{"id":"https://openalex.org/W4386351417","doi":"https://doi.org/10.48550/arxiv.2308.15900","title":"Data reduction for directed feedback vertex set on graphs without long induced cycles","display_name":"Data reduction for directed feedback vertex set on graphs without long induced cycles","publication_year":2023,"publication_date":"2023-08-30","ids":{"openalex":"https://openalex.org/W4386351417","doi":"https://doi.org/10.48550/arxiv.2308.15900"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2308.15900","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2308.15900","pdf_url":"https://arxiv.org/pdf/2308.15900","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":null,"raw_type":"text"},"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2308.15900","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5063708205","display_name":"Jona Dirks","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Dirks, Jona","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5092819380","display_name":"Enna Gerhard","orcid":"https://orcid.org/0000-0002-7767-6637"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Gerhard, Enna","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5002401893","display_name":"Mario Grobler","orcid":"https://orcid.org/0000-0001-8103-6440"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Grobler, Mario","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5051065386","display_name":"Amer E. Mouawad","orcid":"https://orcid.org/0000-0003-2481-4968"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mouawad, Amer E.","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5073548944","display_name":"Sebastian Siebertz","orcid":"https://orcid.org/0000-0002-6347-1198"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Siebertz, Sebastian","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5063708205"],"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9713000059127808,"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":0.9713000059127808,"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":0.9577000141143799,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9538000226020813,"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":0.7920151352882385},{"id":"https://openalex.org/keywords/treewidth","display_name":"Treewidth","score":0.7538967132568359},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5986481308937073},{"id":"https://openalex.org/keywords/planar-graph","display_name":"Planar graph","score":0.5583869814872742},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.5476237535476685},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5254144668579102},{"id":"https://openalex.org/keywords/feedback-vertex-set","display_name":"Feedback vertex set","score":0.48867252469062805},{"id":"https://openalex.org/keywords/omega","display_name":"Omega","score":0.4370124340057373},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.4218413829803467},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.40588077902793884},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4007878303527832},{"id":"https://openalex.org/keywords/pathwidth","display_name":"Pathwidth","score":0.390066921710968},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.12859094142913818},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.0760597288608551}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7920151352882385},{"id":"https://openalex.org/C132569581","wikidata":"https://www.wikidata.org/wiki/Q5067368","display_name":"Treewidth","level":5,"score":0.7538967132568359},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5986481308937073},{"id":"https://openalex.org/C101837359","wikidata":"https://www.wikidata.org/wiki/Q547823","display_name":"Planar graph","level":3,"score":0.5583869814872742},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5476237535476685},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5254144668579102},{"id":"https://openalex.org/C28723256","wikidata":"https://www.wikidata.org/wiki/Q1400918","display_name":"Feedback vertex set","level":4,"score":0.48867252469062805},{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.4370124340057373},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.4218413829803467},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.40588077902793884},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4007878303527832},{"id":"https://openalex.org/C43517604","wikidata":"https://www.wikidata.org/wiki/Q7144893","display_name":"Pathwidth","level":4,"score":0.390066921710968},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.12859094142913818},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.0760597288608551},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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":2,"locations":[{"id":"pmh:oai:arXiv.org:2308.15900","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2308.15900","pdf_url":"https://arxiv.org/pdf/2308.15900","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":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2308.15900","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2308.15900","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:2308.15900","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2308.15900","pdf_url":"https://arxiv.org/pdf/2308.15900","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":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4386351417.pdf"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W1511821218","https://openalex.org/W2175868772","https://openalex.org/W1587078595","https://openalex.org/W2124176527","https://openalex.org/W2985636744","https://openalex.org/W2125058377","https://openalex.org/W2465927132","https://openalex.org/W4301463689","https://openalex.org/W2605313623","https://openalex.org/W2133160845"],"abstract_inverted_index":{"We":[0,61,96,113,175,203,256],"study":[1,98],"reduction":[2,209],"rules":[3,223,226],"for":[4,116,129,150,211,240],"Directed":[5],"Feedback":[6],"Vertex":[7],"Set":[8,46],"(DFVS)":[9],"on":[10,186],"directed":[11,92],"graphs":[12,101,105,130,167,188],"without":[13,19,133,168,189],"long":[14,173],"cycles.":[15,174],"A":[16],"DFVS":[17,185,213,243],"instance":[18,28,47],"cycles":[20,35,56,78,135,190],"longer":[21],"than":[22,139,194],"$d$":[23,140,195],"naturally":[24],"corresponds":[25],"to":[26,64,235],"an":[27,37],"of":[29,79,89,100,136,191,231,251,263],"$d$-Hitting":[30,45],"Set,":[31],"however,":[32],"enumerating":[33,54],"all":[34,55,225],"in":[36,153,199,228],"$n$-vertex":[38],"graph":[39],"and":[40,73,183,214],"then":[41,97],"kernelizing":[42],"the":[43,87,217,229,246,252,260],"resulting":[44],"can":[48,57,142,196],"be":[49,197],"too":[50],"costly,":[51],"as":[52],"already":[53],"take":[58],"time":[59,154,200],"$\u03a9(n^d)$.":[60],"show":[62,176],"how":[63],"compute":[65,143],"a":[66,90,124,144,206,237],"kernel":[67,145,239],"with":[68,146,220],"at":[69,74,81],"most":[70,75,82,158],"$2^dk^d$":[71],"vertices":[72,149],"$d^{3d}k^d$":[76],"induced":[77,134],"length":[80,137,192],"$d$,":[83],"where":[84],"$k$":[85],"is":[86,123],"size":[88],"minimum":[91],"feedback":[93,247],"vertex":[94,248],"set.":[95],"classes":[99,160,179],"whose":[102],"underlying":[103,253],"undirected":[104],"have":[106,180],"bounded":[107],"expansion":[108],"or":[109,171],"are":[110,163],"nowhere":[111,118],"dense.":[112],"prove":[114,215],"that":[115,128,177,216],"every":[117],"dense":[119],"class":[120],"$\\mathscr{C}$":[121],"there":[122],"function":[125],"$f_\\mathscr{C}(d,\u03b5)$":[126],"such":[127],"$G\\in":[131],"\\mathscr{C}$":[132],"greater":[138,193],"we":[141,161],"$f_\\mathscr{C}(d,\u03b5)\\cdot":[147,155],"k^{1+\u03b5}$":[148],"any":[151,169],"$\u03b5>0$":[152],"n^{O(1)}$.":[156,202],"The":[157],"restricted":[159],"consider":[162],"strongly":[164],"connected":[165],"planar":[166,187],"(induced":[170],"non-induced)":[172],"these":[178],"treewidth":[181],"$O(d)$":[182],"hence":[184],"solved":[198],"$2^{O(d)}\\cdot":[201],"finally":[204],"present":[205],"new":[207],"data":[208],"rule":[210,218],"general":[212],"together":[219],"two":[221],"standard":[222],"subsumes":[224],"applied":[227],"work":[230],"Bergougnoux":[232],"et":[233],"al.\\":[234],"obtain":[236],"polynomial":[238],"DFVS[FVS],":[241],"i.e.,":[242],"parameterized":[244],"by":[245,258],"set":[249],"number":[250],"(undirected)":[254],"graph.":[255],"conclude":[257],"studying":[259],"LP-based":[261],"approximation":[262],"DFVS.":[264]},"counts_by_year":[],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}