","display_name":"Dilation (metric space)","score":0.8328053951263428},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8102543950080872},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7863723635673523},{"id":"https://openalex.org/keywords/convex-polygon","display_name":"Convex polygon","score":0.7119072079658508},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.490090012550354},{"id":"https://openalex.org/keywords/shortest-path-problem","display_name":"Shortest path problem","score":0.4875585436820984},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.44497784972190857},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.434017539024353},{"id":"https://openalex.org/keywords/polygon","display_name":"Polygon (computer graphics)","score":0.42196860909461975},{"id":"https://openalex.org/keywords/path","display_name":"Path (computing)","score":0.4128292500972748},{"id":"https://openalex.org/keywords/binary-logarithm","display_name":"Binary logarithm","score":0.41158103942871094},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.2921046316623688},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.11594906449317932},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.07458147406578064}],"concepts":[{"id":"https://openalex.org/C2780757906","wikidata":"https://www.wikidata.org/wiki/Q5276676","display_name":"Dilation (metric space)","level":2,"score":0.8328053951263428},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8102543950080872},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7863723635673523},{"id":"https://openalex.org/C2780034980","wikidata":"https://www.wikidata.org/wiki/Q3259505","display_name":"Convex polygon","level":3,"score":0.7119072079658508},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.490090012550354},{"id":"https://openalex.org/C22590252","wikidata":"https://www.wikidata.org/wiki/Q1058754","display_name":"Shortest path problem","level":3,"score":0.4875585436820984},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.44497784972190857},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.434017539024353},{"id":"https://openalex.org/C190694206","wikidata":"https://www.wikidata.org/wiki/Q3276654","display_name":"Polygon (computer graphics)","level":3,"score":0.42196860909461975},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.4128292500972748},{"id":"https://openalex.org/C63553672","wikidata":"https://www.wikidata.org/wiki/Q581168","display_name":"Binary logarithm","level":2,"score":0.41158103942871094},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2921046316623688},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.11594906449317932},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.07458147406578064},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"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/C126042441","wikidata":"https://www.wikidata.org/wiki/Q1324888","display_name":"Frame (networking)","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1142/s0218195910003207","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218195910003207","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 &amp; Applications","raw_type":"journal-article"},{"id":"pmh:662870","is_oa":false,"landing_page_url":"http://library.tue.nl/csp/dare/LinkToRepository.csp?recordnumber=662870","pdf_url":null,"source":{"id":"https://openalex.org/S4406923046","display_name":"TU/e Research Portal (Eindhoven University of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":null},{"id":"pmh:oai:oasis.postech.ac.kr:2014.oak/26487","is_oa":false,"landing_page_url":"https://oasis.postech.ac.kr/handle/2014.oak/26487","pdf_url":null,"source":{"id":"https://openalex.org/S4306401965","display_name":"Open Access System for Information Sharing (Pohang University of Science and Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I123900574","host_organization_name":"Pohang University of Science and Technology","host_organization_lineage":["https://openalex.org/I123900574"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article; Proceedings Paper"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W421157177","https://openalex.org/W1505970908","https://openalex.org/W1555007779","https://openalex.org/W1744317798","https://openalex.org/W2035300538","https://openalex.org/W2048557227","https://openalex.org/W2054011861","https://openalex.org/W2065889331","https://openalex.org/W2068790848","https://openalex.org/W2070164574","https://openalex.org/W2071776560","https://openalex.org/W2074863496","https://openalex.org/W2076014803","https://openalex.org/W2102902634","https://openalex.org/W2109157304","https://openalex.org/W2126150987","https://openalex.org/W2126876121","https://openalex.org/W2132026455","https://openalex.org/W2162487598","https://openalex.org/W2165621523","https://openalex.org/W2203464362","https://openalex.org/W3098722153"],"related_works":["https://openalex.org/W2314484939","https://openalex.org/W4240339429","https://openalex.org/W2154141401","https://openalex.org/W2105729287","https://openalex.org/W338234595","https://openalex.org/W2220384749","https://openalex.org/W2794864174","https://openalex.org/W1585992543","https://openalex.org/W2123516473","https://openalex.org/W1991526295"],"abstract_inverted_index":{"Consider":[0],"a":[1,58,66,92,109,127,144],"geometric":[2],"network":[3],"G":[4,18,32,48],"in":[5,17,31,47,73,77,91,119,165],"the":[6,20,23,34,51,74,84,104,130,134,149],"plane.":[7],"The":[8,39],"dilation":[9,41,52,115,150],"between":[10,27,37],"any":[11],"two":[12],"vertices":[13,46,72],"x":[14,28],"and":[15,29],"y":[16,30],"is":[19,49,61,100,126,141],"ratio":[21],"of":[22,45,53,86,95,112,151,160],"shortest":[24],"path":[25,94,111,153],"distance":[26,36],"to":[33,148],"Euclidean":[35],"them.":[38],"maximum":[40],"over":[42],"all":[43,157],"pairs":[44],"called":[50],"G.":[54],"In":[55],"this":[56],"paper,":[57],"randomized":[59],"algorithm":[60],"presented":[62],"which,":[63],"when":[64],"given":[65],"polygonal":[67,93,110],"cycle":[68],"C":[69,87,125,154],"on":[70],"n":[71],"plane,":[75],"computes":[76],"O(n":[78,120,166],"log":[79,121,167],"3":[80],"n)":[81,122,168],"expected":[82],"time,":[83],"edge":[85,105],"whose":[88,106],"removal":[89,107],"results":[90],"smallest":[96],"possible":[97,114],"dilation.":[98],"It":[99],"also":[101],"shown":[102,142],"that":[103,143],"gives":[108],"largest":[113],"can":[116,162],"be":[117,163],"computed":[118,164],"time.":[123,170],"If":[124],"convex":[128],"polygon,":[129],"running":[131],"time":[132],"for":[133,156],"latter":[135],"problem":[136],"becomes":[137],"O(n).":[138],"Finally,":[139],"it":[140],"(1":[145],"-":[146],"\u03f5)-approximation":[147],"every":[152],"\\{e},":[155],"edges":[158],"e":[159],"C,":[161],"total":[169]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
