{"id":"https://openalex.org/W7148333558","doi":"https://doi.org/10.48550/arxiv.2604.00331","title":"A Unified Framework for Analysis of Randomized Greedy Matching Algorithms","display_name":"A Unified Framework for Analysis of Randomized Greedy Matching Algorithms","publication_year":2026,"publication_date":"2026-04-01","ids":{"openalex":"https://openalex.org/W7148333558","doi":"https://doi.org/10.48550/arxiv.2604.00331"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2604.00331","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.00331","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":null,"license_id":null,"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.2604.00331","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5049873439","display_name":"Mahsa Derakhshan","orcid":"https://orcid.org/0000-0002-8147-0113"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Derakhshan, Mahsa","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5132795904","display_name":"Tao Yu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yu, Tao","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5049873439"],"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/T10991","display_name":"Game Theory and Voting Systems","score":0.633899986743927,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10991","display_name":"Game Theory and Voting Systems","score":0.633899986743927,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T12288","display_name":"Optimization and Search Problems","score":0.1526000052690506,"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":0.08609999716281891,"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/matching","display_name":"Matching (statistics)","score":0.5615000128746033},{"id":"https://openalex.org/keywords/greedy-algorithm","display_name":"Greedy algorithm","score":0.5482000112533569},{"id":"https://openalex.org/keywords/approximation-algorithm","display_name":"Approximation algorithm","score":0.545199990272522},{"id":"https://openalex.org/keywords/bipartite-graph","display_name":"Bipartite graph","score":0.4643000066280365},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.4596000015735626},{"id":"https://openalex.org/keywords/randomized-algorithm","display_name":"Randomized algorithm","score":0.43970000743865967},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.428600013256073},{"id":"https://openalex.org/keywords/ranking","display_name":"Ranking (information retrieval)","score":0.39149999618530273}],"concepts":[{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.5615000128746033},{"id":"https://openalex.org/C51823790","wikidata":"https://www.wikidata.org/wiki/Q504353","display_name":"Greedy algorithm","level":2,"score":0.5482000112533569},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.545199990272522},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5078999996185303},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5016000270843506},{"id":"https://openalex.org/C197657726","wikidata":"https://www.wikidata.org/wiki/Q174733","display_name":"Bipartite graph","level":3,"score":0.4643000066280365},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.4596000015735626},{"id":"https://openalex.org/C128669082","wikidata":"https://www.wikidata.org/wiki/Q583461","display_name":"Randomized algorithm","level":2,"score":0.43970000743865967},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4296000003814697},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.428600013256073},{"id":"https://openalex.org/C189430467","wikidata":"https://www.wikidata.org/wiki/Q7293293","display_name":"Ranking (information retrieval)","level":2,"score":0.39149999618530273},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.38749998807907104},{"id":"https://openalex.org/C2781249084","wikidata":"https://www.wikidata.org/wiki/Q908656","display_name":"Preference","level":2,"score":0.3626999855041504},{"id":"https://openalex.org/C122818955","wikidata":"https://www.wikidata.org/wiki/Q1060343","display_name":"Independent set","level":3,"score":0.3571999967098236},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3513000011444092},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.34709998965263367},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.32510000467300415},{"id":"https://openalex.org/C47458327","wikidata":"https://www.wikidata.org/wiki/Q910404","display_name":"Random graph","level":3,"score":0.31060001254081726},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.30489999055862427},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.30149999260902405},{"id":"https://openalex.org/C196921405","wikidata":"https://www.wikidata.org/wiki/Q786431","display_name":"Online algorithm","level":2,"score":0.2922999858856201},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2904999852180481},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.289900004863739},{"id":"https://openalex.org/C72545166","wikidata":"https://www.wikidata.org/wiki/Q10866593","display_name":"3-dimensional matching","level":4,"score":0.26429998874664307},{"id":"https://openalex.org/C126221529","wikidata":"https://www.wikidata.org/wiki/Q3116070","display_name":"Greedy randomized adaptive search procedure","level":3,"score":0.26429998874664307},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.2621999979019165}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2604.00331","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.00331","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2604.00331","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.00331","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","score":0.5349763035774231,"id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Randomized":[0],"greedy":[1,30,106],"algorithms":[2,66,90,107],"form":[3,226],"one":[4],"of":[5,26,37,89,154,163,175,182],"the":[6,24,35,54,103,109,117,128,160,179],"simplest":[7],"yet":[8],"most":[9],"effective":[10],"approaches":[11],"for":[12,46,85,99,108,156,195,217,246],"computing":[13],"approximate":[14],"matchings":[15],"in":[16,41],"graphs.":[17,205,235],"In":[18,115,236],"this":[19,87],"paper,":[20],"we":[21,171,238,265],"focus":[22],"on":[23,159,178,203],"class":[25,229],"vertex-iterative":[27],"(VI)":[28],"randomized":[29,105],"matching":[31,197,201],"algorithms,":[32],"which":[33],"process":[34],"vertices":[36],"a":[38,60,73,82,140,173],"graph":[39],"$G=(V,E)$":[40],"some":[42],"order":[43,62,119,138,144],"$\u03c0$":[44,77],"and,":[45],"each":[47,70],"vertex":[48],"$v$,":[49],"greedily":[50],"match":[51],"it":[52,93],"to":[53,59,72,94,212],"first":[55],"available":[56],"neighbor":[57],"according":[58],"preference":[61,130,143],"$\u03c3(v)$.":[63,79],"Various":[64],"VI":[65],"have":[67],"been":[68],"studied,":[69],"corresponding":[71],"different":[74],"distribution":[75],"over":[76],"and":[78,91,101,111,125,139,198,233,252],"We":[80,149],"develop":[81],"unified":[83],"framework":[84,208],"analyzing":[86],"family":[88],"use":[92],"obtain":[95,150,172],"improved":[96,214],"approximation":[97,152,193,215],"ratios":[98,194,216],"Ranking":[100,241,268],"FRanking,":[102,170],"state-of-the-art":[104,192],"random-order":[110],"adversarial-order":[112],"settings,":[113],"respectively.":[114],"Ranking,":[116,157],"decision":[118,137],"is":[120,242,269],"drawn":[121],"uniformly":[122,141],"at":[123,243,262,270],"random":[124,142],"used":[126],"as":[127],"common":[129],"order,":[131],"whereas":[132],"FRanking":[133],"uses":[134],"an":[135,151,227],"adversarial":[136],"shared":[145],"by":[146],"all":[147],"vertices.":[148],"ratio":[153,174],"$0.560$":[155],"improving":[158,177],"$0.5469$":[161],"bound":[162,181],"Derakhshan":[164],"et":[165,184],"al.":[166,185],"[SODA":[167],"2026].":[168],"For":[169,254],"$0.539$,":[176],"$0.521$":[180],"Huang":[183],"[JACM":[186],"2020].":[187],"These":[188],"results":[189],"also":[190,209],"imply":[191],"oblivious":[196],"fully":[199],"online":[200],"problems":[202],"general":[204,231],"Our":[206],"analysis":[207],"enables":[210],"us":[211],"prove":[213,266],"graphs":[218,225,232,247,255],"with":[219],"no":[220],"short":[221],"odd":[222,258],"cycles.":[223],"Such":[224],"intermediate":[228],"between":[230],"bipartite":[234],"particular,":[237],"show":[239],"that":[240,248,267],"least":[244,263,271],"$0.570$-competitive":[245],"are":[249],"both":[250],"triangle-free":[251],"pentagon-free.":[253],"whose":[256],"shortest":[257],"cycle":[259],"has":[260],"length":[261],"$129$,":[264],"$0.615$-competitive.":[272]},"counts_by_year":[],"updated_date":"2026-04-03T16:44:17.987007","created_date":"2026-04-03T00:00:00"}