{"id":"https://openalex.org/W7223661613","doi":"https://doi.org/10.48550/arxiv.2610.32798","title":"Proximity Theorem and FPT Algorithm for Minimum Group-labeled Matroid Bases","display_name":"Proximity Theorem and FPT Algorithm for Minimum Group-labeled Matroid Bases","publication_year":2026,"publication_date":"2026-10-23","ids":{"openalex":"https://openalex.org/W7223661613","doi":"https://doi.org/10.48550/arxiv.2610.32798"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.32798","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.32798","pdf_url":"https://arxiv.org/pdf/2610.32798","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.32798","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5159633074","display_name":"Siyue Liu","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]},{"id":"https://openalex.org/I98285908","display_name":"The University of Osaka","ror":"https://ror.org/035t8zc32","country_code":"JP","type":"education","lineage":["https://openalex.org/I98285908"]}],"countries":["JP","US"],"is_corresponding":false,"raw_author_name":"Liu, Siyue","raw_affiliation_strings":["Carnegie Mellon University , Pittsburgh , USA","Center , The University of Osaka , Osaka , Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Carnegie Mellon University , Pittsburgh , USA","institution_ids":["https://openalex.org/I74973139"]},{"raw_affiliation_string":"Center , The University of Osaka , Osaka , Japan","institution_ids":["https://openalex.org/I98285908"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5056811970","display_name":"Taihei Oki","orcid":"https://orcid.org/0000-0002-6862-9484","observed_orcids":["https://orcid.org/0000-0002-6862-9484"]},"institutions":[{"id":"https://openalex.org/I205349734","display_name":"Hokkaido University","ror":"https://ror.org/02e16g702","country_code":"JP","type":"education","lineage":["https://openalex.org/I205349734"]},{"id":"https://openalex.org/I4210110652","display_name":"RIKEN","ror":"https://ror.org/01sjwvz98","country_code":"JP","type":"facility","lineage":["https://openalex.org/I4210110652"]},{"id":"https://openalex.org/I4210126580","display_name":"RIKEN Center for Advanced Intelligence Project","ror":"https://ror.org/03ckxwf91","country_code":"JP","type":"facility","lineage":["https://openalex.org/I4210110652","https://openalex.org/I4210126580"]},{"id":"https://openalex.org/I4405287179","display_name":"Institute for Chemical Reaction Design and Discovery","ror":"https://ror.org/04as0kt69","country_code":"JP","type":"facility","lineage":["https://openalex.org/I205349734","https://openalex.org/I4405287179"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Oki, Taihei","raw_affiliation_strings":["Center for Advanced Intelligence Project , RIKEN , Tokyo , Japan","Institute for Chemical Reaction Design and Discovery (ICReDD) , Hokkaido University , Sapporo , Hokkaido , Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for Advanced Intelligence Project , RIKEN , Tokyo , Japan","institution_ids":["https://openalex.org/I4210110652","https://openalex.org/I4210126580"]},{"raw_affiliation_string":"Institute for Chemical Reaction Design and Discovery (ICReDD) , Hokkaido University , Sapporo , Hokkaido , Japan","institution_ids":["https://openalex.org/I205349734","https://openalex.org/I4405287179"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5159646972","display_name":"Chao Xu","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I150229711","display_name":"University of Electronic Science and Technology of China","ror":"https://ror.org/04qr3zq92","country_code":"CN","type":"education","lineage":["https://openalex.org/I150229711"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xu, Chao","raw_affiliation_strings":["University of Electronic Science and Technology of China , Chengdu , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Electronic Science and Technology of China , Chengdu , China","institution_ids":["https://openalex.org/I150229711"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":7,"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":0.8446999788284302,"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":0.8446999788284302,"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":0.1509000062942505,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.0017000000225380063,"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/matroid-bases","display_name":"matroid bases","score":0.9570000171661377},{"id":"https://openalex.org/keywords/fixed-parameter-tractable-algorithms","display_name":"fixed-parameter tractable algorithms","score":0.9480000138282776},{"id":"https://openalex.org/keywords/exchange-algorithm","display_name":"exchange algorithm","score":0.32600000500679016}],"concepts":[{"id":"https://openalex.org/C165464430","wikidata":"https://www.wikidata.org/wiki/Q1570441","display_name":"Parameterized complexity","level":2,"score":0.7972999811172485},{"id":"https://openalex.org/C42058472","wikidata":"https://www.wikidata.org/wiki/Q810214","display_name":"Base (topology)","level":2,"score":0.710099995136261},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.682200014591217},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6366000175476074},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5206999778747559},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.49399998784065247},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.46889999508857727},{"id":"https://openalex.org/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.4577000141143799},{"id":"https://openalex.org/C106286213","wikidata":"https://www.wikidata.org/wiki/Q898572","display_name":"Matroid","level":2,"score":0.3707999885082245},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.3125999867916107},{"id":"https://openalex.org/C3018263672","wikidata":"https://www.wikidata.org/wiki/Q1296251","display_name":"Efficient algorithm","level":2,"score":0.27160000801086426},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.25049999356269836}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.32798","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.32798","pdf_url":"https://arxiv.org/pdf/2610.32798","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2610.32798","doi":"https://doi.org/10.48550/arxiv.2610.32798","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.32798","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.32798","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.32798","pdf_url":"https://arxiv.org/pdf/2610.32798","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320334764","display_name":"Japan Society for the Promotion of Science","ror":"https://ror.org/00hhkn466"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7223661613.pdf","grobid_xml":"https://content.openalex.org/works/W7223661613.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W7214002820"],"related_works":["https://openalex.org/W7025027579","https://openalex.org/W6940383195","https://openalex.org/W7221364310","https://openalex.org/W4404848070","https://openalex.org/W7221076663","https://openalex.org/W7214002820","https://openalex.org/W4398180118","https://openalex.org/W111452217","https://openalex.org/W278318464","https://openalex.org/W7057834316"],"abstract_inverted_index":{"Let":[0],"$M$":[1],"be":[2,8,22,50],"a":[3,9,45,110,127],"matroid,":[4],"let":[5,19],"$\\ell:E(M)\\to":[6],"G$":[7,21],"labeling":[10],"of":[11,32,83,129],"its":[12,33],"elements":[13,34],"by":[14,67,115,124],"an":[15,105,120],"abelian":[16],"group,":[17],"and":[18,72,88],"$F\\subseteq":[20],"finite.":[23],"A":[24],"base":[25,48,55,113],"is":[26,35,78],"$F$-avoiding":[27,47,112],"if":[28],"the":[29,63,81],"label":[30],"sum":[31],"not":[36],"in":[37,86,101],"$F$.":[38],"We":[39,117],"prove":[40],"that,":[41],"for":[42],"arbitrary":[43],"costs,":[44],"min-cost":[46,54,111],"can":[49],"obtained":[51],"from":[52],"any":[53],"using":[56],"at":[57],"most":[58],"$|F|$":[59],"exchanges.":[60],"This":[61],"resolves":[62],"weighted":[64],"proximity":[65,96],"conjecture":[66],"H\u00f6rsch,":[68],"Imolay,":[69],"Mizutani,":[70],"Oki,":[71],"Schwarcz.":[73],"Our":[74],"main":[75],"technical":[76],"tool":[77],"to":[79],"replace":[80],"assumption":[82],"Schrijver--Seymour":[84],"Conjecture":[85],"Liu":[87],"Xu's":[89],"earlier":[90,102],"work":[91,103],"with":[92,99],"Kemperman--Scherk":[93],"Theorem.":[94],"The":[95],"theorem":[97],"combined":[98],"approaches":[100],"gives":[104],"FPT":[106,121],"algorithm":[107,122],"that":[108],"finds":[109],"parameterized":[114,123],"$|G|$.":[116],"additionally":[118],"give":[119],"$|F|$,":[125],"answering":[126],"question":[128],"H\u00f6rsch":[130],"et":[131],"al.":[132]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-27T00:00:00"}
