{"id":"https://openalex.org/W2495547542","doi":"https://doi.org/10.1137/110843071","title":"Subset Feedback Vertex Set Is Fixed-Parameter Tractable","display_name":"Subset Feedback Vertex Set Is Fixed-Parameter Tractable","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W2495547542","doi":"https://doi.org/10.1137/110843071","mag":"2495547542"},"language":"en","primary_location":{"id":"doi:10.1137/110843071","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110843071","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1004.2972","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5037989463","display_name":"Marek Cygan","orcid":"https://orcid.org/0000-0003-2472-2975"},"institutions":[{"id":"https://openalex.org/I4654613","display_name":"University of Warsaw","ror":"https://ror.org/039bjqg32","country_code":"PL","type":"education","lineage":["https://openalex.org/I4654613"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Marek Cygan","raw_affiliation_strings":["Uniwersytet Warszawski, Wydzia\u0142 Matematyki Informatyki i Mechaniki, Instytut Informatyki"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Uniwersytet Warszawski, Wydzia\u0142 Matematyki Informatyki i Mechaniki, Instytut Informatyki","institution_ids":["https://openalex.org/I4654613"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5059330513","display_name":"Marcin Pilipczuk","orcid":"https://orcid.org/0000-0001-5680-7397"},"institutions":[{"id":"https://openalex.org/I4654613","display_name":"University of Warsaw","ror":"https://ror.org/039bjqg32","country_code":"PL","type":"education","lineage":["https://openalex.org/I4654613"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Marcin Pilipczuk","raw_affiliation_strings":["Uniwersytet Warszawski, Wydzia\u0142 Matematyki Informatyki i Mechaniki, Instytut Informatyki"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Uniwersytet Warszawski, Wydzia\u0142 Matematyki Informatyki i Mechaniki, Instytut Informatyki","institution_ids":["https://openalex.org/I4654613"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5000479623","display_name":"Micha\u0142 Pilipczuk","orcid":"https://orcid.org/0000-0001-7891-1988"},"institutions":[{"id":"https://openalex.org/I4654613","display_name":"University of Warsaw","ror":"https://ror.org/039bjqg32","country_code":"PL","type":"education","lineage":["https://openalex.org/I4654613"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Micha\u0142 Pilipczuk","raw_affiliation_strings":["Uniwersytet Warszawski, Wydzia\u0142 Matematyki Informatyki i Mechaniki, Instytut Informatyki"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Uniwersytet Warszawski, Wydzia\u0142 Matematyki Informatyki i Mechaniki, Instytut Informatyki","institution_ids":["https://openalex.org/I4654613"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5083165224","display_name":"Jakub Onufry Wojtaszczyk","orcid":null},"institutions":[{"id":"https://openalex.org/I4654613","display_name":"University of Warsaw","ror":"https://ror.org/039bjqg32","country_code":"PL","type":"education","lineage":["https://openalex.org/I4654613"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Jakub Onufry Wojtaszczyk","raw_affiliation_strings":["Uniwersytet Warszawski, Wydzia\u0142 Matematyki Informatyki i Mechaniki, Instytut Informatyki"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Uniwersytet Warszawski, Wydzia\u0142 Matematyki Informatyki i Mechaniki, Instytut Informatyki","institution_ids":["https://openalex.org/I4654613"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I4654613"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.2536187,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"27","issue":"1","first_page":"290","last_page":"309"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.30070000886917114,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.30070000886917114,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.25209999084472656,"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/T11269","display_name":"Algorithms and Data Compression","score":0.09149999916553497,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/kernelization","display_name":"Kernelization","score":0.928700864315033},{"id":"https://openalex.org/keywords/feedback-vertex-set","display_name":"Feedback vertex set","score":0.8900130987167358},{"id":"https://openalex.org/keywords/parameterized-complexity","display_name":"Parameterized complexity","score":0.7319868206977844},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.7195489406585693},{"id":"https://openalex.org/keywords/neighbourhood","display_name":"Neighbourhood (mathematics)","score":0.5370482802391052},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5222652554512024},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.48648592829704285},{"id":"https://openalex.org/keywords/feedback-arc-set","display_name":"Feedback arc set","score":0.462402880191803},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4481632709503174},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4417412281036377},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.39627599716186523},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.36572277545928955},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.0768837034702301}],"concepts":[{"id":"https://openalex.org/C207225210","wikidata":"https://www.wikidata.org/wiki/Q1759539","display_name":"Kernelization","level":3,"score":0.928700864315033},{"id":"https://openalex.org/C28723256","wikidata":"https://www.wikidata.org/wiki/Q1400918","display_name":"Feedback vertex set","level":4,"score":0.8900130987167358},{"id":"https://openalex.org/C165464430","wikidata":"https://www.wikidata.org/wiki/Q1570441","display_name":"Parameterized complexity","level":2,"score":0.7319868206977844},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.7195489406585693},{"id":"https://openalex.org/C161677786","wikidata":"https://www.wikidata.org/wiki/Q2478475","display_name":"Neighbourhood (mathematics)","level":2,"score":0.5370482802391052},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5222652554512024},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.48648592829704285},{"id":"https://openalex.org/C157951044","wikidata":"https://www.wikidata.org/wiki/Q1400910","display_name":"Feedback arc set","level":5,"score":0.462402880191803},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4481632709503174},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4417412281036377},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.39627599716186523},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.36572277545928955},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.0768837034702301},{"id":"https://openalex.org/C22149727","wikidata":"https://www.wikidata.org/wiki/Q7940747","display_name":"Voltage graph","level":4,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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":6,"locations":[{"id":"doi:10.1137/110843071","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110843071","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1004.2972","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1004.2972","pdf_url":"https://arxiv.org/pdf/1004.2972","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"mag:2950152085","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1004.2972.pdf","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.308.4587","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.308.4587","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://static.googleusercontent.com/external_content/untrusted_dlcp/research.google.com/en/us/pubs/archive/37375.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.762.8052","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.762.8052","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/1004.2972.pdf","raw_type":"text"},{"id":"doi:10.48550/arxiv.1004.2972","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1004.2972","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1004.2972","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1004.2972","pdf_url":"https://arxiv.org/pdf/1004.2972","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321042","display_name":"Fundacja na rzecz Nauki Polskiej","ror":"https://ror.org/048zd9m77"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2495547542.pdf","grobid_xml":"https://content.openalex.org/works/W2495547542.grobid-xml"},"referenced_works_count":17,"referenced_works":["https://openalex.org/W1971393213","https://openalex.org/W1974810008","https://openalex.org/W1979312598","https://openalex.org/W1997576329","https://openalex.org/W2000065147","https://openalex.org/W2016088388","https://openalex.org/W2025304499","https://openalex.org/W2043644213","https://openalex.org/W2051856222","https://openalex.org/W2070745908","https://openalex.org/W2072261513","https://openalex.org/W2091977535","https://openalex.org/W2121641644","https://openalex.org/W2125350407","https://openalex.org/W2146221397","https://openalex.org/W2157295389","https://openalex.org/W2171796957"],"related_works":["https://openalex.org/W2950152085","https://openalex.org/W2920720604","https://openalex.org/W2048322630","https://openalex.org/W2964258819","https://openalex.org/W3213442239","https://openalex.org/W2950239217","https://openalex.org/W2952085137","https://openalex.org/W2940485869","https://openalex.org/W1570850681","https://openalex.org/W2125455032","https://openalex.org/W2952146213","https://openalex.org/W3007257280","https://openalex.org/W205406847","https://openalex.org/W3196355770","https://openalex.org/W2944564962","https://openalex.org/W2284430037","https://openalex.org/W3017448922","https://openalex.org/W2950812152","https://openalex.org/W3039254663","https://openalex.org/W2914383530"],"abstract_inverted_index":{"The":[0,155],"classical":[1],"Feedback":[2,35,81],"Vertex":[3,36,82],"Set":[4,37,83],"problem":[5,161,185],"asks,":[6],"for":[7,101],"a":[8,19,40,57,70,91,102,235],"given":[9,201],"undirected":[10],"graph":[11,33],"$G$":[12],"and":[13,49,52,73,98,124,170,225],"an":[14,86,196],"integer":[15],"$k$,":[16],"to":[17,203,233],"find":[18],"set":[20,92,103],"of":[21,43,60,76,96,104,118,157,210],"at":[22,105],"most":[23,106],"$k$":[24,107],"vertices":[25,108],"that":[26,109,183,246],"hits":[27,110],"all":[28,111],"the":[29,32,46,63,77,132,159,200,208,220,242],"cycles":[30,113],"in":[31,45,62,121,172],"$G$.":[34],"has":[38],"attracted":[39],"large":[41],"amount":[42],"research":[44],"parameterized":[47,190],"setting,":[48],"subsequent":[50],"fixed-parameter":[51,163,187,250],"kernelization":[53,216],"algorithms":[54],"have":[55],"been":[56],"rich":[58],"source":[59],"ideas":[61],"field.":[64],"In":[65],"this":[66,176,184],"paper":[67],"we":[68,99,194],"consider":[69],"more":[71],"general":[72],"difficult":[74],"version":[75],"problem,":[78,244],"named":[79],"Subset":[80],"(Subset-FVS),":[84],"where":[85],"instance":[87,202],"comes":[88],"additionally":[89],"with":[90,207],"$S":[93],"\\subseteq":[94],"V$":[95],"vertices,":[97],"ask":[100],"simple":[112],"passing":[114],"through":[115],"$S$.":[116],"Because":[117],"its":[119],"applications":[120],"circuit":[122],"testing":[123],"genetic":[125],"linkage":[126],"analysis,":[127],"Subset-FVS":[128,160,243],"was":[129,165],"studied":[130],"from":[131],"approximation":[133],"algorithm":[134,197,240],"perspective":[135],"by":[136,168,181,191,213],"Even":[137],"et":[138],"al.":[139],"[SIAM":[140],"J.":[141,149],"Discrete":[142],"Math.,":[143],"13":[144],"(2000),":[145,152],"pp.":[146,153],"225--267;":[147],"SIAM":[148],"Comput.,":[150],"30":[151],"1231--1252].":[154],"question":[156,177],"whether":[158],"is":[162,186,248],"tractable":[164,188],"posed":[166],"independently":[167],"Kawarabayashi":[169],"Saurabh":[171],"2009.":[173],"We":[174,179],"answer":[175],"affirmatively.":[178],"begin":[180],"showing":[182],"when":[189],"$|S|$.":[192],"Next":[193],"present":[195],"which":[198],"reduces":[199],"$2^k":[204],"n^{O(1)}$":[205,238],"instances":[206],"size":[209],"$S$":[211],"bounded":[212],"$O(k^3)$,":[214],"using":[215],"techniques":[217],"such":[218],"as":[219],"$2$-expansion":[221],"lemma,":[222],"Menger's":[223],"theorem,":[224],"Gallai's":[226],"theorem.":[227],"These":[228],"two":[229],"facts":[230],"allow":[231],"us":[232],"give":[234],"$2^{O(k\\log":[236],"k)}":[237],"time":[239],"solving":[241],"proving":[245],"it":[247],"indeed":[249],"tractable.":[251]},"counts_by_year":[],"updated_date":"2026-07-15T18:14:33.161393","created_date":"2025-10-10T00:00:00"}