{"id":"https://openalex.org/W2047088053","doi":"https://doi.org/10.1109/21.23105","title":"Hierarchies and planarity theory","display_name":"Hierarchies and planarity theory","publication_year":1988,"publication_date":"1988-01-01","ids":{"openalex":"https://openalex.org/W2047088053","doi":"https://doi.org/10.1109/21.23105","mag":"2047088053"},"language":"en","primary_location":{"is_oa":false,"landing_page_url":"https://doi.org/10.1109/21.23105","pdf_url":null,"source":{"id":"https://openalex.org/S76152103","display_name":"IEEE Transactions on Systems Man and Cybernetics","issn_l":"0018-9472","issn":["0018-9472","2168-2909"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false},"type":"article","type_crossref":"journal-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/A5038655759","display_name":"Giuseppe Di Battista","orcid":"https://orcid.org/0000-0003-4224-1550"},"institutions":[],"countries":["IT"],"is_corresponding":false,"raw_author_name":"G. Di Battista","raw_affiliation_strings":["Dipartimento di Informatica e Sistemistica, Universita delgi Studi di Roma, Roma, Italy"],"affiliations":[{"raw_affiliation_string":"Dipartimento di Informatica e Sistemistica, Universita delgi Studi di Roma, Roma, Italy","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5058595042","display_name":"Enrico Nardelli","orcid":"https://orcid.org/0000-0001-9451-2899"},"institutions":[{"id":"https://openalex.org/I4210162062","display_name":"Istituto di Analisi dei Sistemi ed Informatica Antonio Ruberti","ror":"https://ror.org/054ye0e45","country_code":"IT","type":"facility","lineage":["https://openalex.org/I4210155236","https://openalex.org/I4210162062"]},{"id":"https://openalex.org/I4210155236","display_name":"National Research Council","ror":"https://ror.org/04zaypm56","country_code":"IT","type":"nonprofit","lineage":["https://openalex.org/I4210155236"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"E. Nardelli","raw_affiliation_strings":["Istituto di Analisi dei sistemi ed Informatica, Italian National Research Council (CNR), Roma, Italy"],"affiliations":[{"raw_affiliation_string":"Istituto di Analisi dei sistemi ed Informatica, Italian National Research Council (CNR), Roma, Italy","institution_ids":["https://openalex.org/I4210162062","https://openalex.org/I4210155236"]}]}],"institution_assertions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.0,"has_fulltext":true,"fulltext_origin":"ngrams","cited_by_count":68,"citation_normalized_percentile":{"value":0.940156,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":95,"max":96},"biblio":{"volume":"18","issue":"6","first_page":"1035","last_page":"1046"},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9987,"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"}},"topics":[{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9987,"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/T11269","display_name":"Algorithms and Data Compression","score":0.9921,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9896,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/planarity-testing","display_name":"Planarity testing","score":0.8605275},{"id":"https://openalex.org/keywords/diagrammatic-reasoning","display_name":"Diagrammatic reasoning","score":0.772002},{"id":"https://openalex.org/keywords/characterization","display_name":"Characterization","score":0.52737117}],"concepts":[{"id":"https://openalex.org/C68260962","wikidata":"https://www.wikidata.org/wiki/Q7200967","display_name":"Planarity testing","level":2,"score":0.8605275},{"id":"https://openalex.org/C106624574","wikidata":"https://www.wikidata.org/wiki/Q5270387","display_name":"Diagrammatic reasoning","level":2,"score":0.772002},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.70977116},{"id":"https://openalex.org/C2778143727","wikidata":"https://www.wikidata.org/wiki/Q1820650","display_name":"Readability","level":2,"score":0.6311608},{"id":"https://openalex.org/C31170391","wikidata":"https://www.wikidata.org/wiki/Q188619","display_name":"Hierarchy","level":2,"score":0.6026025},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.5421366},{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.52737117},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5003946},{"id":"https://openalex.org/C162307627","wikidata":"https://www.wikidata.org/wiki/Q204833","display_name":"Enhanced Data Rates for GSM Evolution","level":2,"score":0.43824536},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.41831213},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.40091884},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.36752164},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.27217546},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07356617},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.067094326},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.061004877},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0},{"id":"https://openalex.org/C34447519","wikidata":"https://www.wikidata.org/wiki/Q179522","display_name":"Market economy","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"is_oa":false,"landing_page_url":"https://doi.org/10.1109/21.23105","pdf_url":null,"source":{"id":"https://openalex.org/S76152103","display_name":"IEEE Transactions on Systems Man and Cybernetics","issn_l":"0018-9472","issn":["0018-9472","2168-2909"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false}],"best_oa_location":null,"sustainable_development_goals":[],"grants":[],"datasets":[],"versions":[],"referenced_works_count":17,"referenced_works":["https://openalex.org/W1500432757","https://openalex.org/W1655990431","https://openalex.org/W174566906","https://openalex.org/W1979740931","https://openalex.org/W1987374783","https://openalex.org/W2003741962","https://openalex.org/W2024491681","https://openalex.org/W2045012623","https://openalex.org/W2071123968","https://openalex.org/W2071353749","https://openalex.org/W2094450647","https://openalex.org/W2103754560","https://openalex.org/W2118382442","https://openalex.org/W2148043549","https://openalex.org/W4236067063","https://openalex.org/W4249446313","https://openalex.org/W73391352"],"related_works":["https://openalex.org/W4315704968","https://openalex.org/W4285478380","https://openalex.org/W4254960163","https://openalex.org/W3110264473","https://openalex.org/W3003518673","https://openalex.org/W2972807713","https://openalex.org/W2370831213","https://openalex.org/W2243494072","https://openalex.org/W1964661231","https://openalex.org/W1510038041"],"abstract_inverted_index":{"In":[0],"diagrammatic":[1],"representations":[2],"of":[3,7,10,46,49],"hierarchies":[4,51],"the":[5,8,47],"minimization":[6],"number":[9],"crossings":[11],"between":[12],"edges":[13],"is":[14,29,40,52],"a":[15,27],"well-known":[16],"criterion":[17],"for":[18,24],"improving":[19],"readability.":[20],"An":[21],"efficient":[22],"algorithm":[23],"testing":[25],"if":[26,32],"hierarchy":[28],"planar":[30,50],"(i.e.":[31],"it":[33],"can":[34],"be":[35],"drawn":[36],"without":[37],"edge":[38],"crossings)":[39],"proposed.":[41],"A":[42],"complete":[43],"combinatorial":[44],"characterization":[45],"class":[48],"also":[53],"given.<":[54],">":[57]},"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W2047088053","counts_by_year":[{"year":2023,"cited_by_count":2},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":2}],"updated_date":"2025-01-20T08:41:51.455343","created_date":"2016-06-24"}