{"id":"https://openalex.org/W2123192541","doi":"https://doi.org/10.1007/s00453-010-9456-3","title":"Drawing (Complete) Binary Tanglegrams","display_name":"Drawing (Complete) Binary Tanglegrams","publication_year":2010,"publication_date":"2010-10-14","ids":{"openalex":"https://openalex.org/W2123192541","doi":"https://doi.org/10.1007/s00453-010-9456-3","mag":"2123192541"},"language":"en","primary_location":{"id":"doi:10.1007/s00453-010-9456-3","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00453-010-9456-3","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00453-010-9456-3.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-nc","license_id":"https://openalex.org/licenses/cc-by-nc","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/s00453-010-9456-3.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5077490455","display_name":"Kevin Buchin","orcid":"https://orcid.org/0000-0002-3022-7877"},"institutions":[{"id":"https://openalex.org/I83019370","display_name":"Eindhoven University of Technology","ror":"https://ror.org/02c2kyt77","country_code":"NL","type":"education","lineage":["https://openalex.org/I83019370"]}],"countries":["NL"],"is_corresponding":true,"raw_author_name":"Kevin Buchin","raw_affiliation_strings":["Faculteit Wiskunde en Informatica, TU Eindhoven, Eindhoven, The Netherlands","TU Eindhoven, Faculteit Wiskunde en Informatica, Eindhoven, The Netherlands#TAB#"],"affiliations":[{"raw_affiliation_string":"Faculteit Wiskunde en Informatica, TU Eindhoven, Eindhoven, The Netherlands","institution_ids":["https://openalex.org/I83019370"]},{"raw_affiliation_string":"TU Eindhoven, Faculteit Wiskunde en Informatica, Eindhoven, The Netherlands#TAB#","institution_ids":["https://openalex.org/I83019370"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5086805770","display_name":"Maike Buchin","orcid":"https://orcid.org/0000-0002-3446-4343"},"institutions":[{"id":"https://openalex.org/I83019370","display_name":"Eindhoven University of Technology","ror":"https://ror.org/02c2kyt77","country_code":"NL","type":"education","lineage":["https://openalex.org/I83019370"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Maike Buchin","raw_affiliation_strings":["Faculteit Wiskunde en Informatica, TU Eindhoven, Eindhoven, The Netherlands","TU Eindhoven, Faculteit Wiskunde en Informatica, Eindhoven, The Netherlands#TAB#"],"affiliations":[{"raw_affiliation_string":"Faculteit Wiskunde en Informatica, TU Eindhoven, Eindhoven, The Netherlands","institution_ids":["https://openalex.org/I83019370"]},{"raw_affiliation_string":"TU Eindhoven, Faculteit Wiskunde en Informatica, Eindhoven, The Netherlands#TAB#","institution_ids":["https://openalex.org/I83019370"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5023591555","display_name":"Jaros\u0142aw Byrka","orcid":"https://orcid.org/0000-0002-3387-0913"},"institutions":[{"id":"https://openalex.org/I4210087266","display_name":"Institute of Computer Science","ror":"https://ror.org/003fvp964","country_code":"PL","type":"facility","lineage":["https://openalex.org/I4210087266","https://openalex.org/I99542240"]},{"id":"https://openalex.org/I219388962","display_name":"University of Wroc\u0142aw","ror":"https://ror.org/00yae6e25","country_code":"PL","type":"education","lineage":["https://openalex.org/I219388962"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Jaroslaw Byrka","raw_affiliation_strings":["Institute of Computer Science, University of Wroclaw, Wroclaw, Poland","University of Wroc\u0142aw, Institute of Computer Science, Wroc\u0142aw, Poland"],"affiliations":[{"raw_affiliation_string":"Institute of Computer Science, University of Wroclaw, Wroclaw, Poland","institution_ids":["https://openalex.org/I219388962","https://openalex.org/I4210087266"]},{"raw_affiliation_string":"University of Wroc\u0142aw, Institute of Computer Science, Wroc\u0142aw, Poland","institution_ids":["https://openalex.org/I219388962","https://openalex.org/I4210087266"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5071390048","display_name":"Martin N\u00f6llenburg","orcid":"https://orcid.org/0000-0003-0454-3937"},"institutions":[{"id":"https://openalex.org/I102335020","display_name":"Karlsruhe Institute of Technology","ror":"https://ror.org/04t3en479","country_code":"DE","type":"education","lineage":["https://openalex.org/I102335020","https://openalex.org/I1305996414"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Martin N\u00f6llenburg","raw_affiliation_strings":["Institute of Theoretical Informatics, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany","Karlsruhe Institute of Technology (KIT), Institute of Theoretical Informatics, Karlsruhe, Germany#TAB#"],"affiliations":[{"raw_affiliation_string":"Institute of Theoretical Informatics, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany","institution_ids":["https://openalex.org/I102335020"]},{"raw_affiliation_string":"Karlsruhe Institute of Technology (KIT), Institute of Theoretical Informatics, Karlsruhe, Germany#TAB#","institution_ids":["https://openalex.org/I102335020"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5080521209","display_name":"Yoshio Okamoto","orcid":"https://orcid.org/0000-0002-9826-7074"},"institutions":[{"id":"https://openalex.org/I114531698","display_name":"Tokyo Institute of Technology","ror":"https://ror.org/0112mx960","country_code":"JP","type":"education","lineage":["https://openalex.org/I114531698"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Yoshio Okamoto","raw_affiliation_strings":["Graduate School of Information Science and Engineering, Tokyo Institute of Technology, Tokyo, Japan","Tokyo Institute of Technology, Graduate School of Information Science and Engineering, Tokyo, Japan#TAB#"],"affiliations":[{"raw_affiliation_string":"Graduate School of Information Science and Engineering, Tokyo Institute of Technology, Tokyo, Japan","institution_ids":["https://openalex.org/I114531698"]},{"raw_affiliation_string":"Tokyo Institute of Technology, Graduate School of Information Science and Engineering, Tokyo, Japan#TAB#","institution_ids":["https://openalex.org/I114531698"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5074443763","display_name":"Rodrigo I. Silveira","orcid":"https://orcid.org/0000-0003-0202-4543"},"institutions":[{"id":"https://openalex.org/I9617848","display_name":"Universitat Polit\u00e8cnica de Catalunya","ror":"https://ror.org/03mb6wj31","country_code":"ES","type":"education","lineage":["https://openalex.org/I9617848"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Rodrigo I. Silveira","raw_affiliation_strings":["Departament de Matem\u00e0tica Aplicada II, Universitat Polit\u00e8cnica de Catalunya, Barcelona, Spain","Universitat Polit\u00e8cnica de Catalunya, Departament de Matem\u00e0tica Aplicada II, Barcelona, Spain"],"affiliations":[{"raw_affiliation_string":"Departament de Matem\u00e0tica Aplicada II, Universitat Polit\u00e8cnica de Catalunya, Barcelona, Spain","institution_ids":["https://openalex.org/I9617848"]},{"raw_affiliation_string":"Universitat Polit\u00e8cnica de Catalunya, Departament de Matem\u00e0tica Aplicada II, Barcelona, Spain","institution_ids":["https://openalex.org/I9617848"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5014138072","display_name":"Alexander Wolff","orcid":"https://orcid.org/0000-0001-5872-718X"},"institutions":[{"id":"https://openalex.org/I25974101","display_name":"University of W\u00fcrzburg","ror":"https://ror.org/00fbnyb24","country_code":"DE","type":"education","lineage":["https://openalex.org/I25974101"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Alexander Wolff","raw_affiliation_strings":["Lehrstuhl I, Institut f\u00fcr Informatik, Universit\u00e4t W\u00fcrzburg, W\u00fcrzburg, Germany","Universit\u00e4t W\u00fcrzburg, Lehrstuhl I, Institut f\u00fcr Informatik, W\u00fcrzburg, Germany#TAB#"],"affiliations":[{"raw_affiliation_string":"Lehrstuhl I, Institut f\u00fcr Informatik, Universit\u00e4t W\u00fcrzburg, W\u00fcrzburg, Germany","institution_ids":["https://openalex.org/I25974101"]},{"raw_affiliation_string":"Universit\u00e4t W\u00fcrzburg, Lehrstuhl I, Institut f\u00fcr Informatik, W\u00fcrzburg, Germany#TAB#","institution_ids":["https://openalex.org/I25974101"]}]}],"institutions":[],"countries_distinct_count":5,"institutions_distinct_count":7,"corresponding_author_ids":["https://openalex.org/A5077490455"],"corresponding_institution_ids":["https://openalex.org/I83019370"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":1.4419,"has_fulltext":true,"cited_by_count":28,"citation_normalized_percentile":{"value":0.86482062,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"62","issue":"1-2","first_page":"309","last_page":"332"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.996399998664856,"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":0.996399998664856,"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/T11269","display_name":"Algorithms and Data Compression","score":0.9919000267982483,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.991599977016449,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7982439994812012},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7803507447242737},{"id":"https://openalex.org/keywords/binary-tree","display_name":"Binary tree","score":0.7726147770881653},{"id":"https://openalex.org/keywords/random-binary-tree","display_name":"Random binary tree","score":0.7015873193740845},{"id":"https://openalex.org/keywords/weight-balanced-tree","display_name":"Weight-balanced tree","score":0.6998236775398254},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.6244187951087952},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.604548454284668},{"id":"https://openalex.org/keywords/matching","display_name":"Matching (statistics)","score":0.5098599791526794},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.49545586109161377},{"id":"https://openalex.org/keywords/approximation-algorithm","display_name":"Approximation algorithm","score":0.4772641360759735},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.47058573365211487},{"id":"https://openalex.org/keywords/optimal-binary-search-tree","display_name":"Optimal binary search tree","score":0.45529013872146606},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3993265926837921},{"id":"https://openalex.org/keywords/binary-search-tree","display_name":"Binary search tree","score":0.3483653962612152},{"id":"https://openalex.org/keywords/k-ary-tree","display_name":"K-ary tree","score":0.34786051511764526},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.25357139110565186},{"id":"https://openalex.org/keywords/tree-structure","display_name":"Tree structure","score":0.1971060037612915},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.07686647772789001}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7982439994812012},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7803507447242737},{"id":"https://openalex.org/C197855036","wikidata":"https://www.wikidata.org/wiki/Q380172","display_name":"Binary tree","level":2,"score":0.7726147770881653},{"id":"https://openalex.org/C11829167","wikidata":"https://www.wikidata.org/wiki/Q751292","display_name":"Random binary tree","level":3,"score":0.7015873193740845},{"id":"https://openalex.org/C57900377","wikidata":"https://www.wikidata.org/wiki/Q7979855","display_name":"Weight-balanced tree","level":4,"score":0.6998236775398254},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.6244187951087952},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.604548454284668},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.5098599791526794},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.49545586109161377},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.4772641360759735},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.47058573365211487},{"id":"https://openalex.org/C27628562","wikidata":"https://www.wikidata.org/wiki/Q17154715","display_name":"Optimal binary search tree","level":5,"score":0.45529013872146606},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3993265926837921},{"id":"https://openalex.org/C91154448","wikidata":"https://www.wikidata.org/wiki/Q623818","display_name":"Binary search tree","level":3,"score":0.3483653962612152},{"id":"https://openalex.org/C100560664","wikidata":"https://www.wikidata.org/wiki/Q3608019","display_name":"K-ary tree","level":4,"score":0.34786051511764526},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.25357139110565186},{"id":"https://openalex.org/C163797641","wikidata":"https://www.wikidata.org/wiki/Q2067937","display_name":"Tree structure","level":3,"score":0.1971060037612915},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.07686647772789001},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/s00453-010-9456-3","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00453-010-9456-3","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00453-010-9456-3.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-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithmica","raw_type":"journal-article"},{"id":"pmh:oai:pure.tue.nl:openaire/8489b13a-39ba-41a7-8c57-0a3279663cb9","is_oa":true,"landing_page_url":"https://research.tue.nl/en/publications/8489b13a-39ba-41a7-8c57-0a3279663cb9","pdf_url":null,"source":{"id":"https://openalex.org/S4406922641","display_name":"TU/e Research Portal","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Buchin, K, Buchin, M, Byrka, J, N\u00f6llenburg, M, Okamoto, Y, Silveira, R I & Wolff, A 2012, 'Drawing (complete) binary tanglegrams: hardness, approximation, fixed-parameter tractability', Algorithmica, vol. 62, no. 1-2, pp. 309-332. https://doi.org/10.1007/s00453-010-9456-3","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:tue:oai:pure.tue.nl:publications/8489b13a-39ba-41a7-8c57-0a3279663cb9","is_oa":true,"landing_page_url":"https://research.tue.nl/nl/publications/8489b13a-39ba-41a7-8c57-0a3279663cb9","pdf_url":"https://research.tue.nl/nl/publications/8489b13a-39ba-41a7-8c57-0a3279663cb9","source":{"id":"https://openalex.org/S4306401843","display_name":"Data Archiving and Networked Services (DANS)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1322597698","host_organization_name":"Royal Netherlands Academy of Arts and Sciences","host_organization_lineage":["https://openalex.org/I1322597698"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Algorithmica, 62(1-2), 309 - 332. Springer","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:opus.bibliothek.uni-wuerzburg.de:12462","is_oa":true,"landing_page_url":"https://nbn-resolving.org/urn:nbn:de:bvb:20-opus-124622","pdf_url":null,"source":{"id":"https://openalex.org/S4306401635","display_name":"Online Publication Service of W\u00fcrzburg University (W\u00fcrzburg University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I25974101","host_organization_name":"University of W\u00fcrzburg","host_organization_lineage":["https://openalex.org/I25974101"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"doc-type:article"}],"best_oa_location":{"id":"doi:10.1007/s00453-010-9456-3","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00453-010-9456-3","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00453-010-9456-3.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-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithmica","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1955397877","display_name":null,"funder_award_id":"BU 2419/1-1","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G258765838","display_name":null,"funder_award_id":"639.022.707","funder_id":"https://openalex.org/F4320321800","funder_display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek"},{"id":"https://openalex.org/G2983449479","display_name":null,"funder_award_id":"Scientific Research","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G3119829495","display_name":null,"funder_award_id":"642.065.503","funder_id":"https://openalex.org/F4320321800","funder_display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek"},{"id":"https://openalex.org/G3236194794","display_name":null,"funder_award_id":"Grant-in-Aid","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G3459562248","display_name":null,"funder_award_id":"Grant","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G4355795329","display_name":null,"funder_award_id":"WO 758/4-3","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G477234496","display_name":null,"funder_award_id":"N N206 368839","funder_id":"https://openalex.org/F4320322733","funder_display_name":"Ministerstwo Edukacji i Nauki"},{"id":"https://openalex.org/G4874944895","display_name":null,"funder_award_id":"-in-Aid","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G5365867299","display_name":null,"funder_award_id":"Grant","funder_id":"https://openalex.org/F4320321800","funder_display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek"},{"id":"https://openalex.org/G6009445997","display_name":null,"funder_award_id":"unknown","funder_id":"https://openalex.org/F4320321800","funder_display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek"},{"id":"https://openalex.org/G6052429835","display_name":null,"funder_award_id":"(DFG)","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G629491556","display_name":null,"funder_award_id":"(NWO)","funder_id":"https://openalex.org/F4320321800","funder_display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek"},{"id":"https://openalex.org/G6743243744","display_name":null,"funder_award_id":"unknown","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G7167128334","display_name":null,"funder_award_id":"Grant-in-Aid for Scientific Researc","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G7337825077","display_name":null,"funder_award_id":"Grant-in-Aid for Sc","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G7752643416","display_name":null,"funder_award_id":"Japan","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G8759943101","display_name":null,"funder_award_id":"rant-in-Aid for Scientific Research","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320320915","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052"},{"id":"https://openalex.org/F4320321800","display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek","ror":"https://ror.org/04jsz6e67"},{"id":"https://openalex.org/F4320322733","display_name":"Ministerstwo Edukacji i Nauki","ror":"https://ror.org/05dwvd537"},{"id":"https://openalex.org/F4320334764","display_name":"Japan Society for the Promotion of Science","ror":"https://ror.org/00hhkn466"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2123192541.pdf","grobid_xml":"https://content.openalex.org/works/W2123192541.grobid-xml"},"referenced_works_count":26,"referenced_works":["https://openalex.org/W1538145326","https://openalex.org/W1545430420","https://openalex.org/W1571037334","https://openalex.org/W1594683133","https://openalex.org/W1596218290","https://openalex.org/W1600949489","https://openalex.org/W1643794750","https://openalex.org/W1826394648","https://openalex.org/W1895301010","https://openalex.org/W1966697435","https://openalex.org/W1972151695","https://openalex.org/W1985123706","https://openalex.org/W2000602248","https://openalex.org/W2017719595","https://openalex.org/W2030776771","https://openalex.org/W2036004025","https://openalex.org/W2052367117","https://openalex.org/W2060157138","https://openalex.org/W2064854394","https://openalex.org/W2071353749","https://openalex.org/W2079962198","https://openalex.org/W2114148987","https://openalex.org/W2120358419","https://openalex.org/W2952914555","https://openalex.org/W3145128584","https://openalex.org/W4246219036"],"related_works":["https://openalex.org/W2038309235","https://openalex.org/W2364382882","https://openalex.org/W3169685561","https://openalex.org/W1979520615","https://openalex.org/W2501849745","https://openalex.org/W2072157347","https://openalex.org/W2061004850","https://openalex.org/W2004985727","https://openalex.org/W2949895650","https://openalex.org/W2091985989"],"abstract_inverted_index":{"A":[0],"binary":[1,11,96,111,139],"tanglegram":[2,61],"is":[3,34,56,68,74,91,103],"a":[4,7,60,123,145,158],"drawing":[5],"of":[6,9,66,134,147,153],"pair":[8],"rooted":[10],"trees":[12,38,108,140],"whose":[13],"leaf":[14],"sets":[15],"are":[16,22,39,109],"in":[17,31],"one-to-one":[18],"correspondence;":[19],"matching":[20],"leaves":[21],"connected":[23],"by":[24],"inter-tree":[25,47],"edges.":[26],"For":[27,113],"applications,":[28],"for":[29,95,138,149],"example,":[30],"phylogenetics,":[32],"it":[33],"essential":[35],"that":[36,45,58,71,80,84,100,130],"both":[37,107],"drawn":[40],"without":[41],"edge":[42],"crossings":[43,52,67],"and":[44,70,122,155],"the":[46,63,72,86,101,131,135,151],"edges":[48],"have":[49],"as":[50,53],"few":[51],"possible.":[54],"It":[55],"known":[57],"finding":[59],"with":[62,77],"minimum":[64],"number":[65],"NP-hard":[69,104],"problem":[73,102,137],"fixed-parameter":[75,126],"tractable":[76],"respect":[78],"to":[79,144],"number.":[81],"We":[82,98,128],"prove":[83],"under":[85],"Unique":[87],"Games":[88],"Conjecture":[89],"there":[90],"no":[92],"constant-factor":[93],"approximation":[94],"trees.":[97,112],"show":[99,129],"even":[105],"if":[106],"complete":[110],"this":[114],"case":[115],"we":[116],"give":[117],"an":[118],"O(n":[119],"3)-time":[120],"2-approximation":[121],"new,":[124],"simple":[125],"algorithm.":[127],"maximization":[132],"version":[133,146],"dual":[136],"can":[141],"be":[142],"reduced":[143],"MaxCut":[148],"which":[150],"algorithm":[152],"Goemans":[154],"Williamson":[156],"yields":[157],"0.878-approximation.":[159]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2018,"cited_by_count":3},{"year":2016,"cited_by_count":3}],"updated_date":"2026-04-16T08:26:57.006410","created_date":"2025-10-10T00:00:00"}
