{"id":"https://openalex.org/W4416190484","doi":"https://doi.org/10.48550/arxiv.2511.08210","title":"Forgetting Alternation and Blossoms: A New Framework for Fast Matching Augmentation and Its Applications to Sequential/Distributed/Streaming Computation","display_name":"Forgetting Alternation and Blossoms: A New Framework for Fast Matching Augmentation and Its Applications to Sequential/Distributed/Streaming Computation","publication_year":2025,"publication_date":"2025-11-11","ids":{"openalex":"https://openalex.org/W4416190484","doi":"https://doi.org/10.48550/arxiv.2511.08210"},"language":null,"primary_location":{"id":"pmh:oai:arXiv.org:2511.08210","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2511.08210","pdf_url":"https://arxiv.org/pdf/2511.08210","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":null,"raw_type":"text"},"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2511.08210","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101050681","display_name":"Taisuke Izumi","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Izumi, Taisuke","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5037751789","display_name":"Naoki Kitamura","orcid":"https://orcid.org/0000-0002-3143-7200"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kitamura, Naoki","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5039274625","display_name":"Yutaro Yamaguchi","orcid":"https://orcid.org/0000-0002-1919-7195"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yamaguchi, Yutaro","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5101050681"],"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/T10772","display_name":"Distributed systems and fault tolerance","score":0.5404000282287598,"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/T10772","display_name":"Distributed systems and fault tolerance","score":0.5404000282287598,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.15360000729560852,"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/T12292","display_name":"Graph Theory and Algorithms","score":0.1071000024676323,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/correctness","display_name":"Correctness","score":0.5867999792098999},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.5685999989509583},{"id":"https://openalex.org/keywords/matching","display_name":"Matching (statistics)","score":0.44519999623298645},{"id":"https://openalex.org/keywords/alternation","display_name":"Alternation (linguistics)","score":0.44269999861717224},{"id":"https://openalex.org/keywords/cardinality","display_name":"Cardinality (data modeling)","score":0.37369999289512634},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.3555000126361847},{"id":"https://openalex.org/keywords/data-structure","display_name":"Data structure","score":0.34940001368522644},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.34529998898506165}],"concepts":[{"id":"https://openalex.org/C55439883","wikidata":"https://www.wikidata.org/wiki/Q360812","display_name":"Correctness","level":2,"score":0.5867999792098999},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.5685999989509583},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5098000168800354},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4869000017642975},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.4607999920845032},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.44519999623298645},{"id":"https://openalex.org/C26826806","wikidata":"https://www.wikidata.org/wiki/Q438358","display_name":"Alternation (linguistics)","level":2,"score":0.44269999861717224},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4058000147342682},{"id":"https://openalex.org/C87117476","wikidata":"https://www.wikidata.org/wiki/Q362383","display_name":"Cardinality (data modeling)","level":2,"score":0.37369999289512634},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.36739999055862427},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.3555000126361847},{"id":"https://openalex.org/C162319229","wikidata":"https://www.wikidata.org/wiki/Q175263","display_name":"Data structure","level":2,"score":0.34940001368522644},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.34529998898506165},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.3434000015258789},{"id":"https://openalex.org/C140745168","wikidata":"https://www.wikidata.org/wiki/Q1210082","display_name":"Tree traversal","level":2,"score":0.30709999799728394},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.287200003862381},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.2849999964237213},{"id":"https://openalex.org/C114466953","wikidata":"https://www.wikidata.org/wiki/Q6034165","display_name":"Initialization","level":2,"score":0.27549999952316284},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.26969999074935913},{"id":"https://openalex.org/C42058472","wikidata":"https://www.wikidata.org/wiki/Q810214","display_name":"Base (topology)","level":2,"score":0.25429999828338623},{"id":"https://openalex.org/C94461902","wikidata":"https://www.wikidata.org/wiki/Q2762418","display_name":"Formal proof","level":3,"score":0.2524000108242035},{"id":"https://openalex.org/C68859911","wikidata":"https://www.wikidata.org/wiki/Q1503724","display_name":"Pattern matching","level":2,"score":0.25099998712539673}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2511.08210","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2511.08210","pdf_url":"https://arxiv.org/pdf/2511.08210","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2511.08210","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2511.08210","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:2511.08210","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2511.08210","pdf_url":"https://arxiv.org/pdf/2511.08210","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1069223013","display_name":null,"funder_award_id":"JSPS KAKENHI","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G3459562248","display_name":null,"funder_award_id":"Grant","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G4636223006","display_name":null,"funder_award_id":"JSPS KAK","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G577723003","display_name":"Integrated Techniques and Applications of Enumeration, Optimization, and SAT-Solving Based on Discrete Structure Manipulation","funder_award_id":"25H01114","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G6555438610","display_name":"\u73fe\u5b9f\u7684\u306a\u5165\u529b\u306b\u5bfe\u3057\u3066\u81ea\u5df1\u6700\u9069\u5316\u3059\u308b\u5206\u6563\u30b0\u30e9\u30d5\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u8a2d\u8a08\u6280\u6cd5","funder_award_id":"23K24825","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G7299783129","display_name":"\u8010\u6545\u969c\u6027\u3092\u8003\u616e\u3057\u305f\u5206\u6563\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u8a2d\u8a08","funder_award_id":"23K16838","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G7752643416","display_name":null,"funder_award_id":"Japan","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G8430481527","display_name":null,"funder_award_id":"Number","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"}],"funders":[{"id":"https://openalex.org/F4320334764","display_name":"Japan Society for the Promotion of Science","ror":"https://ror.org/00hhkn466"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4416190484.pdf"},"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Finding":[0],"a":[1,6,84,126,166,182,215,279],"maximum":[2],"cardinality":[3],"matching":[4,154],"in":[5,29,40,75,109,135,196,249],"graph":[7],"is":[8,23,33,47,52,58,148,165,219,290],"one":[9,35],"of":[10,36,104,143,168,193,238,278,282,286,291],"the":[11,27,37,43,66,69,98,105,117,131,141,151,191,233,250,262,268,276],"most":[12],"fundamental":[13],"problems.":[14],"An":[15],"algorithm":[16,45,71],"proposed":[17],"by":[18,97,174],"Micali":[19],"and":[20,51,155,177,199,225,252,259],"Vazirani":[21,77],"(1980)":[22],"well-known":[24],"to":[25,82,149,180,228],"solve":[26],"problem":[28],"$O(m\\sqrt{n})$":[30],"time,":[31],"which":[32,61,218,289],"still":[34],"fastest":[38],"algorithms":[39,248,256,272],"general.":[41],"While":[42],"MV":[44,234],"itself":[46],"not":[48],"so":[49],"complicated":[50],"indeed":[53],"convincing,":[54],"its":[55,230],"correctness":[56,231],"proof":[57,86],"extremely":[59],"challenging,":[60],"can":[62],"be":[63],"seen":[64],"from":[65],"history:":[67],"after":[68],"first":[70],"paper":[72],"had":[73],"appeared":[74],"1980,":[76],"has":[78],"made":[79],"several":[80],"attempts":[81],"give":[83,202],"complete":[85],"for":[87,206],"more":[88,223],"than":[89,232],"40":[90],"years.":[91],"It":[92],"seems,":[93],"roughly":[94],"speaking,":[95],"caused":[96],"nice":[99],"but":[100,222],"highly":[101],"complex":[102],"structure":[103,128,188,211],"shortest":[106,132],"alternating":[107,133,169],"paths":[108,134],"general":[110,136],"graphs":[111,137],"that":[112],"are":[113,257,273],"deeply":[114],"intertwined":[115],"with":[116],"so-called":[118],"(nested)":[119],"blossoms.":[120,144],"In":[121],"this":[122],"paper,":[123],"we":[124,200,213,241],"propose":[125,214],"new":[127,216,244],"theorem":[129,189],"on":[130,209,267,275],"without":[138],"taking":[139],"into":[140],"details":[142],"The":[145,271],"high-level":[146],"idea":[147],"forget":[150],"alternation":[152],"(of":[153],"non-matching":[156],"edges)":[157],"as":[158,160],"early":[159],"possible.":[161],"A":[162],"key":[163],"ingredient":[164],"notion":[167],"base":[170],"trees":[171],"(ABTs)":[172],"introduced":[173],"Izumi,":[175],"Kitamura,":[176],"Yamaguchi":[178],"(2024)":[179],"develop":[181],"nearly":[183],"linear-time":[184],"distributed":[185,251],"algorithm.":[186,235],"Our":[187],"refines":[190],"properties":[192],"ABTs":[194],"exploited":[195],"their":[197],"algorithm,":[198,217],"also":[201,242],"simpler":[203],"alternative":[204],"proofs":[205],"them.":[207],"Based":[208],"our":[210,239],"theorem,":[212],"slightly":[220],"slower":[221],"implementable":[224],"much":[226],"easier":[227],"confirm":[229],"As":[236],"applications":[237],"framework,":[240],"present":[243],"$(1":[245],"-":[246],"\u03b5)$-approximation":[247],"semi-streaming":[253],"settings.":[254],"Both":[255],"deterministic,":[258],"substantially":[260],"improve":[261],"best":[263],"known":[264],"upper":[265],"bounds":[266],"running":[269],"time.":[270],"built":[274],"top":[277],"novel":[280],"framework":[281],"amplifying":[283],"approximation":[284],"factors":[285],"given":[287],"matchings,":[288],"independent":[292],"interest.":[293]},"counts_by_year":[],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-11-13T00:00:00"}