{"id":"https://openalex.org/W4405076280","doi":"https://doi.org/10.1145/3707208","title":"Faster Matroid Partition Algorithms","display_name":"Faster Matroid Partition Algorithms","publication_year":2024,"publication_date":"2024-12-05","ids":{"openalex":"https://openalex.org/W4405076280","doi":"https://doi.org/10.1145/3707208"},"language":"en","primary_location":{"id":"doi:10.1145/3707208","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3707208","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/3707208","source":{"id":"https://openalex.org/S137348503","display_name":"ACM Transactions on Algorithms","issn_l":"1549-6325","issn":["1549-6325","1549-6333"],"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 Transactions on Algorithms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://dl.acm.org/doi/pdf/10.1145/3707208","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5015314222","display_name":"Tatsuya Terao","orcid":"https://orcid.org/0000-0002-3530-2194"},"institutions":[{"id":"https://openalex.org/I22299242","display_name":"Kyoto University","ror":"https://ror.org/02kpeqv85","country_code":"JP","type":"education","lineage":["https://openalex.org/I22299242"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Tatsuya Terao","raw_affiliation_strings":["Research Institute for Mathematical Sciences, Kyoto University, Kyoto, Japan"],"raw_orcid":"https://orcid.org/0000-0002-3530-2194","affiliations":[{"raw_affiliation_string":"Research Institute for Mathematical Sciences, Kyoto University, Kyoto, Japan","institution_ids":["https://openalex.org/I22299242"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5015314222"],"corresponding_institution_ids":["https://openalex.org/I22299242"],"apc_list":null,"apc_paid":null,"fwci":0.3364,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.63516257,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"21","issue":"2","first_page":"1","last_page":"26"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10829","display_name":"Interconnection Networks and Systems","score":0.9994000196456909,"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"}},"topics":[{"id":"https://openalex.org/T10829","display_name":"Interconnection Networks and Systems","score":0.9994000196456909,"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"}},{"id":"https://openalex.org/T12923","display_name":"Digital Image Processing Techniques","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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":0.9987999796867371,"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/matroid","display_name":"Matroid","score":0.8690935969352722},{"id":"https://openalex.org/keywords/partition","display_name":"Partition (number theory)","score":0.6589415073394775},{"id":"https://openalex.org/keywords/weighted-matroid","display_name":"Weighted matroid","score":0.6093370914459229},{"id":"https://openalex.org/keywords/matroid-partitioning","display_name":"Matroid partitioning","score":0.6021623611450195},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5475645065307617},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.47783517837524414},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4651312232017517},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.46245718002319336},{"id":"https://openalex.org/keywords/oriented-matroid","display_name":"Oriented matroid","score":0.44703546166419983},{"id":"https://openalex.org/keywords/graphic-matroid","display_name":"Graphic matroid","score":0.4088936746120453},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.39209312200546265}],"concepts":[{"id":"https://openalex.org/C106286213","wikidata":"https://www.wikidata.org/wiki/Q898572","display_name":"Matroid","level":2,"score":0.8690935969352722},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.6589415073394775},{"id":"https://openalex.org/C124344645","wikidata":"https://www.wikidata.org/wiki/Q7979897","display_name":"Weighted matroid","level":5,"score":0.6093370914459229},{"id":"https://openalex.org/C22425182","wikidata":"https://www.wikidata.org/wiki/Q6787906","display_name":"Matroid partitioning","level":4,"score":0.6021623611450195},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5475645065307617},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.47783517837524414},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4651312232017517},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.46245718002319336},{"id":"https://openalex.org/C178621168","wikidata":"https://www.wikidata.org/wiki/Q16155113","display_name":"Oriented matroid","level":4,"score":0.44703546166419983},{"id":"https://openalex.org/C111034964","wikidata":"https://www.wikidata.org/wiki/Q5597156","display_name":"Graphic matroid","level":3,"score":0.4088936746120453},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.39209312200546265}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/3707208","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3707208","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/3707208","source":{"id":"https://openalex.org/S137348503","display_name":"ACM Transactions on Algorithms","issn_l":"1549-6325","issn":["1549-6325","1549-6333"],"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 Transactions on Algorithms","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1145/3707208","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3707208","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/3707208","source":{"id":"https://openalex.org/S137348503","display_name":"ACM Transactions on Algorithms","issn_l":"1549-6325","issn":["1549-6325","1549-6333"],"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 Transactions on Algorithms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4405076280.pdf"},"referenced_works_count":25,"referenced_works":["https://openalex.org/W1968695791","https://openalex.org/W1986126741","https://openalex.org/W2020927880","https://openalex.org/W2054232722","https://openalex.org/W2060129302","https://openalex.org/W2071863116","https://openalex.org/W2107547393","https://openalex.org/W2149317019","https://openalex.org/W2157529519","https://openalex.org/W2295819159","https://openalex.org/W2367448765","https://openalex.org/W2931109031","https://openalex.org/W2962877742","https://openalex.org/W2972052550","https://openalex.org/W2988480584","https://openalex.org/W3132265628","https://openalex.org/W3169287155","https://openalex.org/W3183933450","https://openalex.org/W4233985254","https://openalex.org/W4234130962","https://openalex.org/W4324106303","https://openalex.org/W4376639493","https://openalex.org/W4389615669","https://openalex.org/W4390575981","https://openalex.org/W6820289075"],"related_works":["https://openalex.org/W2400862597","https://openalex.org/W1984819493","https://openalex.org/W2058489697","https://openalex.org/W2625145881","https://openalex.org/W2159059797","https://openalex.org/W2072414647","https://openalex.org/W4246417054","https://openalex.org/W2106233458","https://openalex.org/W4226057593","https://openalex.org/W2006784845"],"abstract_inverted_index":{"In":[0,60],"the":[1,76,152,169,179,187],"matroid":[2,65,97,182,195],"partitioning":[3],"problem,":[4],"we":[5,22,132],"are":[6],"given":[7],"\\(k\\)":[8,189],"matroids":[9],"\\(\\mathcal{M}_{1}=(V,\\mathcal{I}_{1}),\\dots,\\mathcal{M}_{k}=(V,\\mathcal{I}_{k})\\)":[10],"defined":[11],"over":[12],"a":[13,26,40,50,64,96,134,165,194],"common":[14],"ground":[15],"set":[16,28,41],"\\(V\\)":[17],"of":[18,31,53,125,151,168,186],"\\(n\\)":[19],"elements,":[20],"and":[21,160,164],"need":[23],"to":[24,94],"find":[25],"partitionable":[27,46],"\\(S\\subseteq":[29,42],"V\\)":[30,43],"largest":[32],"possible":[33],"cardinality,":[34],"denoted":[35],"by":[36,156],"\\(p\\)":[37],".":[38,59,89,111,190],"Here,":[39],"is":[44,84,93,115],"called":[45],"if":[47],"there":[48],"exists":[49],"partition":[51,66,98,196],"\\((S_{1},\\dots,S_{k})\\)":[52],"\\(S\\)":[54],"with":[55],"\\(S_{i}\\in\\mathcal{I}_{i}\\)":[56],"for":[57,181],"\\(i=1,\\ldots,k\\)":[58],"1986,":[61],"Cunningham":[62],"presented":[63],"algorithm":[67,99,197],"that":[68,100,124,198],"uses":[69,101,199],"\\(O(np^{3/2}+kn)\\)":[70],"independence":[71,106,170],"oracle":[72,107,171,202],"queries,":[73,108],"which":[74,121,141],"was":[75],"previously":[77],"known":[78],"best":[79],"algorithm.":[80,127],"This":[81,112],"query":[82,113,172],"complexity":[83,114],"\\(O(n^{5/2})\\)":[85],"when":[86,117],"\\(k\\leq":[87,118],"n\\)":[88,119],"Our":[90,174],"main":[91],"result":[92],"present":[95,133,193],"\\(\\tilde{O}(k^{\\prime":[102],"1/3}np":[103],"+":[104],"kn)\\)":[105],"where":[109],"\\(k^{\\prime}=\\min\\{k,p\\}\\)":[110],"\\(\\tilde{O}(n^{7/3})\\)":[116],",":[120,140],"improves":[122],"upon":[123],"Cunningham\u2019s":[126],"To":[128],"obtain":[129],"our":[130],"algorithm,":[131],"new":[135,146],"approach":[136],"edge":[137],"recycling":[138],"augmentation":[139],"can":[142],"be":[143],"attained":[144],"through":[145],"ideas:":[147],"an":[148],"efficient":[149],"utilization":[150],"binary":[153],"search":[154],"technique":[155],"Nguy":[157],"\\(\\tilde{{\\hat{\\text{e}}}}\\)":[158],"n":[159],"Chakrabarty":[161],"et":[162],"al.":[163],"careful":[166],"analysis":[167,175],"complexity.":[173],"differs":[176],"significantly":[177],"from":[178],"one":[180],"intersection":[183],"algorithms,":[184],"because":[185],"parameter":[188],"We":[191],"also":[192],"\\(\\tilde{O}((n+k)\\sqrt{p})\\)":[200],"rank":[201],"queries.":[203]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
