{"id":"https://openalex.org/W7151933649","doi":"https://doi.org/10.48550/arxiv.2604.05528","title":"Parameterized algorithms for $k$-Inversion","display_name":"Parameterized algorithms for $k$-Inversion","publication_year":2026,"publication_date":"2026-04-07","ids":{"openalex":"https://openalex.org/W7151933649","doi":"https://doi.org/10.48550/arxiv.2604.05528"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2604.05528","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.05528","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":false,"raw_source_name":null,"raw_type":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2604.05528","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5133203756","display_name":"Dhanyamol Antony","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Antony, Dhanyamol","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5133220025","display_name":"L. Sunil Chandran","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chandran, L. Sunil","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5012172898","display_name":"Dalu Jacob","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jacob, Dalu","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5133212471","display_name":"R. B. Sandeep","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sandeep, R. B.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"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":0.7684000134468079,"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":0.7684000134468079,"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":0.18330000340938568,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.020899999886751175,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/directed-graph","display_name":"Directed graph","score":0.5827000141143799},{"id":"https://openalex.org/keywords/feedback-arc-set","display_name":"Feedback arc set","score":0.4505999982357025},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.43720000982284546},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.41589999198913574},{"id":"https://openalex.org/keywords/parameterized-complexity","display_name":"Parameterized complexity","score":0.4034999907016754},{"id":"https://openalex.org/keywords/tuple","display_name":"Tuple","score":0.3935999870300293},{"id":"https://openalex.org/keywords/comparability-graph","display_name":"Comparability graph","score":0.3921000063419342},{"id":"https://openalex.org/keywords/treewidth","display_name":"Treewidth","score":0.3752000033855438},{"id":"https://openalex.org/keywords/null-graph","display_name":"Null graph","score":0.3734999895095825}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6744999885559082},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6553999781608582},{"id":"https://openalex.org/C146380142","wikidata":"https://www.wikidata.org/wiki/Q1137726","display_name":"Directed graph","level":2,"score":0.5827000141143799},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5059999823570251},{"id":"https://openalex.org/C157951044","wikidata":"https://www.wikidata.org/wiki/Q1400910","display_name":"Feedback arc set","level":5,"score":0.4505999982357025},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.43720000982284546},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.41589999198913574},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4059000015258789},{"id":"https://openalex.org/C165464430","wikidata":"https://www.wikidata.org/wiki/Q1570441","display_name":"Parameterized complexity","level":2,"score":0.4034999907016754},{"id":"https://openalex.org/C118930307","wikidata":"https://www.wikidata.org/wiki/Q600590","display_name":"Tuple","level":2,"score":0.3935999870300293},{"id":"https://openalex.org/C198414033","wikidata":"https://www.wikidata.org/wiki/Q5155607","display_name":"Comparability graph","level":5,"score":0.3921000063419342},{"id":"https://openalex.org/C132569581","wikidata":"https://www.wikidata.org/wiki/Q5067368","display_name":"Treewidth","level":5,"score":0.3752000033855438},{"id":"https://openalex.org/C17169500","wikidata":"https://www.wikidata.org/wiki/Q3033506","display_name":"Null graph","level":5,"score":0.3734999895095825},{"id":"https://openalex.org/C3018234147","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Undirected graph","level":3,"score":0.3734999895095825},{"id":"https://openalex.org/C43413943","wikidata":"https://www.wikidata.org/wiki/Q4927193","display_name":"Block graph","level":5,"score":0.3580000102519989},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.349700003862381},{"id":"https://openalex.org/C38754835","wikidata":"https://www.wikidata.org/wiki/Q2003238","display_name":"Strongly connected component","level":2,"score":0.3287999927997589},{"id":"https://openalex.org/C161677786","wikidata":"https://www.wikidata.org/wiki/Q2478475","display_name":"Neighbourhood (mathematics)","level":2,"score":0.2978000044822693},{"id":"https://openalex.org/C136975688","wikidata":"https://www.wikidata.org/wiki/Q1320634","display_name":"Tournament","level":2,"score":0.296999990940094},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.27730000019073486},{"id":"https://openalex.org/C18819970","wikidata":"https://www.wikidata.org/wiki/Q3035340","display_name":"Butterfly graph","level":5,"score":0.27320000529289246},{"id":"https://openalex.org/C28723256","wikidata":"https://www.wikidata.org/wiki/Q1400918","display_name":"Feedback vertex set","level":4,"score":0.2648000121116638},{"id":"https://openalex.org/C101837359","wikidata":"https://www.wikidata.org/wiki/Q547823","display_name":"Planar graph","level":3,"score":0.2612999975681305},{"id":"https://openalex.org/C146661039","wikidata":"https://www.wikidata.org/wiki/Q2915204","display_name":"Dominating set","level":4,"score":0.2599000036716461},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.2587999999523163},{"id":"https://openalex.org/C64339825","wikidata":"https://www.wikidata.org/wiki/Q722659","display_name":"Graph property","level":5,"score":0.257999986410141},{"id":"https://openalex.org/C19332903","wikidata":"https://www.wikidata.org/wiki/Q7623247","display_name":"Strength of a graph","level":5,"score":0.2565999925136566}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2604.05528","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.05528","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":"doi:10.48550/arxiv.2604.05528","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.05528","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":false,"raw_source_name":null,"raw_type":"article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Inversion":[0],"of":[1,24,37,48,77,92,113,136,167,189,220],"a":[2,9,42,70,74,93,110,145,164,193],"directed":[3,15,55,94,205],"graph":[4,16,56,82,95,188],"$D$":[5,19,38,78,96,108],"with":[6,39,62,207],"respect":[7,40,63],"to":[8,41,64,105,163,177],"vertex":[10,49],"subset":[11],"$Y$":[12],"is":[13,51,72,83,104,130,192],"the":[14,22,35,54,80,86,89,102,128,168,185,190,218,221],"obtained":[17,57],"from":[18],"by":[20,58,151],"reversing":[21],"direction":[23],"every":[25,133],"arc":[26],"whose":[27],"endpoints":[28],"both":[29],"lie":[30],"in":[31],"$Y$.":[32],"More":[33],"generally,":[34],"inversion":[36],"tuple":[43,71],"$(Y_1,":[44],"Y_2,":[45,66],"\\ldots,":[46,67],"Y_\\ell)$":[47],"subsets":[50],"defined":[52],"as":[53],"successively":[59],"applying":[60],"inversions":[61],"$Y_1,":[65],"Y_\\ell$.":[68],"Such":[69],"called":[73],"\\emph{decycling":[75],"family}":[76],"if":[79],"resulting":[81],"acyclic.":[84],"In":[85,156],"\\textsc{$k$-Inversion}":[87,183,202],"problem,":[88],"input":[90,191],"consists":[91],"and":[97,101,143,172],"an":[98,179,199],"integer":[99],"$k$,":[100,137],"task":[103],"decide":[106],"whether":[107],"admits":[109],"decycling":[111],"family":[112],"size":[114],"at":[115],"most":[116],"$k$.":[117],"Alon":[118],"et":[119],"al.\\":[120],"(SIAM":[121],"J.\\":[122],"Discrete":[123],"Math.,":[124],"2024)":[125],"proved":[126],"that":[127],"problem":[129,169],"NP-complete":[131],"for":[132,153,182,201],"fixed":[134],"value":[135],"thereby":[138],"ruling":[139],"out":[140],"XP":[141],"algorithms,":[142],"presented":[144],"fixed-parameter":[146],"tractable":[147],"(FPT)":[148],"algorithm":[149,162,181,200],"parameterized":[150],"$k$":[152],"tournament":[154],"inputs.":[155],"this":[157,175],"paper,":[158],"we":[159,197],"generalize":[160],"their":[161],"broader":[165],"variant":[166],"on":[170,203],"tournaments":[171],"subsequently":[173],"use":[174],"result":[176],"obtain":[178,198],"FPT":[180],"when":[184],"underlying":[186,222],"undirected":[187],"block":[194],"graph.":[195,223],"Furthermore,":[196],"general":[204],"graphs":[206],"running":[208],"time":[209],"$2^{O(\\mathrm{tw}(k":[210],"+":[211],"\\mathrm{tw}))}":[212],"\\cdot":[213],"n^{O(1)}$,":[214],"where":[215],"$\\mathrm{tw}$":[216],"denotes":[217],"treewidth":[219]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2026-04-09T00:00:00"}
