{"id":"https://openalex.org/W4360889771","doi":"https://doi.org/10.48550/arxiv.2303.12850","title":"Polyhedral Aspects of Feedback Vertex Set and Pseudoforest Deletion Set","display_name":"Polyhedral Aspects of Feedback Vertex Set and Pseudoforest Deletion Set","publication_year":2023,"publication_date":"2023-03-22","ids":{"openalex":"https://openalex.org/W4360889771","doi":"https://doi.org/10.48550/arxiv.2303.12850"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2303.12850","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2303.12850","pdf_url":"https://arxiv.org/pdf/2303.12850","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":"","raw_type":"text"},"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2303.12850","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5011591780","display_name":"Karthekeyan Chandrasekaran","orcid":"https://orcid.org/0000-0002-3421-7238"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chandrasekaran, Karthekeyan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5036503505","display_name":"Chandra Chekuri","orcid":"https://orcid.org/0000-0003-3035-1699"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chekuri, Chandra","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5001781037","display_name":"Samuel Fiorini","orcid":"https://orcid.org/0000-0002-6845-9008"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Fiorini, Samuel","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5083306523","display_name":"Shubhang Kulkarni","orcid":"https://orcid.org/0000-0002-1670-6011"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kulkarni, Shubhang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5023809656","display_name":"Stefan Weltge","orcid":"https://orcid.org/0000-0002-0102-8326"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Weltge, Stefan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":5,"corresponding_author_ids":[],"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.984499990940094,"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":0.984499990940094,"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":0.9765999913215637,"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/T12288","display_name":"Optimization and Search Problems","score":0.9587000012397766,"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/combinatorics","display_name":"Combinatorics","score":0.6694496273994446},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.6335003972053528},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.6194218397140503},{"id":"https://openalex.org/keywords/feedback-vertex-set","display_name":"Feedback vertex set","score":0.5924193263053894},{"id":"https://openalex.org/keywords/approximation-algorithm","display_name":"Approximation algorithm","score":0.5551877021789551},{"id":"https://openalex.org/keywords/linear-programming-relaxation","display_name":"Linear programming relaxation","score":0.5461491346359253},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.5031372904777527},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.49659663438796997},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4958401620388031},{"id":"https://openalex.org/keywords/parameterized-complexity","display_name":"Parameterized complexity","score":0.48395851254463196},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.4838070273399353},{"id":"https://openalex.org/keywords/undirected-graph","display_name":"Undirected graph","score":0.480844110250473},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.43890848755836487},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.41611552238464355},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4096395671367645},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.39091694355010986},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.29655539989471436},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.253821462392807}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6694496273994446},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.6335003972053528},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.6194218397140503},{"id":"https://openalex.org/C28723256","wikidata":"https://www.wikidata.org/wiki/Q1400918","display_name":"Feedback vertex set","level":4,"score":0.5924193263053894},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.5551877021789551},{"id":"https://openalex.org/C25360446","wikidata":"https://www.wikidata.org/wiki/Q1512771","display_name":"Linear programming relaxation","level":3,"score":0.5461491346359253},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.5031372904777527},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.49659663438796997},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4958401620388031},{"id":"https://openalex.org/C165464430","wikidata":"https://www.wikidata.org/wiki/Q1570441","display_name":"Parameterized complexity","level":2,"score":0.48395851254463196},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.4838070273399353},{"id":"https://openalex.org/C3018234147","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Undirected graph","level":3,"score":0.480844110250473},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.43890848755836487},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.41611552238464355},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4096395671367645},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.39091694355010986},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.29655539989471436},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.253821462392807},{"id":"https://openalex.org/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"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/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2303.12850","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2303.12850","pdf_url":"https://arxiv.org/pdf/2303.12850","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":"","raw_type":"text"},{"id":"doi:10.48550/arxiv.2303.12850","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2303.12850","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:2303.12850","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2303.12850","pdf_url":"https://arxiv.org/pdf/2303.12850","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":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2064821865","display_name":"AF: Small: Faster and Better Algorithms for, and via, Mathematical Programming Relaxations","funder_award_id":"1910149","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G346530407","display_name":null,"funder_award_id":"CCF-1910149","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5234195991","display_name":"AF: Small: Cuts, Connectivity and Partitioning in Graphs, Hypergraphs and Beyond","funder_award_id":"1907937","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5827077194","display_name":"AF: Small: Collaborative Research: Matrix Signings and Algorithms for Expanders and Combinatorial Nullstellensatz","funder_award_id":"1814613","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7305375270","display_name":null,"funder_award_id":"451026932","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G847537906","display_name":null,"funder_award_id":"CCF-1907937","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320328568","display_name":"Hausdorff Center for Mathematics","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4360889771.pdf","grobid_xml":"https://content.openalex.org/works/W4360889771.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2402064113","https://openalex.org/W2593080689","https://openalex.org/W1991979416","https://openalex.org/W3215145351","https://openalex.org/W2396010974","https://openalex.org/W2254726702","https://openalex.org/W43934320","https://openalex.org/W4387498444","https://openalex.org/W2395976569","https://openalex.org/W4286853492"],"abstract_inverted_index":{"We":[0,253],"consider":[1],"the":[2,61,76,199,230,249,269],"feedback":[3],"vertex":[4,22],"set":[5,234],"problem":[6,48,235],"in":[7,146,176,190,201,242],"undirected":[8,17],"graphs":[9],"(FVS).":[10],"The":[11,24,187],"input":[12],"to":[13,27,196,248],"FVS":[14,43,93,155,170,220],"is":[15,26,41,44,85,130,183],"an":[16,208,256],"graph":[18],"$G=(V,E)$":[19],"with":[20,94],"non-negative":[21],"costs.":[23],"goal":[25],"find":[28],"a":[29,45,53,95,112,117,151,246,261,272],"minimum":[30],"cost":[31],"subset":[32],"of":[33,78,99,154,211],"vertices":[34],"$S":[35],"\\subseteq":[36],"V$":[37],"such":[38],"that":[39,126,198],"$G-S$":[40],"acyclic.":[42],"well-known":[46],"NP-hard":[47],"and":[49,70,107,124,137,156,179,203,226,265],"does":[50],"not":[51],"admit":[52],"$(2-\u03b5)$-approximation":[54],"for":[55,81,92,116,134,140,169,215,219,229,239,260,263,268,275],"any":[56],"fixed":[57],"$\u03b5&gt;":[58],"0$":[59],"assuming":[60],"Unique":[62],"Games":[63],"Conjecture.":[64],"There":[65],"are":[66,221,241],"combinatorial":[67],"$2$-approximation":[68],"algorithms":[69,80],"also":[71,139,193,254],"primal-dual":[72],"based":[73],"$2$-approximations.":[74],"Despite":[75],"existence":[77],"these":[79],"several":[82],"decades,":[83],"there":[84],"no":[86],"known":[87],"polynomial-time":[88],"solvable":[89],"LP":[90,114],"relaxation":[91,115],"provable":[96],"integrality":[97,128,181,209],"gap":[98,129,145,182,210],"at":[100,131,184,212],"most":[101,132,185,213],"$2$.":[102,186],"More":[103],"recent":[104],"work":[105],"(Chekuri":[106,202],"Madan,":[108,204],"SODA":[109,205],"'16)":[110,206],"developed":[111],"polynomial-sized":[113],"more":[118],"general":[119],"problem,":[120],"namely":[121],"Subset":[122,135],"FVS,":[123,136,264],"showed":[125],"its":[127],"$13$":[133],"hence":[138],"FVS.":[141,216],"Motivated":[142],"by":[143,223,245],"this":[144,160,191],"our":[147],"knowledge,":[148],"we":[149,162],"undertake":[150],"polyhedral":[152,227],"study":[153],"related":[157],"problems.":[158],"In":[159],"work,":[161],"formulate":[163],"new":[164,188,224],"integer":[165],"linear":[166],"programs":[167],"(ILPs)":[168],"whose":[171,180],"LP-relaxation":[172,262],"can":[173],"be":[174],"solved":[175],"polynomial":[177],"time,":[178],"insights":[189],"process":[192],"enable":[194],"us":[195],"prove":[197],"formulation":[200],"has":[207],"$2$":[214],"Our":[217,237],"results":[218,228],"inspired":[222,244],"formulations":[225,238],"closely-related":[231],"pseudoforest":[232],"deletion":[233],"(PFDS).":[236],"PFDS":[240],"turn":[243],"connection":[247],"densest":[250],"subgraph":[251],"problem.":[252],"conjecture":[255,270],"extreme":[257],"point":[258],"property":[259],"give":[266],"evidence":[267],"via":[271],"corresponding":[273],"result":[274],"PFDS.":[276]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
