{"id":"https://openalex.org/W4213108070","doi":"https://doi.org/10.1007/s10951-021-00719-1","title":"An analysis of the parameterized complexity of periodic timetabling","display_name":"An analysis of the parameterized complexity of periodic timetabling","publication_year":2022,"publication_date":"2022-02-15","ids":{"openalex":"https://openalex.org/W4213108070","doi":"https://doi.org/10.1007/s10951-021-00719-1"},"language":"en","primary_location":{"id":"doi:10.1007/s10951-021-00719-1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10951-021-00719-1","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10951-021-00719-1.pdf","source":{"id":"https://openalex.org/S91278097","display_name":"Journal of Scheduling","issn_l":"1094-6136","issn":["1094-6136","1099-1425"],"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":"Journal of Scheduling","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/s10951-021-00719-1.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5042594597","display_name":"Niels Lindner","orcid":"https://orcid.org/0000-0002-8337-4387"},"institutions":[{"id":"https://openalex.org/I195893171","display_name":"Zuse Institute Berlin","ror":"https://ror.org/02eva5865","country_code":"DE","type":"facility","lineage":["https://openalex.org/I195893171"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Niels Lindner","raw_affiliation_strings":["Zuse Institute Berlin, Takustr. 7, 14195 Berlin, Germany","Zuse Institute Berlin, Takustr. 7, 14195, Berlin, Germany"],"raw_orcid":"https://orcid.org/0000-0002-8337-4387","affiliations":[{"raw_affiliation_string":"Zuse Institute Berlin, Takustr. 7, 14195 Berlin, Germany","institution_ids":["https://openalex.org/I195893171"]},{"raw_affiliation_string":"Zuse Institute Berlin, Takustr. 7, 14195, Berlin, Germany","institution_ids":["https://openalex.org/I195893171"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5029344320","display_name":"Julian Reisch","orcid":"https://orcid.org/0000-0002-5620-1093"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Julian Reisch","raw_affiliation_strings":["Synoptics GmbH, Chemnitzer Str. 48b, 01187, Dresden, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Synoptics GmbH, Chemnitzer Str. 48b, 01187, Dresden, Germany","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5042594597"],"corresponding_institution_ids":["https://openalex.org/I195893171"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":1.2176,"has_fulltext":true,"cited_by_count":9,"citation_normalized_percentile":{"value":0.80903056,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"25","issue":"2","first_page":"157","last_page":"176"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9990000128746033,"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":0.9990000128746033,"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/T10142","display_name":"Formal Methods in Verification","score":0.9941999912261963,"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/T11596","display_name":"Constraint Satisfaction and Optimization","score":0.9922999739646912,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/treewidth","display_name":"Treewidth","score":0.833417534828186},{"id":"https://openalex.org/keywords/parameterized-complexity","display_name":"Parameterized complexity","score":0.7598505020141602},{"id":"https://openalex.org/keywords/vertex-cover","display_name":"Vertex cover","score":0.599256157875061},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5777161717414856},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.5201428532600403},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5023376941680908},{"id":"https://openalex.org/keywords/benchmarking","display_name":"Benchmarking","score":0.47483521699905396},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.450361043214798},{"id":"https://openalex.org/keywords/steiner-tree-problem","display_name":"Steiner tree problem","score":0.44184282422065735},{"id":"https://openalex.org/keywords/partial-k-tree","display_name":"Partial k-tree","score":0.42904573678970337},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3923425078392029},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3757264018058777},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.3711867332458496},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3435782790184021},{"id":"https://openalex.org/keywords/pathwidth","display_name":"Pathwidth","score":0.19464078545570374},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.0913853645324707}],"concepts":[{"id":"https://openalex.org/C132569581","wikidata":"https://www.wikidata.org/wiki/Q5067368","display_name":"Treewidth","level":5,"score":0.833417534828186},{"id":"https://openalex.org/C165464430","wikidata":"https://www.wikidata.org/wiki/Q1570441","display_name":"Parameterized complexity","level":2,"score":0.7598505020141602},{"id":"https://openalex.org/C40687702","wikidata":"https://www.wikidata.org/wiki/Q11515519","display_name":"Vertex cover","level":3,"score":0.599256157875061},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5777161717414856},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.5201428532600403},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5023376941680908},{"id":"https://openalex.org/C86251818","wikidata":"https://www.wikidata.org/wiki/Q816754","display_name":"Benchmarking","level":2,"score":0.47483521699905396},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.450361043214798},{"id":"https://openalex.org/C76220878","wikidata":"https://www.wikidata.org/wiki/Q1764144","display_name":"Steiner tree problem","level":2,"score":0.44184282422065735},{"id":"https://openalex.org/C128764233","wikidata":"https://www.wikidata.org/wiki/Q7140374","display_name":"Partial k-tree","level":5,"score":0.42904573678970337},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3923425078392029},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3757264018058777},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.3711867332458496},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3435782790184021},{"id":"https://openalex.org/C43517604","wikidata":"https://www.wikidata.org/wiki/Q7144893","display_name":"Pathwidth","level":4,"score":0.19464078545570374},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.0913853645324707},{"id":"https://openalex.org/C144133560","wikidata":"https://www.wikidata.org/wiki/Q4830453","display_name":"Business","level":0,"score":0.0},{"id":"https://openalex.org/C162853370","wikidata":"https://www.wikidata.org/wiki/Q39809","display_name":"Marketing","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s10951-021-00719-1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10951-021-00719-1","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10951-021-00719-1.pdf","source":{"id":"https://openalex.org/S91278097","display_name":"Journal of Scheduling","issn_l":"1094-6136","issn":["1094-6136","1099-1425"],"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":"Journal of Scheduling","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:spr:jsched:v:25:y:2022:i:2:d:10.1007_s10951-021-00719-1","is_oa":false,"landing_page_url":"http://link.springer.com/10.1007/s10951-021-00719-1","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"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":"article"},{"id":"pmh:oai:econstor.eu:10419/308737","is_oa":true,"landing_page_url":"https://hdl.handle.net/10419/308737","pdf_url":null,"source":{"id":"https://openalex.org/S4306401696","display_name":"Econstor (Econstor)","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"doc-type:article"}],"best_oa_location":{"id":"doi:10.1007/s10951-021-00719-1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10951-021-00719-1","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10951-021-00719-1.pdf","source":{"id":"https://openalex.org/S91278097","display_name":"Journal of Scheduling","issn_l":"1094-6136","issn":["1094-6136","1099-1425"],"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":"Journal of Scheduling","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1372115314","display_name":null,"funder_award_id":"EXC-2046","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G2117824717","display_name":null,"funder_award_id":"project ID: 390685689","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G2990895770","display_name":null,"funder_award_id":"EXC-2046/1, project ID: 390685689","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G3568794162","display_name":null,"funder_award_id":"EXC-2046/1, project ID: 390685689","funder_id":"https://openalex.org/F4320330291","funder_display_name":"Berlin Mathematics Research Center MATH+"},{"id":"https://openalex.org/G3684656814","display_name":null,"funder_award_id":"MATH+ (EXC-2046/1","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G7354608348","display_name":null,"funder_award_id":"EXC-2046/1","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G7362566262","display_name":null,"funder_award_id":"EXC-2046/1","funder_id":"https://openalex.org/F4320330291","funder_display_name":"Berlin Mathematics Research Center MATH+"},{"id":"https://openalex.org/G7725451807","display_name":"EXC 2046: MATH+: Berlin Mathematics Research Center","funder_award_id":"390685689","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G8964763783","display_name":null,"funder_award_id":"390685689","funder_id":"https://openalex.org/F4320330291","funder_display_name":"Berlin Mathematics Research Center MATH+"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320330291","display_name":"Berlin Mathematics Research Center MATH+","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4213108070.pdf","grobid_xml":"https://content.openalex.org/works/W4213108070.grobid-xml"},"referenced_works_count":38,"referenced_works":["https://openalex.org/W28746272","https://openalex.org/W1551429295","https://openalex.org/W1657638245","https://openalex.org/W1991755800","https://openalex.org/W1993522985","https://openalex.org/W1995561296","https://openalex.org/W2002722727","https://openalex.org/W2005079828","https://openalex.org/W2007761372","https://openalex.org/W2019137761","https://openalex.org/W2047871605","https://openalex.org/W2059372025","https://openalex.org/W2083963621","https://openalex.org/W2090397489","https://openalex.org/W2103715966","https://openalex.org/W2113019421","https://openalex.org/W2130062124","https://openalex.org/W2132022337","https://openalex.org/W2401610261","https://openalex.org/W2560192442","https://openalex.org/W2748301739","https://openalex.org/W2749505903","https://openalex.org/W2751935900","https://openalex.org/W2756618291","https://openalex.org/W2794267717","https://openalex.org/W2888998666","https://openalex.org/W2914414140","https://openalex.org/W2921186940","https://openalex.org/W2963352550","https://openalex.org/W2963809597","https://openalex.org/W2991245656","https://openalex.org/W3106486826","https://openalex.org/W4213368513","https://openalex.org/W4244290607","https://openalex.org/W4292230561","https://openalex.org/W4301808069","https://openalex.org/W6996888795","https://openalex.org/W7037795299"],"related_works":["https://openalex.org/W101378340","https://openalex.org/W1588220234","https://openalex.org/W2027513055","https://openalex.org/W2735537192","https://openalex.org/W4300462175","https://openalex.org/W2542138745","https://openalex.org/W3000445495","https://openalex.org/W3013389333","https://openalex.org/W2797680869","https://openalex.org/W4213108070"],"abstract_inverted_index":{"Abstract":[0],"Public":[1],"transportation":[2],"networks":[3,70,88,167,201],"are":[4,83],"typically":[5],"operated":[6],"with":[7,150,168,190,202],"a":[8,28,63,76,105,203],"periodic":[9,12,24],"timetable.":[10],"The":[11],"event":[13],"scheduling":[14],"problem":[15,138,149],"(PESP)":[16],"is":[17,27,62,75,108,114,118,123,139],"the":[18,36,39,60,69,72,102,112,116,121,129,136,146,185,213,218,222,235,239],"standard":[19],"mathematical":[20],"modeling":[21],"tool":[22],"for":[23,86,128],"timetabling.":[25],"PESP":[26,50,106,133,189],"computationally":[29],"very":[30],"challenging":[31],"problem:":[32],"For":[33,199],"example,":[34],"solving":[35],"instances":[37],"of":[38,47,71,89,104,131,145,188,217,224,238],"benchmarking":[40,240],"library":[41,241],"PESPlib":[42],"to":[43,79,152],"optimality":[44],"seems":[45],"out":[46],"reach.":[48],"Since":[49],"can":[51,158],"be":[52],"solved":[53],"in":[54,68,215],"linear":[55],"time":[56],"on":[57,165,179,212,234],"trees,":[58],"and":[59,209,221],"treewidth":[61,113],"rather":[64],"small":[65],"graph":[66],"parameter":[67],"PESPlib,":[73],"it":[74],"natural":[77],"question":[78],"ask":[80],"whether":[81],"there":[82],"polynomial-time":[84],"algorithms":[85,164,177],"input":[87,166],"bounded":[90,169,191],"treewidth,":[91,153],"or":[92,120,171,195],"even":[93,110],"better,":[94],"fixed-parameter":[95],"tractable":[96],"algorithms.":[97],"We":[98,173,182],"show":[99,143],"that":[100,156],"deciding":[101],"feasibility":[103,137,148],"instance":[107,237],"NP-hard":[109],"when":[111],"2,":[115,119],"branchwidth":[117,214],"carvingwidth":[122,223],"3.":[124],"Analogous":[125],"results":[126],"hold":[127],"optimization":[130],"reduced":[132],"instances,":[134],"where":[135],"trivial.":[140],"Moreover,":[141],"we":[142,157,206,230],"W[1]-hardness":[144],"general":[147],"respect":[151],"which":[154],"means":[155],"most":[159],"likely":[160],"only":[161],"accomplish":[162],"pseudo-polynomial-time":[163],"tree-":[170],"branchwidth.":[172],"present":[174],"two":[175],"such":[176],"based":[178],"dynamic":[180],"programming.":[181],"further":[183],"analyze":[184],"parameterized":[186],"complexity":[187],"cyclomatic":[192],"number,":[193],"diameter,":[194],"vertex":[196],"cover":[197],"number.":[198],"event-activity":[200],"special\u2014but":[204],"standard\u2014structure,":[205],"give":[207],"explicit":[208],"sharp":[210],"bounds":[211],"terms":[216],"maximum":[219],"degree":[220],"an":[225],"underlying":[226],"line":[227],"network.":[228],"Finally,":[229],"investigate":[231],"several":[232],"parameters":[233],"smallest":[236],"PESPlib.":[242]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":4}],"updated_date":"2026-06-22T08:00:12.763002","created_date":"2025-10-10T00:00:00"}
