{"id":"https://openalex.org/W4404193691","doi":"https://doi.org/10.1007/s00453-024-01282-9","title":"Optimal Algorithms for Online b-Matching with Variable Vertex Capacities","display_name":"Optimal Algorithms for Online b-Matching with Variable Vertex Capacities","publication_year":2024,"publication_date":"2024-11-08","ids":{"openalex":"https://openalex.org/W4404193691","doi":"https://doi.org/10.1007/s00453-024-01282-9"},"language":"lv","primary_location":{"id":"doi:10.1007/s00453-024-01282-9","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00453-024-01282-9","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00453-024-01282-9.pdf","source":{"id":"https://openalex.org/S89324355","display_name":"Algorithmica","issn_l":"0178-4617","issn":["0178-4617","1432-0541"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithmica","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00453-024-01282-9.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5074909595","display_name":"Susanne Albers","orcid":"https://orcid.org/0000-0001-5848-5360"},"institutions":[{"id":"https://openalex.org/I62916508","display_name":"Technical University of Munich","ror":"https://ror.org/02kkvpp62","country_code":"DE","type":"education","lineage":["https://openalex.org/I62916508"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Susanne Albers","raw_affiliation_strings":["Department of Computer Science, Technical University of Munich, Garching, Germany"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Technical University of Munich, Garching, Germany","institution_ids":["https://openalex.org/I62916508"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5103269021","display_name":"Sebastian Schubert","orcid":"https://orcid.org/0000-0002-3883-2297"},"institutions":[{"id":"https://openalex.org/I62916508","display_name":"Technical University of Munich","ror":"https://ror.org/02kkvpp62","country_code":"DE","type":"education","lineage":["https://openalex.org/I62916508"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Sebastian Schubert","raw_affiliation_strings":["Department of Computer Science, Technical University of Munich, Garching, Germany"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Technical University of Munich, Garching, Germany","institution_ids":["https://openalex.org/I62916508"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5074909595"],"corresponding_institution_ids":["https://openalex.org/I62916508"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":0.3406,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.62805366,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"87","issue":"2","first_page":"167","last_page":"190"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12288","display_name":"Optimization and Search Problems","score":1.0,"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/T12288","display_name":"Optimization and Search Problems","score":1.0,"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/T11478","display_name":"Caching and Content Delivery","score":0.9952999949455261,"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/T12101","display_name":"Advanced Bandit Algorithms Research","score":0.9829000234603882,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.6226650476455688},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.5569244027137756},{"id":"https://openalex.org/keywords/matching","display_name":"Matching (statistics)","score":0.5144312977790833},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5051999688148499},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4941418468952179},{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.4356618821620941},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.43322238326072693},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3958234190940857},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3254089653491974},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.3213356137275696},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.08949002623558044}],"concepts":[{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.6226650476455688},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5569244027137756},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.5144312977790833},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5051999688148499},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4941418468952179},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.4356618821620941},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.43322238326072693},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3958234190940857},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3254089653491974},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.3213356137275696},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.08949002623558044},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s00453-024-01282-9","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00453-024-01282-9","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00453-024-01282-9.pdf","source":{"id":"https://openalex.org/S89324355","display_name":"Algorithmica","issn_l":"0178-4617","issn":["0178-4617","1432-0541"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithmica","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s00453-024-01282-9","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00453-024-01282-9","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00453-024-01282-9.pdf","source":{"id":"https://openalex.org/S89324355","display_name":"Algorithmica","issn_l":"0178-4617","issn":["0178-4617","1432-0541"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithmica","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2363520468","display_name":null,"funder_award_id":"277991500","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G6743243744","display_name":null,"funder_award_id":"unknown","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G8330397625","display_name":null,"funder_award_id":"Funding","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G8928656450","display_name":null,"funder_award_id":"Projekt DEAL","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320323383","display_name":"Technische Universit\u00e4t M\u00fcnchen","ror":"https://ror.org/02kkvpp62"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4404193691.pdf","grobid_xml":"https://content.openalex.org/works/W4404193691.grobid-xml"},"referenced_works_count":27,"referenced_works":["https://openalex.org/W1496647032","https://openalex.org/W1501694180","https://openalex.org/W1996313212","https://openalex.org/W2048837158","https://openalex.org/W2051294918","https://openalex.org/W2079669094","https://openalex.org/W2085938855","https://openalex.org/W2104224720","https://openalex.org/W2131951207","https://openalex.org/W2155096670","https://openalex.org/W2160702061","https://openalex.org/W2162656786","https://openalex.org/W2899702797","https://openalex.org/W2949565166","https://openalex.org/W2972193181","https://openalex.org/W2974337481","https://openalex.org/W3035275081","https://openalex.org/W3126370525","https://openalex.org/W4205598973","https://openalex.org/W4231916799","https://openalex.org/W4240320731","https://openalex.org/W4247154108","https://openalex.org/W4250340495","https://openalex.org/W4288346441","https://openalex.org/W4298227433","https://openalex.org/W4316652250","https://openalex.org/W4383557903"],"related_works":["https://openalex.org/W1972035260","https://openalex.org/W2064563243","https://openalex.org/W4250775169","https://openalex.org/W4301594054","https://openalex.org/W2794488505","https://openalex.org/W4309231192","https://openalex.org/W3125889879","https://openalex.org/W3124422538","https://openalex.org/W2295467472","https://openalex.org/W3046451053"],"abstract_inverted_index":{"Abstract":[0],"We":[1,132,188],"study":[2,121,178],"the":[3,72,109,112,122,135,161,172,179,191,201,222,284,293,306],"b":[4,295,307],"-matching":[5,296,308],"problem,":[6],"which":[7],"generalizes":[8],"classical":[9],"online":[10,94,140],"matching":[11,76],"introduced":[12],"by":[13,159,183,239],"Karp,":[14,184],"Vazirani":[15,17,185],"and":[16,95,138,156,167,186,252,310],"(STOC":[18],"1990).":[19],"Consider":[20],"a":[21,57,60,152,197,233,301,312],"bipartite":[22],"graph":[23,259],"$$G=(S\\dot{\\cup":[24],"}R,E)$$":[25],"<mml:math":[26,48,63,82,209,241,265],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[27,49,64,83,210,242,266],"<mml:mrow>":[28,50,84,211,267,270],"<mml:mi>G</mml:mi>":[29],"<mml:mo>=</mml:mo>":[30],"<mml:mo>(</mml:mo>":[31],"<mml:mi>S</mml:mi>":[32,53,273],"<mml:mover>":[33],"<mml:mo>\u222a</mml:mo>":[34],"<mml:mo>\u02d9</mml:mo>":[35],"</mml:mover>":[36],"<mml:mi>R</mml:mi>":[37,87],"<mml:mo>,</mml:mo>":[38],"<mml:mi>E</mml:mi>":[39],"<mml:mo>)</mml:mo>":[40],"</mml:mrow>":[41,54,88,217,274,280],"</mml:math>":[42,55,69,89,218,247,281],".":[43],"Every":[44],"vertex":[45],"$$s\\in":[46],"S$$":[47],"<mml:mi>s</mml:mi>":[51,67,245,271,278],"<mml:mo>\u2208</mml:mo>":[52,86,272],"is":[56,106,227],"server":[58,223,237],"with":[59,260],"capacity":[61,251],"$$b_s$$":[62,240],"<mml:msub>":[65,243,268,276],"<mml:mi>b</mml:mi>":[66,244,277],"</mml:msub>":[68,246,275,279],",":[70,219],"indicating":[71],"number":[73],"of":[74,111,164,174,200,207,221,249],"possible":[75],"partners.":[77],"The":[78,104],"vertices":[79,248,282],"$$r\\in":[80],"R$$":[81],"<mml:mi>r</mml:mi>":[85],"are":[90],"requests":[91],"that":[92,134,190],"arrive":[93],"must":[96],"be":[97],"matched":[98],"immediately":[99],"to":[100,107,117,230,232,253,292],"an":[101,204],"eligible":[102],"server.":[103],"goal":[105],"maximize":[108],"cardinality":[110],"constructed":[113],"matching.":[114],"In":[115,171],"contrast":[116],"earlier":[118],"work,":[119],"we":[120,150,177,288,299],"general":[123],"setting":[124],"where":[125],"servers":[126],"may":[127],"have":[128],"arbitrary,":[129],"individual":[130],"capacities.":[131,224],"prove":[133,189],"most":[136],"natural":[137],"simple":[139],"algorithms":[141,176],"achieve":[142],"optimal":[143,205],"competitive":[144],"ratios.":[145],"As":[146],"for":[147,305],"deterministic":[148],"algorithms,":[149],"give":[151],"greedy":[153],"algorithm":[154,182],"RelativeBalance":[155],"analyze":[157],"it":[158,226],"extending":[160],"primal-dual":[162,313],"framework":[163],"Devanur,":[165],"Jain":[166],"Kleinberg":[168],"(SODA":[169],"2013).":[170],"area":[173],"randomized":[175],"celebrated":[180],"Ranking":[181,193,256],"Vazirani.":[187],"original":[192],"strategy,":[194],"simply":[195],"picking":[196],"random":[198],"permutation":[199],"servers,":[202],"achieves":[203],"competitiveness":[206],"$$1-1/e$$":[208],"<mml:mn>1</mml:mn>":[212,214],"<mml:mo>-</mml:mo>":[213],"<mml:mo>/</mml:mo>":[215],"<mml:mi>e</mml:mi>":[216],"independently":[220],"Hence":[225],"not":[228],"necessary":[229],"resort":[231],"reduction,":[234],"replacing":[235],"every":[236],"s":[238],"unit":[250],"then":[254],"run":[255],"on":[257,283],"this":[258,290],"$$\\sum":[261],"_{s\\in":[262],"S}":[263],"b_s$$":[264],"<mml:mo>\u2211</mml:mo>":[269],"left-hand":[285],"side.":[286],"Additionally,":[287],"extend":[289],"result":[291],"vertex-weighted":[294],"problem.":[297],"Technically,":[298],"formulate":[300],"new":[302],"configuration":[303],"LP":[304],"problem":[309],"conduct":[311],"analysis.":[314]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-04-16T08:26:57.006410","created_date":"2025-10-10T00:00:00"}
