{"id":"https://openalex.org/W4386556461","doi":"https://doi.org/10.48550/arxiv.2309.01264","title":"Upward and Orthogonal Planarity are W[1]-hard Parameterized by Treewidth","display_name":"Upward and Orthogonal Planarity are W[1]-hard Parameterized by Treewidth","publication_year":2023,"publication_date":"2023-09-03","ids":{"openalex":"https://openalex.org/W4386556461","doi":"https://doi.org/10.48550/arxiv.2309.01264"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2309.01264","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2309.01264","pdf_url":"https://arxiv.org/pdf/2309.01264","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2309.01264","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5048942396","display_name":"Bart M. P. Jansen","orcid":"https://orcid.org/0000-0001-8204-1268"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Jansen, Bart M. P.","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5061490516","display_name":"Liana Khazaliya","orcid":"https://orcid.org/0009-0002-3012-7240"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Khazaliya, Liana","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5029516206","display_name":"Philipp Kindermann","orcid":"https://orcid.org/0000-0001-5764-7719"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kindermann, Philipp","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008995859","display_name":"Giuseppe Liotta","orcid":"https://orcid.org/0000-0002-2886-9694"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Liotta, Giuseppe","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5006763389","display_name":"Fabrizio Montecchiani","orcid":"https://orcid.org/0000-0002-0543-8912"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Montecchiani, Fabrizio","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5102983476","display_name":"Kirill Simonov","orcid":"https://orcid.org/0000-0001-9436-7310"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Simonov, Kirill","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5048942396"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9976999759674072,"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":0.9976999759674072,"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/T12292","display_name":"Graph Theory and Algorithms","score":0.9947999715805054,"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/T10743","display_name":"Software Testing and Debugging Techniques","score":0.9909999966621399,"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":0.9665945768356323},{"id":"https://openalex.org/keywords/treewidth","display_name":"Treewidth","score":0.8987151384353638},{"id":"https://openalex.org/keywords/parameterized-complexity","display_name":"Parameterized complexity","score":0.8918734788894653},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.60566645860672},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.571685791015625},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.5619785785675049},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4708157181739807},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4458846151828766},{"id":"https://openalex.org/keywords/pathwidth","display_name":"Pathwidth","score":0.29657524824142456},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.0981530249118805}],"concepts":[{"id":"https://openalex.org/C68260962","wikidata":"https://www.wikidata.org/wiki/Q7200967","display_name":"Planarity testing","level":2,"score":0.9665945768356323},{"id":"https://openalex.org/C132569581","wikidata":"https://www.wikidata.org/wiki/Q5067368","display_name":"Treewidth","level":5,"score":0.8987151384353638},{"id":"https://openalex.org/C165464430","wikidata":"https://www.wikidata.org/wiki/Q1570441","display_name":"Parameterized complexity","level":2,"score":0.8918734788894653},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.60566645860672},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.571685791015625},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.5619785785675049},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4708157181739807},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4458846151828766},{"id":"https://openalex.org/C43517604","wikidata":"https://www.wikidata.org/wiki/Q7144893","display_name":"Pathwidth","level":4,"score":0.29657524824142456},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.0981530249118805},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2309.01264","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2309.01264","pdf_url":"https://arxiv.org/pdf/2309.01264","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"doi:10.48550/arxiv.2309.01264","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2309.01264","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2309.01264","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2309.01264","pdf_url":"https://arxiv.org/pdf/2309.01264","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1382289185","display_name":null,"funder_award_id":"Y1329","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G2447788411","display_name":null,"funder_award_id":"unknown","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G2493728679","display_name":null,"funder_award_id":"DFG 411362735","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G2813764235","display_name":null,"funder_award_id":"10.47379/ICT22029","funder_id":"https://openalex.org/F4320321003","funder_display_name":"Vienna Science and Technology Fund"},{"id":"https://openalex.org/G4447653093","display_name":null,"funder_award_id":"Network","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G630843984","display_name":"Logics for Computer Science Program at TU Wien","funder_award_id":"101034440","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G762232396","display_name":null,"funder_award_id":"Project","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G7697800524","display_name":null,"funder_award_id":"411362735","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G7842005466","display_name":null,"funder_award_id":"Horizon 2020","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G7850098718","display_name":null,"funder_award_id":"COFUND","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G8184292771","display_name":null,"funder_award_id":"Project","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G8318064016","display_name":null,"funder_award_id":"Horizon","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G8368575583","display_name":"Rigorous Search Space Reduction","funder_award_id":"803421","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"}],"funders":[{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320321003","display_name":"Vienna Science and Technology Fund","ror":"https://ror.org/01f9mc681"},{"id":"https://openalex.org/F4320321181","display_name":"Austrian Science Fund","ror":"https://ror.org/013tf3c58"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4386556461.pdf"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W3214675586","https://openalex.org/W3046835365","https://openalex.org/W4386556461","https://openalex.org/W2075531723","https://openalex.org/W4390681281","https://openalex.org/W2113684989","https://openalex.org/W4390681428","https://openalex.org/W4285659194","https://openalex.org/W4389814085","https://openalex.org/W4386269540"],"abstract_inverted_index":{"Upward":[0],"planarity":[1,5,80,106],"testing":[2,6,81,107],"and":[3,97],"Rectilinear":[4],"are":[7,18,36],"central":[8],"problems":[9,35,44,108],"in":[10,46,53,74,131],"graph":[11],"drawing.":[12],"It":[13],"is":[14,56,89],"known":[15,123],"that":[16,32,85,98,121],"they":[17],"both":[19,79],"NP-complete,":[20],"but":[21],"XP":[22],"when":[23],"parameterized":[24,38,91],"by":[25,39,92],"treewidth.":[26,116],"In":[27],"this":[28],"paper":[29],"we":[30],"show":[31,120],"these":[33],"two":[34,47],"W[1]-hard":[37,90],"treewidth,":[40],"which":[41,67],"answers":[42],"open":[43],"posed":[45],"earlier":[48],"papers.":[49],"The":[50],"key":[51],"step":[52,73],"our":[54],"proof":[55,77],"an":[57,71],"analysis":[58],"of":[59,66,102],"the":[60,75,86,99,105,115,122],"All-or-Nothing":[61],"Flow":[62],"problem,":[63],"a":[64],"generalization":[65],"was":[68],"used":[69],"as":[70],"intermediate":[72],"NP-completeness":[76],"for":[78],"problems.":[82],"We":[83],"prove":[84],"flow":[87],"problem":[88],"treewidth":[93],"on":[94],"planar":[95],"graphs,":[96],"existing":[100],"chain":[101],"reductions":[103,118],"to":[104,129],"can":[109],"be":[110,127],"adapted":[111],"without":[112],"blowing":[113],"up":[114],"Our":[117],"also":[119],"$n^{O(tw)}$-time":[124],"algorithms":[125],"cannot":[126],"improved":[128],"run":[130],"time":[132],"$n^{o(tw)}$":[133],"unless":[134],"ETH":[135],"fails.":[136]},"counts_by_year":[],"updated_date":"2026-04-20T07:46:08.049788","created_date":"2025-10-10T00:00:00"}
