{"id":"https://openalex.org/W4401314930","doi":"https://doi.org/10.1007/s00453-024-01260-1","title":"On the Parameterized Complexity of Bend-Minimum Orthogonal Planarity","display_name":"On the Parameterized Complexity of Bend-Minimum Orthogonal Planarity","publication_year":2024,"publication_date":"2024-08-04","ids":{"openalex":"https://openalex.org/W4401314930","doi":"https://doi.org/10.1007/s00453-024-01260-1"},"language":"en","primary_location":{"id":"doi:10.1007/s00453-024-01260-1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00453-024-01260-1","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00453-024-01260-1.pdf","source":{"id":"https://openalex.org/S89324355","display_name":"Algorithmica","issn_l":"0178-4617","issn":["0178-4617","1432-0541"],"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":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithmica","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00453-024-01260-1.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5029525801","display_name":"Emilio Di Giacomo","orcid":"https://orcid.org/0000-0002-9794-1928"},"institutions":[{"id":"https://openalex.org/I27483092","display_name":"University of Perugia","ror":"https://ror.org/00x27da85","country_code":"IT","type":"education","lineage":["https://openalex.org/I27483092"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Emilio Di Giacomo","raw_affiliation_strings":["Department of Engineering, University of Perugia, Perugia, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Engineering, University of Perugia, Perugia, Italy","institution_ids":["https://openalex.org/I27483092"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5018323496","display_name":"Walter Didimo","orcid":"https://orcid.org/0000-0002-4379-6059"},"institutions":[{"id":"https://openalex.org/I27483092","display_name":"University of Perugia","ror":"https://ror.org/00x27da85","country_code":"IT","type":"education","lineage":["https://openalex.org/I27483092"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Walter Didimo","raw_affiliation_strings":["Department of Engineering, University of Perugia, Perugia, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Engineering, University of Perugia, Perugia, Italy","institution_ids":["https://openalex.org/I27483092"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008995859","display_name":"Giuseppe Liotta","orcid":"https://orcid.org/0000-0002-2886-9694"},"institutions":[{"id":"https://openalex.org/I27483092","display_name":"University of Perugia","ror":"https://ror.org/00x27da85","country_code":"IT","type":"education","lineage":["https://openalex.org/I27483092"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Giuseppe Liotta","raw_affiliation_strings":["Department of Engineering, University of Perugia, Perugia, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Engineering, University of Perugia, Perugia, Italy","institution_ids":["https://openalex.org/I27483092"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5006763389","display_name":"Fabrizio Montecchiani","orcid":"https://orcid.org/0000-0002-0543-8912"},"institutions":[{"id":"https://openalex.org/I27483092","display_name":"University of Perugia","ror":"https://ror.org/00x27da85","country_code":"IT","type":"education","lineage":["https://openalex.org/I27483092"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Fabrizio Montecchiani","raw_affiliation_strings":["Department of Engineering, University of Perugia, Perugia, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Engineering, University of Perugia, Perugia, Italy","institution_ids":["https://openalex.org/I27483092"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5049528595","display_name":"Giacomo Ortali","orcid":"https://orcid.org/0000-0002-4481-698X"},"institutions":[{"id":"https://openalex.org/I27483092","display_name":"University of Perugia","ror":"https://ror.org/00x27da85","country_code":"IT","type":"education","lineage":["https://openalex.org/I27483092"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Giacomo Ortali","raw_affiliation_strings":["Department of Engineering, University of Perugia, Perugia, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Engineering, University of Perugia, Perugia, Italy","institution_ids":["https://openalex.org/I27483092"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5018323496","https://openalex.org/A5049528595"],"corresponding_institution_ids":["https://openalex.org/I27483092"],"apc_list":{"value":2890,"currency":"USD","value_usd":2890},"apc_paid":{"value":2890,"currency":"USD","value_usd":2890},"fwci":0.8834,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.77331518,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":"86","issue":"10","first_page":"3231","last_page":"3251"},"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/T12923","display_name":"Digital Image Processing Techniques","score":0.9983999729156494,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9983000159263611,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/parameterized-complexity","display_name":"Parameterized complexity","score":0.890880823135376},{"id":"https://openalex.org/keywords/planarity-testing","display_name":"Planarity testing","score":0.8389220237731934},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.6795600652694702},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5258339643478394},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.49508967995643616},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.47201722860336304},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.435799777507782},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.33958590030670166},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.33750221133232117}],"concepts":[{"id":"https://openalex.org/C165464430","wikidata":"https://www.wikidata.org/wiki/Q1570441","display_name":"Parameterized complexity","level":2,"score":0.890880823135376},{"id":"https://openalex.org/C68260962","wikidata":"https://www.wikidata.org/wiki/Q7200967","display_name":"Planarity testing","level":2,"score":0.8389220237731934},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.6795600652694702},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5258339643478394},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.49508967995643616},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.47201722860336304},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.435799777507782},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.33958590030670166},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.33750221133232117}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s00453-024-01260-1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00453-024-01260-1","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00453-024-01260-1.pdf","source":{"id":"https://openalex.org/S89324355","display_name":"Algorithmica","issn_l":"0178-4617","issn":["0178-4617","1432-0541"],"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":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithmica","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s00453-024-01260-1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00453-024-01260-1","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00453-024-01260-1.pdf","source":{"id":"https://openalex.org/S89324355","display_name":"Algorithmica","issn_l":"0178-4617","issn":["0178-4617","1432-0541"],"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":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithmica","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2371663900","display_name":null,"funder_award_id":"PRIN Proj. 2022TS4Y3N","funder_id":"https://openalex.org/F4320331528","funder_display_name":"Ministero dell'Universit\u00e0 e della Ricerca"},{"id":"https://openalex.org/G8077106450","display_name":null,"funder_award_id":"PRIN Proj. 2022ME9Z78","funder_id":"https://openalex.org/F4320331528","funder_display_name":"Ministero dell'Universit\u00e0 e della Ricerca"}],"funders":[{"id":"https://openalex.org/F4320326523","display_name":"Universit\u00e0 degli Studi di Perugia","ror":"https://ror.org/00x27da85"},{"id":"https://openalex.org/F4320331528","display_name":"Ministero dell'Universit\u00e0 e della Ricerca","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4401314930.pdf","grobid_xml":"https://content.openalex.org/works/W4401314930.grobid-xml"},"referenced_works_count":19,"referenced_works":["https://openalex.org/W1534309112","https://openalex.org/W1605390268","https://openalex.org/W1964849735","https://openalex.org/W1994556169","https://openalex.org/W2002025203","https://openalex.org/W2018091581","https://openalex.org/W2083597100","https://openalex.org/W2095981233","https://openalex.org/W2102664288","https://openalex.org/W2117205241","https://openalex.org/W2142363072","https://openalex.org/W2890307102","https://openalex.org/W2998897772","https://openalex.org/W3216500139","https://openalex.org/W4200514496","https://openalex.org/W4317393908","https://openalex.org/W4323925872","https://openalex.org/W4390681281","https://openalex.org/W4390681428"],"related_works":["https://openalex.org/W1986447712","https://openalex.org/W2110193191","https://openalex.org/W4390681428","https://openalex.org/W4386269540","https://openalex.org/W2171811389","https://openalex.org/W1598441350","https://openalex.org/W1539117866","https://openalex.org/W2041837101","https://openalex.org/W2998616538","https://openalex.org/W2964749573"],"abstract_inverted_index":{"Abstract":[0],"Computing":[1],"planar":[2,39],"orthogonal":[3,43,173,248,308],"drawings":[4],"with":[5,175,311],"the":[6,14,34,57,61,69,74,79,90,98,120,150,189,210,222,280,306,314],"minimum":[7],"number":[8,75,80,151],"of":[9,13,36,71,77,82,84,97,152,154,165],"bends":[10,46,179],"is":[11,23,63,167,181,186,191,199,224],"one":[12],"most":[15,87,157,177],"studied":[16],"topics":[17],"in":[18,50,105,146,194,245],"Graph":[19,264],"Drawing.":[20],"The":[21],"problem":[22,62,121,190,223,310],"known":[24],"to":[25,32,298,313],"be":[26],"NP-hard,":[27],"even":[28],"when":[29,66,125,184],"we":[30,219,295],"want":[31],"test":[33],"existence":[35],"a":[37,140,239,293,300],"rectilinear":[38,142],"drawing,":[40],"i.e.,":[41],"an":[42,172,201,204],"drawing":[44,174],"without":[45],"(Garg":[47],"and":[48,89,247,266,321],"Tamassia":[49],"SIAM":[51],"J":[52,106],"Comput":[53,107],"31(2):601\u2013625,":[54],"2001).":[55],"From":[56],"parameterized":[58,67,126,148,193,207,226,252,302],"complexity":[59],"perspective,":[60],"fixed-parameter":[64,123],"tractable":[65,124],"by":[68,117,128,149,209,227,253],"sum":[70],"three":[72,315],"parameters:":[73],"b":[76,178,317],"bends,":[78],"k":[81,185,195,212,319],"vertices":[83,153],"degree":[85,155],"at":[86,156,176],"two,":[88],"treewidth":[91],"$$\\textsf{tw}$$":[92,322],"<mml:math":[93,130,229,283,323],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[94,131,230,284,324],"<mml:mi>tw</mml:mi>":[95,234,288,325],"</mml:math>":[96,137,236,290,326],"input":[99],"graph":[100],"(Di":[101],"Giacomo":[102],"et":[103,243],"al.":[104,244],"Syst":[108],"Sci":[109],"125:129\u2013148,":[110],"2022).":[111],"We":[112,159],"improve":[113],"this":[114],"last":[115],"result":[116,241],"showing":[118],"that":[119,162,221,276],"remains":[122],"only":[127,208],"$$b+k$$":[129],"<mml:mrow>":[132,231,285],"<mml:mi>b</mml:mi>":[133,286],"<mml:mo>+</mml:mo>":[134,233,287],"<mml:mi>k</mml:mi>":[135,232],"</mml:mrow>":[136,235,289],".":[138,291,327],"As":[139,292],"consequence,":[141,294],"planarity":[143,249,309],"testing":[144],"lies":[145],"FPT":[147,202],"two.":[158],"also":[160],"prove":[161,220],"our":[163],"choice":[164],"parameters":[166,316],"minimal,":[168],"as":[169],"deciding":[170],"if":[171],"exists":[180],"already":[182],"NP-hard":[183],"zero":[187],"(i.e.,":[188],"para-NP-hard":[192],");":[196],"hence,":[197],"there":[198],"neither":[200],"nor":[203],"XP":[205],"algorithm":[206],"parameter":[211],"(unless":[213],"P":[214],"=":[215],"NP).":[216],"In":[217],"addition,":[218],"W[1]-hard":[225,251],"$$k+\\textsf{tw}$$":[228],",":[237,318,320],"complementing":[238],"recent":[240],"(Jansen":[242],"Upward":[246],"are":[250,296],"treewidth.":[254],"CoRR,":[255],"abs/2309.01264,":[256],"2023;":[257],"in:":[258],"Bekos":[259],"MA,":[260],"Chimani":[261],"M":[262],"(eds)":[263],"Drawing":[265],"Network":[267],"Visualization,":[268],"vol":[269],"14466,":[270],"Springer,":[271],"Cham,":[272],"pp":[273],"203\u2013217,":[274],"2023)":[275],"shows":[277],"W[1]-hardness":[278],"for":[279,305],"parameterization":[281],"$$b+\\textsf{tw}$$":[282],"able":[297],"trace":[299],"clear":[301],"tractability":[303],"landscape":[304],"bend-minimum":[307],"respect":[312]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}