{"id":"https://openalex.org/W1519266598","doi":"https://doi.org/10.1007/3-540-36136-7_50","title":"Simultaneous Embedding of a Planar Graph and Its Dual on the Grid","display_name":"Simultaneous Embedding of a Planar Graph and Its Dual on the Grid","publication_year":2002,"publication_date":"2002-01-01","ids":{"openalex":"https://openalex.org/W1519266598","doi":"https://doi.org/10.1007/3-540-36136-7_50","mag":"1519266598"},"language":"en","primary_location":{"id":"doi:10.1007/3-540-36136-7_50","is_oa":false,"landing_page_url":"https://doi.org/10.1007/3-540-36136-7_50","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"book-chapter","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/A5066274617","display_name":"Cesim Erten","orcid":"https://orcid.org/0000-0002-8149-7113"},"institutions":[{"id":"https://openalex.org/I138006243","display_name":"University of Arizona","ror":"https://ror.org/03m2x1q45","country_code":"US","type":"education","lineage":["https://openalex.org/I138006243"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Cesim Erten","raw_affiliation_strings":["Department of Computer Science, University of Arizona, USA"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Arizona, USA","institution_ids":["https://openalex.org/I138006243"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5003147292","display_name":"Stephen Kobourov","orcid":"https://orcid.org/0000-0002-0477-2724"},"institutions":[{"id":"https://openalex.org/I138006243","display_name":"University of Arizona","ror":"https://ror.org/03m2x1q45","country_code":"US","type":"education","lineage":["https://openalex.org/I138006243"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Stephen G. Kobourov","raw_affiliation_strings":["Department of Computer Science, University of Arizona, USA"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Arizona, USA","institution_ids":["https://openalex.org/I138006243"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5066274617"],"corresponding_institution_ids":["https://openalex.org/I138006243"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":1.9083,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.83193277,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"575","last_page":"587"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9995999932289124,"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":0.9995999932289124,"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":0.9865999817848206,"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/T11106","display_name":"Data Management and Algorithms","score":0.9811000227928162,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/planar-graph","display_name":"Planar graph","score":0.7402886152267456},{"id":"https://openalex.org/keywords/dual-graph","display_name":"Dual graph","score":0.6944007873535156},{"id":"https://openalex.org/keywords/embedding","display_name":"Embedding","score":0.680208683013916},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.660545825958252},{"id":"https://openalex.org/keywords/planar-straight-line-graph","display_name":"Planar straight-line graph","score":0.5883170962333679},{"id":"https://openalex.org/keywords/grid","display_name":"Grid","score":0.573988139629364},{"id":"https://openalex.org/keywords/dual","display_name":"Dual (grammatical number)","score":0.5724459886550903},{"id":"https://openalex.org/keywords/graph-embedding","display_name":"Graph embedding","score":0.5701661109924316},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5212638974189758},{"id":"https://openalex.org/keywords/lattice-graph","display_name":"Lattice graph","score":0.5158321261405945},{"id":"https://openalex.org/keywords/dual-polyhedron","display_name":"Dual polyhedron","score":0.493962824344635},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.48049628734588623},{"id":"https://openalex.org/keywords/book-embedding","display_name":"Book embedding","score":0.45637381076812744},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.39967915415763855},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.38177943229675293},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.36092227697372437},{"id":"https://openalex.org/keywords/voltage-graph","display_name":"Voltage graph","score":0.20862749218940735},{"id":"https://openalex.org/keywords/1-planar-graph","display_name":"1-planar graph","score":0.18465673923492432},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.08071288466453552},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.06815502047538757}],"concepts":[{"id":"https://openalex.org/C101837359","wikidata":"https://www.wikidata.org/wiki/Q547823","display_name":"Planar graph","level":3,"score":0.7402886152267456},{"id":"https://openalex.org/C169827030","wikidata":"https://www.wikidata.org/wiki/Q2294516","display_name":"Dual graph","level":4,"score":0.6944007873535156},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.680208683013916},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.660545825958252},{"id":"https://openalex.org/C131930043","wikidata":"https://www.wikidata.org/wiki/Q7200964","display_name":"Planar straight-line graph","level":5,"score":0.5883170962333679},{"id":"https://openalex.org/C187691185","wikidata":"https://www.wikidata.org/wiki/Q2020720","display_name":"Grid","level":2,"score":0.573988139629364},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.5724459886550903},{"id":"https://openalex.org/C75564084","wikidata":"https://www.wikidata.org/wiki/Q5597085","display_name":"Graph embedding","level":3,"score":0.5701661109924316},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5212638974189758},{"id":"https://openalex.org/C145580432","wikidata":"https://www.wikidata.org/wiki/Q6497118","display_name":"Lattice graph","level":5,"score":0.5158321261405945},{"id":"https://openalex.org/C105313907","wikidata":"https://www.wikidata.org/wiki/Q1053857","display_name":"Dual polyhedron","level":2,"score":0.493962824344635},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.48049628734588623},{"id":"https://openalex.org/C180222743","wikidata":"https://www.wikidata.org/wiki/Q4942980","display_name":"Book embedding","level":5,"score":0.45637381076812744},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.39967915415763855},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.38177943229675293},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.36092227697372437},{"id":"https://openalex.org/C22149727","wikidata":"https://www.wikidata.org/wiki/Q7940747","display_name":"Voltage graph","level":4,"score":0.20862749218940735},{"id":"https://openalex.org/C102192266","wikidata":"https://www.wikidata.org/wiki/Q4545823","display_name":"1-planar graph","level":4,"score":0.18465673923492432},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.08071288466453552},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06815502047538757},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0},{"id":"https://openalex.org/C124952713","wikidata":"https://www.wikidata.org/wiki/Q8242","display_name":"Literature","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1007/3-540-36136-7_50","is_oa":false,"landing_page_url":"https://doi.org/10.1007/3-540-36136-7_50","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.342.827","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.342.827","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/cs/0206019v1.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.544.7870","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.544.7870","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www2.isikun.edu.tr/personel/cesimerten/dual.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.7.9649","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.7.9649","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.arizona.edu/people/kobourov/dual_drawing.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.90.4626","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.90.4626","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://dimacs.rutgers.edu/Workshops/GeometricGraph/slides/kobourov.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W1485262373","https://openalex.org/W1611906545","https://openalex.org/W1981505946","https://openalex.org/W1984308317","https://openalex.org/W1987374783","https://openalex.org/W2003525146","https://openalex.org/W2003689196","https://openalex.org/W2006448585","https://openalex.org/W2013871179","https://openalex.org/W2034666435","https://openalex.org/W2038318850","https://openalex.org/W2045870980","https://openalex.org/W2060868888","https://openalex.org/W2066423045","https://openalex.org/W2082205964","https://openalex.org/W2082388593","https://openalex.org/W2083176195","https://openalex.org/W2120892678","https://openalex.org/W2156153879"],"related_works":["https://openalex.org/W1525489434","https://openalex.org/W2123605750","https://openalex.org/W2003472496","https://openalex.org/W2083552626","https://openalex.org/W1509623594","https://openalex.org/W2002025203","https://openalex.org/W2083207663","https://openalex.org/W2949720595","https://openalex.org/W1519266598","https://openalex.org/W1988951373"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}