{"id":"https://openalex.org/W2030591046","doi":"https://doi.org/10.1142/s0129054106004297","title":"CONVEX DRAWINGS OF PLANE GRAPHS OF MINIMUM OUTER APICES","display_name":"CONVEX DRAWINGS OF PLANE GRAPHS OF MINIMUM OUTER APICES","publication_year":2006,"publication_date":"2006-09-18","ids":{"openalex":"https://openalex.org/W2030591046","doi":"https://doi.org/10.1142/s0129054106004297","mag":"2030591046"},"language":"en","primary_location":{"id":"doi:10.1142/s0129054106004297","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0129054106004297","pdf_url":null,"source":{"id":"https://openalex.org/S68047077","display_name":"International Journal of Foundations of Computer Science","issn_l":"0129-0541","issn":["0129-0541","1793-6373"],"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 Foundations of Computer Science","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/A5108354107","display_name":"Kazuyuki Miura","orcid":null},"institutions":[{"id":"https://openalex.org/I58089638","display_name":"Fukushima University","ror":"https://ror.org/03zjb7z20","country_code":"JP","type":"education","lineage":["https://openalex.org/I58089638"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"KAZUYUKI MIURA","raw_affiliation_strings":["Faculty of Symbiotic Systems Science, Fukushima University, Fukushima 960-1296, Japan","Faculty of Symbiotic Systems Science, Fukushima University, Fukushima, 960-1296 Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Symbiotic Systems Science, Fukushima University, Fukushima 960-1296, Japan","institution_ids":["https://openalex.org/I58089638"]},{"raw_affiliation_string":"Faculty of Symbiotic Systems Science, Fukushima University, Fukushima, 960-1296 Japan","institution_ids":["https://openalex.org/I58089638"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5078769863","display_name":"Machiko Azuma","orcid":null},"institutions":[{"id":"https://openalex.org/I201537933","display_name":"Tohoku University","ror":"https://ror.org/01dq60k83","country_code":"JP","type":"education","lineage":["https://openalex.org/I201537933"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"MACHIKO AZUMA","raw_affiliation_strings":["Graduate School of Information Sciences, Tohoku University, Aoba-yama 05, Sendai 980-8579, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Graduate School of Information Sciences, Tohoku University, Aoba-yama 05, Sendai 980-8579, Japan","institution_ids":["https://openalex.org/I201537933"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5033580185","display_name":"Takao Nishizeki","orcid":null},"institutions":[{"id":"https://openalex.org/I201537933","display_name":"Tohoku University","ror":"https://ror.org/01dq60k83","country_code":"JP","type":"education","lineage":["https://openalex.org/I201537933"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"TAKAO NISHIZEKI","raw_affiliation_strings":["Graduate School of Information Sciences, Tohoku University, Aoba-yama 05, Sendai 980-8579, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Graduate School of Information Sciences, Tohoku University, Aoba-yama 05, Sendai 980-8579, Japan","institution_ids":["https://openalex.org/I201537933"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.0286,"has_fulltext":false,"cited_by_count":16,"citation_normalized_percentile":{"value":0.91033884,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"17","issue":"05","first_page":"1115","last_page":"1127"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9915000200271606,"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":0.9915000200271606,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9733999967575073,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12176","display_name":"Optimization and Packing Problems","score":0.9684000015258789,"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/combinatorics","display_name":"Combinatorics","score":0.7127967476844788},{"id":"https://openalex.org/keywords/convex-polygon","display_name":"Convex polygon","score":0.6524606943130493},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6096932291984558},{"id":"https://openalex.org/keywords/rectilinear-polygon","display_name":"Rectilinear polygon","score":0.5370333194732666},{"id":"https://openalex.org/keywords/polygon-covering","display_name":"Polygon covering","score":0.517486572265625},{"id":"https://openalex.org/keywords/convex-set","display_name":"Convex set","score":0.4830775558948517},{"id":"https://openalex.org/keywords/star-shaped-polygon","display_name":"Star-shaped polygon","score":0.4824853241443634},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.47958293557167053},{"id":"https://openalex.org/keywords/polygon","display_name":"Polygon (computer graphics)","score":0.4103708565235138},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.266418993473053},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.19100135564804077},{"id":"https://openalex.org/keywords/simple-polygon","display_name":"Simple polygon","score":0.17863857746124268},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.14835765957832336}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7127967476844788},{"id":"https://openalex.org/C2780034980","wikidata":"https://www.wikidata.org/wiki/Q3259505","display_name":"Convex polygon","level":3,"score":0.6524606943130493},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6096932291984558},{"id":"https://openalex.org/C170542616","wikidata":"https://www.wikidata.org/wiki/Q7303186","display_name":"Rectilinear polygon","level":4,"score":0.5370333194732666},{"id":"https://openalex.org/C187778580","wikidata":"https://www.wikidata.org/wiki/Q18389289","display_name":"Polygon covering","level":3,"score":0.517486572265625},{"id":"https://openalex.org/C49870271","wikidata":"https://www.wikidata.org/wiki/Q193657","display_name":"Convex set","level":4,"score":0.4830775558948517},{"id":"https://openalex.org/C96366933","wikidata":"https://www.wikidata.org/wiki/Q2122886","display_name":"Star-shaped polygon","level":5,"score":0.4824853241443634},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.47958293557167053},{"id":"https://openalex.org/C190694206","wikidata":"https://www.wikidata.org/wiki/Q3276654","display_name":"Polygon (computer graphics)","level":3,"score":0.4103708565235138},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.266418993473053},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.19100135564804077},{"id":"https://openalex.org/C197949415","wikidata":"https://www.wikidata.org/wiki/Q782746","display_name":"Simple polygon","level":3,"score":0.17863857746124268},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.14835765957832336},{"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/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0129054106004297","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0129054106004297","pdf_url":null,"source":{"id":"https://openalex.org/S68047077","display_name":"International Journal of Foundations of Computer Science","issn_l":"0129-0541","issn":["0129-0541","1793-6373"],"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 Foundations of Computer Science","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":7,"referenced_works":["https://openalex.org/W193938304","https://openalex.org/W619755549","https://openalex.org/W1994556169","https://openalex.org/W2120892678","https://openalex.org/W4234872298","https://openalex.org/W4240930434","https://openalex.org/W4253380179"],"related_works":["https://openalex.org/W3157966405","https://openalex.org/W1812659169","https://openalex.org/W4287184648","https://openalex.org/W3184287481","https://openalex.org/W4292219087","https://openalex.org/W4297914557","https://openalex.org/W2148315837","https://openalex.org/W3039839808","https://openalex.org/W2661680230","https://openalex.org/W2462884115"],"abstract_inverted_index":{"In":[0,73],"a":[1,5,17,39,45,70,94,107,113,121],"convex":[2,18,31,46,62,71,87,95,122],"drawing":[3,47,96,123],"of":[4,12,59,82,84,104,112,124,130],"plane":[6,40],"graph":[7,41,115],"G,":[8,118],"every":[9],"facial":[10,25],"cycle":[11,26],"G":[13,42,67,91,125],"is":[14,27,48],"drawn":[15],"as":[16],"polygon.":[19,32],"A":[20,33],"polygon":[21,63,88],"for":[22,38,66,90],"the":[23,79,102,127],"outer":[24,30,61,86],"called":[28],"an":[29,60,85],"necessary":[34,65,89],"and":[35,119],"sufficient":[36],"condition":[37],"to":[43,68,92,101],"have":[44,69,93],"known.":[49],"However,":[50],"it":[51],"has":[52],"not":[53],"been":[54],"known":[55],"how":[56],"many":[57],"apices":[58,83,131],"are":[64],"drawing.":[72],"this":[74],"paper,":[75],"we":[76],"show":[77],"that":[78,120],"minimum":[80,128],"number":[81,103,129],"is,":[97],"in":[98,106,135],"effect,":[99],"equal":[100],"leaves":[105],"triconnected":[108],"component":[109],"decomposition":[110],"tree":[111],"new":[114],"constructed":[116],"from":[117],"having":[126],"can":[132],"be":[133],"found":[134],"linear":[136],"time.":[137]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
