{"id":"https://openalex.org/W2143693959","doi":"https://doi.org/10.1007/s00224-011-9312-0","title":"A Note on Exact Algorithms for Vertex Ordering Problems on Graphs","display_name":"A Note on Exact Algorithms for Vertex Ordering Problems on Graphs","publication_year":2011,"publication_date":"2011-01-20","ids":{"openalex":"https://openalex.org/W2143693959","doi":"https://doi.org/10.1007/s00224-011-9312-0","mag":"2143693959"},"language":"en","primary_location":{"id":"doi:10.1007/s00224-011-9312-0","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00224-011-9312-0","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00224-011-9312-0.pdf","source":{"id":"https://openalex.org/S4210177266","display_name":"Theory of Computing Systems","issn_l":"1432-4350","issn":["1432-4350","1433-0490"],"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":"Theory of Computing Systems","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/s00224-011-9312-0.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5032730524","display_name":"Hans L. Bodlaender","orcid":"https://orcid.org/0000-0002-9297-3330"},"institutions":[{"id":"https://openalex.org/I193662353","display_name":"Utrecht University","ror":"https://ror.org/04pp8hn57","country_code":"NL","type":"education","lineage":["https://openalex.org/I193662353"]}],"countries":["NL"],"is_corresponding":true,"raw_author_name":"Hans L. Bodlaender","raw_affiliation_strings":["Department of Information and Computing Sciences, Utrecht University, P.O. Box 80.089, 3508 TB, Utrecht, The Netherlands","Utrecht University, Department of Information and Computing Sciences, P.O. Box 80.089, 3508 TB, Utrecht, The Netherlands#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Information and Computing Sciences, Utrecht University, P.O. Box 80.089, 3508 TB, Utrecht, The Netherlands","institution_ids":["https://openalex.org/I193662353"]},{"raw_affiliation_string":"Utrecht University, Department of Information and Computing Sciences, P.O. Box 80.089, 3508 TB, Utrecht, The Netherlands#TAB#","institution_ids":["https://openalex.org/I193662353"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5075328697","display_name":"Fedor V. Fomin","orcid":"https://orcid.org/0000-0003-1955-4612"},"institutions":[{"id":"https://openalex.org/I4432739","display_name":"University of Bergen","ror":"https://ror.org/03zga2b32","country_code":"NO","type":"education","lineage":["https://openalex.org/I4432739"]}],"countries":["NO"],"is_corresponding":false,"raw_author_name":"Fedor V. Fomin","raw_affiliation_strings":["Department of Informatics, University of Bergen, 5020, Bergen, Norway","University of Bergen, Department of Informatics, 5020, Bergen, Norway#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Informatics, University of Bergen, 5020, Bergen, Norway","institution_ids":["https://openalex.org/I4432739"]},{"raw_affiliation_string":"University of Bergen, Department of Informatics, 5020, Bergen, Norway#TAB#","institution_ids":["https://openalex.org/I4432739"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5043443150","display_name":"Arie M. C. A. Koster","orcid":"https://orcid.org/0000-0002-8035-7012"},"institutions":[{"id":"https://openalex.org/I887968799","display_name":"RWTH Aachen University","ror":"https://ror.org/04xfq0f34","country_code":"DE","type":"education","lineage":["https://openalex.org/I887968799"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Arie M. C. A. Koster","raw_affiliation_strings":["Lehrstuhl II f\u00fcr Mathematik, RWTH Aachen University, W\u00fcllnerstr. 5b, 52062, Aachen, Germany","RWTH Aachen University, Lehrstuhl II f\u00fcr Mathematik, W\u00fcllnerstr. 5b, 52062, Aachen, Germany#TAB#"],"affiliations":[{"raw_affiliation_string":"Lehrstuhl II f\u00fcr Mathematik, RWTH Aachen University, W\u00fcllnerstr. 5b, 52062, Aachen, Germany","institution_ids":["https://openalex.org/I887968799"]},{"raw_affiliation_string":"RWTH Aachen University, Lehrstuhl II f\u00fcr Mathematik, W\u00fcllnerstr. 5b, 52062, Aachen, Germany#TAB#","institution_ids":["https://openalex.org/I887968799"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5109894460","display_name":"Dieter Kratsch","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Dieter Kratsch","raw_affiliation_strings":["LITA, Universit\u00e9 de Metz, 507045, Metz Cedex 01, France","Universit\u00e9 de Metz, LITA, 507045, Metz Cedex 01, France#TAB#"],"affiliations":[{"raw_affiliation_string":"LITA, Universit\u00e9 de Metz, 507045, Metz Cedex 01, France","institution_ids":[]},{"raw_affiliation_string":"Universit\u00e9 de Metz, LITA, 507045, Metz Cedex 01, France#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5085447779","display_name":"Dimitrios M. Thilikos","orcid":null},"institutions":[{"id":"https://openalex.org/I200777214","display_name":"National and Kapodistrian University of Athens","ror":"https://ror.org/04gnjpq42","country_code":"GR","type":"education","lineage":["https://openalex.org/I200777214"]}],"countries":["GR"],"is_corresponding":false,"raw_author_name":"Dimitrios M. Thilikos","raw_affiliation_strings":["Department of Mathematics, National and Kapodistrian University of Athens, Panepistimioupolis, 15784, Athens, Greece","National and Kapodistrian University of Athens, Department of Mathematics, Panepistimioupolis, 15784, Athens, Greece#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, National and Kapodistrian University of Athens, Panepistimioupolis, 15784, Athens, Greece","institution_ids":["https://openalex.org/I200777214"]},{"raw_affiliation_string":"National and Kapodistrian University of Athens, Department of Mathematics, Panepistimioupolis, 15784, Athens, Greece#TAB#","institution_ids":["https://openalex.org/I200777214"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5032730524"],"corresponding_institution_ids":["https://openalex.org/I193662353"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":8.7244,"has_fulltext":true,"cited_by_count":76,"citation_normalized_percentile":{"value":0.9841984,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"50","issue":"3","first_page":"420","last_page":"432"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9998999834060669,"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":0.9998999834060669,"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9980999827384949,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9969000220298767,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"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/travelling-salesman-problem","display_name":"Travelling salesman problem","score":0.7866407632827759},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.6969174146652222},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.640976071357727},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6085749864578247},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.4739249646663666},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.43326571583747864},{"id":"https://openalex.org/keywords/pspace","display_name":"PSPACE","score":0.42474564909935},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.41240397095680237},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3975251615047455},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.27822962403297424},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.26263976097106934},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.1827177107334137}],"concepts":[{"id":"https://openalex.org/C175859090","wikidata":"https://www.wikidata.org/wiki/Q322212","display_name":"Travelling salesman problem","level":2,"score":0.7866407632827759},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.6969174146652222},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.640976071357727},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6085749864578247},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.4739249646663666},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.43326571583747864},{"id":"https://openalex.org/C197685441","wikidata":"https://www.wikidata.org/wiki/Q500716","display_name":"PSPACE","level":3,"score":0.42474564909935},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.41240397095680237},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3975251615047455},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.27822962403297424},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.26263976097106934},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.1827177107334137},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/s00224-011-9312-0","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00224-011-9312-0","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00224-011-9312-0.pdf","source":{"id":"https://openalex.org/S4210177266","display_name":"Theory of Computing Systems","issn_l":"1432-4350","issn":["1432-4350","1433-0490"],"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":"Theory of Computing Systems","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.148.5007","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.148.5007","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.uu.nl/research/techreps/repo/CS-2009/2009-023.pdf","raw_type":"text"},{"id":"pmh:oai:bora.uib.no:1956/4556","is_oa":true,"landing_page_url":"https://hdl.handle.net/1956/4556","pdf_url":null,"source":{"id":"https://openalex.org/S4306400085","display_name":"Bergen Open Research Archive (BORA) (University of Bergen)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4432739","host_organization_name":"University of Bergen","host_organization_lineage":["https://openalex.org/I4432739"],"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":"","raw_type":"info:eu-repo/semantics/other"},{"id":"pmh:oai:publications.rwth-aachen.de:166138","is_oa":true,"landing_page_url":"https://publications.rwth-aachen.de/record/166138","pdf_url":null,"source":{"id":"https://openalex.org/S4306401362","display_name":"RWTH Publications (RWTH Aachen)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I887968799","host_organization_name":"RWTH Aachen University","host_organization_lineage":["https://openalex.org/I887968799"],"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":"Theory of computing systems 50(3), 420-432 (2011). doi:10.1007/s00224-011-9312-0","raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":{"id":"doi:10.1007/s00224-011-9312-0","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00224-011-9312-0","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00224-011-9312-0.pdf","source":{"id":"https://openalex.org/S4210177266","display_name":"Theory of Computing Systems","issn_l":"1432-4350","issn":["1432-4350","1433-0490"],"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":"Theory of Computing Systems","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G14505348","display_name":null,"funder_award_id":"70/4/8757","funder_id":"https://openalex.org/F4320321800","funder_display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek"},{"id":"https://openalex.org/G3179101803","display_name":null,"funder_award_id":"GR 883/9-3, GR 883/9-4","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G3477929639","display_name":null,"funder_award_id":"70/4/8757","funder_id":"https://openalex.org/F4320323149","funder_display_name":"National and Kapodistrian University of Athens"},{"id":"https://openalex.org/G7646527374","display_name":null,"funder_award_id":"70/4/8757","funder_id":"https://openalex.org/F4320323299","funder_display_name":"Norges Forskningsr\u00e5d"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320321800","display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek","ror":"https://ror.org/04jsz6e67"},{"id":"https://openalex.org/F4320323149","display_name":"National and Kapodistrian University of Athens","ror":"https://ror.org/04gnjpq42"},{"id":"https://openalex.org/F4320323299","display_name":"Norges Forskningsr\u00e5d","ror":"https://ror.org/00epmv149"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2143693959.pdf","grobid_xml":"https://content.openalex.org/works/W2143693959.grobid-xml"},"referenced_works_count":18,"referenced_works":["https://openalex.org/W1542253039","https://openalex.org/W1551907897","https://openalex.org/W1584965761","https://openalex.org/W1813769739","https://openalex.org/W1969186119","https://openalex.org/W2012473793","https://openalex.org/W2030087828","https://openalex.org/W2038049091","https://openalex.org/W2052867211","https://openalex.org/W2057385022","https://openalex.org/W2072099942","https://openalex.org/W2079966248","https://openalex.org/W2087083200","https://openalex.org/W2104739701","https://openalex.org/W2125547222","https://openalex.org/W2168990208","https://openalex.org/W4285719527","https://openalex.org/W4389615669"],"related_works":["https://openalex.org/W1504200807","https://openalex.org/W3117732946","https://openalex.org/W1968954131","https://openalex.org/W2082636129","https://openalex.org/W2963307440","https://openalex.org/W2982557863","https://openalex.org/W2925112333","https://openalex.org/W3190027049","https://openalex.org/W2075449032","https://openalex.org/W2583998759"],"abstract_inverted_index":{"In":[0],"this":[1],"note,":[2],"we":[3],"give":[4],"a":[5,68],"proof":[6],"that":[7],"several":[8],"vertex":[9,71],"ordering":[10,72],"problems":[11,73],"can":[12],"be":[13],"solved":[14],"in":[15,28],"O":[16,22,29],"\u2217(2":[17,23],"n":[18,24,31],")":[19,25,32],"time":[20,33],"and":[21,34,48,57,59],"space,":[26],"or":[27],"\u2217(4":[30],"polynomial":[35],"space.":[36],"The":[37],"algorithms":[38,40],"generalize":[39],"for":[41],"the":[42,76],"Travelling":[43],"Salesman":[44],"Problem":[45],"by":[46],"Held":[47],"Karp":[49],"(J.":[50],"Soc.":[51],"Ind.":[52],"Appl.":[53],"Math.":[54],"10:196\u2013210,":[55],"1962)":[56],"Gurevich":[58],"Shelah":[60],"(SIAM":[61],"J.":[62],"Comput.":[63],"16:486\u2013502,":[64],"1987).":[65],"We":[66],"survey":[67],"number":[69],"of":[70],"to":[74],"which":[75],"results":[77],"apply.":[78]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":9},{"year":2014,"cited_by_count":8},{"year":2013,"cited_by_count":8},{"year":2012,"cited_by_count":8}],"updated_date":"2026-04-21T08:09:41.155169","created_date":"2025-10-10T00:00:00"}
