{"id":"https://openalex.org/W2055127468","doi":"https://doi.org/10.1137/s0097539794280736","title":"On-Line Planarity Testing","display_name":"On-Line Planarity Testing","publication_year":1996,"publication_date":"1996-10-01","ids":{"openalex":"https://openalex.org/W2055127468","doi":"https://doi.org/10.1137/s0097539794280736","mag":"2055127468"},"language":"en","primary_location":{"id":"doi:10.1137/s0097539794280736","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0097539794280736","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","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/A5038655759","display_name":"Giuseppe Di Battista","orcid":"https://orcid.org/0000-0003-4224-1550"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Giuseppe Di Battista","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5079716343","display_name":"Roberto Tamassia","orcid":"https://orcid.org/0000-0003-2445-6064"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Roberto Tamassia","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5038655759"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":8.2447,"has_fulltext":false,"cited_by_count":241,"citation_normalized_percentile":{"value":0.97948902,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":100},"biblio":{"volume":"25","issue":"5","first_page":"956","last_page":"997"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9983000159263611,"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":0.9983000159263611,"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/T12288","display_name":"Optimization and Search Problems","score":0.9980000257492065,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T10743","display_name":"Software Testing and Debugging Techniques","score":0.9975000023841858,"subfield":{"id":"https://openalex.org/subfields/1712","display_name":"Software"},"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":0.9610308408737183},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7508507966995239},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.5851148366928101},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.552435040473938},{"id":"https://openalex.org/keywords/planar-graph","display_name":"Planar graph","score":0.5300324559211731},{"id":"https://openalex.org/keywords/wheel-graph","display_name":"Wheel graph","score":0.5258950591087341},{"id":"https://openalex.org/keywords/planar","display_name":"Planar","score":0.49953675270080566},{"id":"https://openalex.org/keywords/book-embedding","display_name":"Book embedding","score":0.4967051148414612},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4780305325984955},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.36271965503692627},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3516843318939209},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2684817314147949},{"id":"https://openalex.org/keywords/graph-power","display_name":"Graph power","score":0.15545323491096497},{"id":"https://openalex.org/keywords/pathwidth","display_name":"Pathwidth","score":0.15220293402671814}],"concepts":[{"id":"https://openalex.org/C68260962","wikidata":"https://www.wikidata.org/wiki/Q7200967","display_name":"Planarity testing","level":2,"score":0.9610308408737183},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7508507966995239},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5851148366928101},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.552435040473938},{"id":"https://openalex.org/C101837359","wikidata":"https://www.wikidata.org/wiki/Q547823","display_name":"Planar graph","level":3,"score":0.5300324559211731},{"id":"https://openalex.org/C148364342","wikidata":"https://www.wikidata.org/wiki/Q948887","display_name":"Wheel graph","level":5,"score":0.5258950591087341},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.49953675270080566},{"id":"https://openalex.org/C180222743","wikidata":"https://www.wikidata.org/wiki/Q4942980","display_name":"Book embedding","level":5,"score":0.4967051148414612},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4780305325984955},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.36271965503692627},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3516843318939209},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2684817314147949},{"id":"https://openalex.org/C149530733","wikidata":"https://www.wikidata.org/wiki/Q5597091","display_name":"Graph power","level":4,"score":0.15545323491096497},{"id":"https://openalex.org/C43517604","wikidata":"https://www.wikidata.org/wiki/Q7144893","display_name":"Pathwidth","level":4,"score":0.15220293402671814},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/s0097539794280736","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0097539794280736","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.186.5675","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.186.5675","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.brown.edu/research/pubs/pdfs/1996/DiBattista-1996-OPT.pdf","raw_type":"text"},{"id":"pmh:oai:iris.uniroma3.it:11590/145850","is_oa":false,"landing_page_url":"http://hdl.handle.net/11590/145850","pdf_url":null,"source":{"id":"https://openalex.org/S4377196120","display_name":"Iris (Roma Tre University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I119003972","host_organization_name":"Roma Tre University","host_organization_lineage":["https://openalex.org/I119003972"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":51,"referenced_works":["https://openalex.org/W27464104","https://openalex.org/W193938304","https://openalex.org/W205976932","https://openalex.org/W1480770719","https://openalex.org/W1545707055","https://openalex.org/W1597528919","https://openalex.org/W1759483102","https://openalex.org/W1855700180","https://openalex.org/W1875640138","https://openalex.org/W1933276021","https://openalex.org/W1964700557","https://openalex.org/W1976177462","https://openalex.org/W1978438623","https://openalex.org/W1981505946","https://openalex.org/W1985623817","https://openalex.org/W1987374783","https://openalex.org/W1994556169","https://openalex.org/W2002906478","https://openalex.org/W2010255818","https://openalex.org/W2011999472","https://openalex.org/W2017351109","https://openalex.org/W2018804864","https://openalex.org/W2022812949","https://openalex.org/W2024491681","https://openalex.org/W2035471954","https://openalex.org/W2037034819","https://openalex.org/W2039512408","https://openalex.org/W2039972044","https://openalex.org/W2040444410","https://openalex.org/W2044146725","https://openalex.org/W2046946959","https://openalex.org/W2051049045","https://openalex.org/W2053740287","https://openalex.org/W2056711744","https://openalex.org/W2066423045","https://openalex.org/W2083394054","https://openalex.org/W2085849292","https://openalex.org/W2091252880","https://openalex.org/W2094632707","https://openalex.org/W2097890715","https://openalex.org/W2106439532","https://openalex.org/W2120424341","https://openalex.org/W2121473031","https://openalex.org/W2145289828","https://openalex.org/W2148686552","https://openalex.org/W2160212232","https://openalex.org/W2799004609","https://openalex.org/W3022690009","https://openalex.org/W3211329402","https://openalex.org/W4213214460","https://openalex.org/W4234872298"],"related_works":["https://openalex.org/W2373079339","https://openalex.org/W4297837089","https://openalex.org/W4293351855","https://openalex.org/W2578113559","https://openalex.org/W2964235359","https://openalex.org/W4287691299","https://openalex.org/W3047848516","https://openalex.org/W3134933682","https://openalex.org/W2799803339","https://openalex.org/W2953315950"],"abstract_inverted_index":{"The":[0,83],"on-line":[1,48],"planarity-testing":[2],"problem":[3],"consists":[4],"of":[5,51,65,79,81,105],"performing":[6],"the":[7,28,76,93],"following":[8],"operations":[9],"on":[10],"a":[11,18,52],"planar":[12,112],"graph":[13,30,53],"G:":[14],"(i)":[15],"testing":[16,50],"if":[17],"new":[19],"edge":[20,96],"can":[21],"be":[22],"added":[23],"to":[24,108],"G":[25],"so":[26],"that":[27,40,56],"resulting":[29],"is":[31,42,54,75,98],"itself":[32],"planar;":[33],"(ii)":[34],"adding":[35],"vertices":[36,66,80],"and":[37,60,63,67,87,92],"edges":[38,68],"such":[39],"planarity":[41,49],"preserved.":[43],"An":[44],"efficient":[45],"technique":[46,107],"for":[47,85,95,111],"presented":[55],"uses":[57],"$O(n)$":[58],"space":[59],"supports":[61],"tests":[62,86],"insertions":[64,89,97],"in":[69],"$O(\\log":[70],"n)$":[71],"time,":[72],"where":[73],"n":[74],"current":[77],"number":[78],"G.":[82],"bounds":[84],"vertex":[88],"are":[90],"worst-case":[91],"bound":[94],"amortized.":[99],"We":[100],"also":[101],"present":[102],"other":[103],"applications":[104],"this":[106],"dynamic":[109],"algorithms":[110],"graphs.":[113]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":13},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":10},{"year":2019,"cited_by_count":13},{"year":2018,"cited_by_count":9},{"year":2017,"cited_by_count":9},{"year":2016,"cited_by_count":17},{"year":2015,"cited_by_count":15},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":13},{"year":2012,"cited_by_count":8}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}