{"id":"https://openalex.org/W3158263509","doi":"https://doi.org/10.1145/3446429","title":"An Exact Method for the Minimum Feedback Arc Set Problem","display_name":"An Exact Method for the Minimum Feedback Arc Set Problem","publication_year":2021,"publication_date":"2021-04-23","ids":{"openalex":"https://openalex.org/W3158263509","doi":"https://doi.org/10.1145/3446429","mag":"3158263509"},"language":"en","primary_location":{"id":"doi:10.1145/3446429","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3446429","pdf_url":null,"source":{"id":"https://openalex.org/S201104086","display_name":"ACM Journal of Experimental Algorithmics","issn_l":"1084-6654","issn":["1084-6654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Journal of Experimental Algorithmics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5053259149","display_name":"Ali Baharev","orcid":"https://orcid.org/0000-0003-4715-9003"},"institutions":[{"id":"https://openalex.org/I129774422","display_name":"University of Vienna","ror":"https://ror.org/03prydq77","country_code":"AT","type":"education","lineage":["https://openalex.org/I129774422"]}],"countries":["AT"],"is_corresponding":true,"raw_author_name":"Ali Baharev","raw_affiliation_strings":["University of Vienna, Wien, Austria"],"raw_orcid":"https://orcid.org/0000-0003-4715-9003","affiliations":[{"raw_affiliation_string":"University of Vienna, Wien, Austria","institution_ids":["https://openalex.org/I129774422"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5024690956","display_name":"Hermann Schichl","orcid":"https://orcid.org/0000-0003-0183-9150"},"institutions":[{"id":"https://openalex.org/I129774422","display_name":"University of Vienna","ror":"https://ror.org/03prydq77","country_code":"AT","type":"education","lineage":["https://openalex.org/I129774422"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Hermann Schichl","raw_affiliation_strings":["University of Vienna, Wien, Austria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Vienna, Wien, Austria","institution_ids":["https://openalex.org/I129774422"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5055137763","display_name":"Arnold Neumaier","orcid":"https://orcid.org/0000-0002-8328-9641"},"institutions":[{"id":"https://openalex.org/I129774422","display_name":"University of Vienna","ror":"https://ror.org/03prydq77","country_code":"AT","type":"education","lineage":["https://openalex.org/I129774422"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Arnold Neumaier","raw_affiliation_strings":["University of Vienna, Wien, Austria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Vienna, Wien, Austria","institution_ids":["https://openalex.org/I129774422"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5016513861","display_name":"Tobias Achterberg","orcid":"https://orcid.org/0000-0002-0862-7065"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Tobias Achterberg","raw_affiliation_strings":["Gurobi GmbH, Frankfurt am Main"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Gurobi GmbH, Frankfurt am Main","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5053259149"],"corresponding_institution_ids":["https://openalex.org/I129774422"],"apc_list":null,"apc_paid":null,"fwci":2.8918,"has_fulltext":false,"cited_by_count":37,"citation_normalized_percentile":{"value":0.91762854,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"26","issue":null,"first_page":"1","last_page":"28"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9968000054359436,"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":0.9968000054359436,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9961000084877014,"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/T11522","display_name":"VLSI and FPGA Design Techniques","score":0.9944000244140625,"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/feedback-arc-set","display_name":"Feedback arc set","score":0.7581037282943726},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5995556712150574},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.5932116508483887},{"id":"https://openalex.org/keywords/cardinality","display_name":"Cardinality (data modeling)","score":0.5779930353164673},{"id":"https://openalex.org/keywords/scalability","display_name":"Scalability","score":0.5538606643676758},{"id":"https://openalex.org/keywords/maximal-independent-set","display_name":"Maximal independent set","score":0.4967718720436096},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4899274706840515},{"id":"https://openalex.org/keywords/arc","display_name":"Arc (geometry)","score":0.48721736669540405},{"id":"https://openalex.org/keywords/set-cover-problem","display_name":"Set cover problem","score":0.447933554649353},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.43734848499298096},{"id":"https://openalex.org/keywords/independent-set","display_name":"Independent set","score":0.4252532124519348},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4009140431880951},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.40082287788391113},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.3468644618988037},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.21176064014434814},{"id":"https://openalex.org/keywords/chordal-graph","display_name":"Chordal graph","score":0.16215303540229797},{"id":"https://openalex.org/keywords/1-planar-graph","display_name":"1-planar graph","score":0.12490692734718323},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.07829666137695312}],"concepts":[{"id":"https://openalex.org/C157951044","wikidata":"https://www.wikidata.org/wiki/Q1400910","display_name":"Feedback arc set","level":5,"score":0.7581037282943726},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5995556712150574},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.5932116508483887},{"id":"https://openalex.org/C87117476","wikidata":"https://www.wikidata.org/wiki/Q362383","display_name":"Cardinality (data modeling)","level":2,"score":0.5779930353164673},{"id":"https://openalex.org/C48044578","wikidata":"https://www.wikidata.org/wiki/Q727490","display_name":"Scalability","level":2,"score":0.5538606643676758},{"id":"https://openalex.org/C18359143","wikidata":"https://www.wikidata.org/wiki/Q7888149","display_name":"Maximal independent set","level":5,"score":0.4967718720436096},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4899274706840515},{"id":"https://openalex.org/C83415579","wikidata":"https://www.wikidata.org/wiki/Q161973","display_name":"Arc (geometry)","level":2,"score":0.48721736669540405},{"id":"https://openalex.org/C100808899","wikidata":"https://www.wikidata.org/wiki/Q1192100","display_name":"Set cover problem","level":3,"score":0.447933554649353},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.43734848499298096},{"id":"https://openalex.org/C122818955","wikidata":"https://www.wikidata.org/wiki/Q1060343","display_name":"Independent set","level":3,"score":0.4252532124519348},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4009140431880951},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.40082287788391113},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.3468644618988037},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.21176064014434814},{"id":"https://openalex.org/C160446614","wikidata":"https://www.wikidata.org/wiki/Q1322892","display_name":"Chordal graph","level":3,"score":0.16215303540229797},{"id":"https://openalex.org/C102192266","wikidata":"https://www.wikidata.org/wiki/Q4545823","display_name":"1-planar graph","level":4,"score":0.12490692734718323},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.07829666137695312},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","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/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.0},{"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/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/3446429","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3446429","pdf_url":null,"source":{"id":"https://openalex.org/S201104086","display_name":"ACM Journal of Experimental Algorithmics","issn_l":"1084-6654","issn":["1084-6654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Journal of Experimental Algorithmics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Industry, innovation and infrastructure","id":"https://metadata.un.org/sdg/9","score":0.5}],"awards":[{"id":"https://openalex.org/G1611280903","display_name":null,"funder_award_id":"P27891-N32","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"}],"funders":[{"id":"https://openalex.org/F4320321181","display_name":"Austrian Science Fund","ror":"https://ror.org/013tf3c58"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":112,"referenced_works":["https://openalex.org/W5833057","https://openalex.org/W22051696","https://openalex.org/W180698138","https://openalex.org/W1518179162","https://openalex.org/W1519532587","https://openalex.org/W1523214132","https://openalex.org/W1605955342","https://openalex.org/W1875185230","https://openalex.org/W1903496173","https://openalex.org/W1964985116","https://openalex.org/W1965226070","https://openalex.org/W1974624244","https://openalex.org/W1975433230","https://openalex.org/W1975442866","https://openalex.org/W1980321924","https://openalex.org/W1980481456","https://openalex.org/W1986978101","https://openalex.org/W1988502684","https://openalex.org/W1992401944","https://openalex.org/W1998141884","https://openalex.org/W2010762484","https://openalex.org/W2011717535","https://openalex.org/W2014328192","https://openalex.org/W2015987140","https://openalex.org/W2016061569","https://openalex.org/W2016590962","https://openalex.org/W2029894006","https://openalex.org/W2030461260","https://openalex.org/W2030784593","https://openalex.org/W2031002162","https://openalex.org/W2035700242","https://openalex.org/W2036257443","https://openalex.org/W2038225707","https://openalex.org/W2040431927","https://openalex.org/W2040831377","https://openalex.org/W2041984665","https://openalex.org/W2042649619","https://openalex.org/W2044489104","https://openalex.org/W2045095115","https://openalex.org/W2045792022","https://openalex.org/W2050781862","https://openalex.org/W2056590617","https://openalex.org/W2057084070","https://openalex.org/W2058702778","https://openalex.org/W2058937865","https://openalex.org/W2061762037","https://openalex.org/W2063980384","https://openalex.org/W2063999066","https://openalex.org/W2065984865","https://openalex.org/W2070745908","https://openalex.org/W2071353749","https://openalex.org/W2071629762","https://openalex.org/W2078007422","https://openalex.org/W2080090262","https://openalex.org/W2081828561","https://openalex.org/W2082806890","https://openalex.org/W2083323965","https://openalex.org/W2083342911","https://openalex.org/W2083791897","https://openalex.org/W2088442730","https://openalex.org/W2092334295","https://openalex.org/W2092413888","https://openalex.org/W2099103397","https://openalex.org/W2103649698","https://openalex.org/W2106984527","https://openalex.org/W2115826669","https://openalex.org/W2116087731","https://openalex.org/W2118382442","https://openalex.org/W2120358419","https://openalex.org/W2125563564","https://openalex.org/W2130606003","https://openalex.org/W2132022337","https://openalex.org/W2133629649","https://openalex.org/W2135986386","https://openalex.org/W2141072246","https://openalex.org/W2144622220","https://openalex.org/W2147258698","https://openalex.org/W2147507759","https://openalex.org/W2149740397","https://openalex.org/W2152241581","https://openalex.org/W2157054705","https://openalex.org/W2160969485","https://openalex.org/W2162446609","https://openalex.org/W2163322487","https://openalex.org/W2167975570","https://openalex.org/W2202036903","https://openalex.org/W2222122796","https://openalex.org/W2318031348","https://openalex.org/W2336259629","https://openalex.org/W2399100674","https://openalex.org/W2484653057","https://openalex.org/W2498234897","https://openalex.org/W2527193322","https://openalex.org/W2561675875","https://openalex.org/W2592574264","https://openalex.org/W2752885492","https://openalex.org/W2761627086","https://openalex.org/W2905110430","https://openalex.org/W2913028927","https://openalex.org/W2953534551","https://openalex.org/W3023311638","https://openalex.org/W4230665353","https://openalex.org/W4231610975","https://openalex.org/W4233794748","https://openalex.org/W4234650083","https://openalex.org/W4238690701","https://openalex.org/W4252973173","https://openalex.org/W4255529553","https://openalex.org/W4291439952","https://openalex.org/W4298227433","https://openalex.org/W4312512934","https://openalex.org/W6940945625"],"related_works":["https://openalex.org/W2103112216","https://openalex.org/W1567570895","https://openalex.org/W1963654174","https://openalex.org/W2963989216","https://openalex.org/W3003449463","https://openalex.org/W4301100693","https://openalex.org/W2804969619","https://openalex.org/W2964258819","https://openalex.org/W1491760138","https://openalex.org/W4292796915"],"abstract_inverted_index":{"A":[0],"feedback":[1,28,41,55,139],"arc":[2,19,29,42,56,140],"set":[3,30,43,49,57,141,156],"of":[4,12,20,31,52,130,147,171,182],"a":[5,10,27,110,127,137,154,186],"directed":[6],"graph":[7],"G":[8,24,68],"is":[9,34,59,100,142],"subset":[11],"its":[13],"arcs":[14],"containing":[15,157],"at":[16],"least":[17],"one":[18],"every":[21],"cycle":[22,118],"in":[23,67,109],".":[25,45],"Finding":[26],"minimum":[32,40,48,54,138],"cardinality":[33],"an":[35,116],"NP-hard":[36],"problem":[37,44,58],"called":[38],"the":[39,47,53,148,180],"Numerically,":[46],"cover":[50],"formulation":[51],"appropriate":[60],"as":[61,63],"long":[62],"all":[64,121],"simple":[65,89,107],"cycles":[66,108,131],"can":[69],"be":[70,134],"enumerated.":[71],"Unfortunately,":[72],"even":[73],"those":[74],"sparse":[75,103,160],"graphs":[76,104,169],"that":[77,105],"are":[78,151,170],"important":[79],"for":[80,102,163,178],"practical":[81,145],"applications":[82],"often":[83],"have":[84],"\u03a9":[85],"(2":[86],"n":[87],")":[88],"cycles.":[90],"Here":[91],"we":[92],"address":[93],"precisely":[94],"such":[95],"situations:":[96],"An":[97],"exact":[98,183],"method":[99,150],"proposed":[101],"enumerates":[106],"lazy":[111],"fashion":[112],"and":[113,174,176],"iteratively":[114],"extends":[115],"incomplete":[117],"matrix.":[119],"In":[120],"cases":[122],"encountered":[123],"so":[124],"far,":[125],"only":[126],"tractable":[128],"number":[129],"has":[132],"to":[133],"enumerated":[135],"until":[136],"found.":[143],"The":[144,166],"limits":[146],"new":[149],"evaluated":[152],"on":[153],"test":[155,168],"computationally":[158],"challenging":[159],"graphs,":[161],"relevant":[162],"industrial":[164],"applications.":[165],"4,468":[167],"varying":[172],"size":[173],"density":[175],"suitable":[177],"testing":[179],"scalability":[181],"algorithms":[184],"over":[185],"wide":[187],"range.":[188]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":10},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2}],"updated_date":"2026-05-18T08:16:58.900851","created_date":"2025-10-10T00:00:00"}