{"id":"https://openalex.org/W2028955990","doi":"https://doi.org/10.1002/(sici)1098-2418(199909)15:2<113::aid-rsa1>3.0.co;2-s","title":"Constructive bounds and exact expectations for the random assignment problem","display_name":"Constructive bounds and exact expectations for the random assignment problem","publication_year":1999,"publication_date":"1999-09-01","ids":{"openalex":"https://openalex.org/W2028955990","doi":"https://doi.org/10.1002/(sici)1098-2418(199909)15:2<113::aid-rsa1>3.0.co;2-s","mag":"2028955990"},"language":"en","primary_location":{"id":"doi:10.1002/(sici)1098-2418(199909)15:2<113::aid-rsa1>3.0.co;2-s","is_oa":false,"landing_page_url":"https://doi.org/10.1002/(sici)1098-2418(199909)15:2<113::aid-rsa1>3.0.co;2-s","pdf_url":null,"source":{"id":"https://openalex.org/S59667848","display_name":"Random Structures and Algorithms","issn_l":"1042-9832","issn":["1042-9832","1098-2418"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Random Structures and Algorithms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5067588072","display_name":"Don Coppersmith","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Don Coppersmith","raw_affiliation_strings":["Department of Mathematical Sciences, IBM T.J. Watson Research Center, P.O. Box 218, Yorktown Heights, NY 10598"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, IBM T.J. Watson Research Center, P.O. Box 218, Yorktown Heights, NY 10598","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5083890565","display_name":"Gregory B. Sorkin","orcid":"https://orcid.org/0000-0003-4935-7820"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Gregory B. Sorkin","raw_affiliation_strings":["Department of Mathematical Sciences, IBM T.J. Watson Research Center, P.O. Box 218, Yorktown Heights, NY 10598"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, IBM T.J. Watson Research Center, P.O. Box 218, Yorktown Heights, NY 10598","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5083890565"],"corresponding_institution_ids":[],"apc_list":{"value":4330,"currency":"USD","value_usd":4330},"apc_paid":null,"fwci":7.6611,"has_fulltext":false,"cited_by_count":72,"citation_normalized_percentile":{"value":0.98440822,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"15","issue":"2","first_page":"113","last_page":"144"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9986000061035156,"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"}},"topics":[{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9986000061035156,"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"}},{"id":"https://openalex.org/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9975000023841858,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9970999956130981,"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/mathematics","display_name":"Mathematics","score":0.8060453534126282},{"id":"https://openalex.org/keywords/bipartite-graph","display_name":"Bipartite graph","score":0.7857633829116821},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.7693793773651123},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7291936874389648},{"id":"https://openalex.org/keywords/constructive","display_name":"Constructive","score":0.6374860405921936},{"id":"https://openalex.org/keywords/limiting","display_name":"Limiting","score":0.5850569009780884},{"id":"https://openalex.org/keywords/constructive-proof","display_name":"Constructive proof","score":0.5687697529792786},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.565650224685669},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5376002192497253},{"id":"https://openalex.org/keywords/matching","display_name":"Matching (statistics)","score":0.5305647850036621},{"id":"https://openalex.org/keywords/random-graph","display_name":"Random graph","score":0.4714432954788208},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.3526684641838074},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.17101022601127625},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.09371700882911682}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8060453534126282},{"id":"https://openalex.org/C197657726","wikidata":"https://www.wikidata.org/wiki/Q174733","display_name":"Bipartite graph","level":3,"score":0.7857633829116821},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.7693793773651123},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7291936874389648},{"id":"https://openalex.org/C2778701210","wikidata":"https://www.wikidata.org/wiki/Q28130034","display_name":"Constructive","level":3,"score":0.6374860405921936},{"id":"https://openalex.org/C188198153","wikidata":"https://www.wikidata.org/wiki/Q1613840","display_name":"Limiting","level":2,"score":0.5850569009780884},{"id":"https://openalex.org/C202854965","wikidata":"https://www.wikidata.org/wiki/Q3044470","display_name":"Constructive proof","level":2,"score":0.5687697529792786},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.565650224685669},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5376002192497253},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.5305647850036621},{"id":"https://openalex.org/C47458327","wikidata":"https://www.wikidata.org/wiki/Q910404","display_name":"Random graph","level":3,"score":0.4714432954788208},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.3526684641838074},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.17101022601127625},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09371700882911682},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1002/(sici)1098-2418(199909)15:2<113::aid-rsa1>3.0.co;2-s","is_oa":false,"landing_page_url":"https://doi.org/10.1002/(sici)1098-2418(199909)15:2<113::aid-rsa1>3.0.co;2-s","pdf_url":null,"source":{"id":"https://openalex.org/S59667848","display_name":"Random Structures and Algorithms","issn_l":"1042-9832","issn":["1042-9832","1098-2418"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Random Structures and Algorithms","raw_type":"journal-article"},{"id":"pmh:oai:researchonline.lse.ac.uk:35511","is_oa":false,"landing_page_url":"https://orcid.org/0000-0003-4935-7820>","pdf_url":null,"source":{"id":"https://openalex.org/S4306401593","display_name":"London School of Economics and Political Science Research Online (London School of Economics and Political Science)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I909854389","host_organization_name":"London School of Economics and Political Science","host_organization_lineage":["https://openalex.org/I909854389"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"PeerReviewed"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W1551519020","https://openalex.org/W1564100130","https://openalex.org/W1980675521","https://openalex.org/W1980848544","https://openalex.org/W1986231013","https://openalex.org/W2003351966","https://openalex.org/W2016806092","https://openalex.org/W2032382962","https://openalex.org/W2065271495","https://openalex.org/W2068121295","https://openalex.org/W2089435411","https://openalex.org/W2089514086","https://openalex.org/W2127470768","https://openalex.org/W2142946851","https://openalex.org/W2479395228","https://openalex.org/W4255770412","https://openalex.org/W4301216918"],"related_works":["https://openalex.org/W4297676365","https://openalex.org/W1645173339","https://openalex.org/W2908698948","https://openalex.org/W4288280572","https://openalex.org/W4320022211","https://openalex.org/W2990042548","https://openalex.org/W4285056899","https://openalex.org/W3049229033","https://openalex.org/W3153884844","https://openalex.org/W2803652637"],"abstract_inverted_index":{"The":[0,59],"random":[1],"assignment":[2],"problem":[3],"is":[4,38,61,70,78,101],"to":[5,63,109],"choose":[6],"a":[7,12,67,92],"minimum-cost":[8],"perfect":[9],"matching":[10],"in":[11,120],"complete":[13,113],"n\u00d7n":[14],"bipartite":[15,115],"graph,":[16],"whose":[17],"edge":[18],"weights":[19],"are":[20],"chosen":[21],"randomly":[22],"from":[23],"some":[24,51,121],"distribution":[25,30],"such":[26],"as":[27],"the":[28,41,75,98,106],"exponential":[29],"with":[31,47],"mean":[32],"1.":[33],"In":[34],"this":[35],"case":[36],"it":[37,119],"known":[39],"that":[40,71,97],"expectation":[42,100],"does":[43],"not":[44],"grow":[45],"unboundedly":[46],"n,":[48,74],"but":[49],"approaches":[50],"limiting":[52,99],"value":[53],"c*":[54],"between":[55],"1.51":[56],"and":[57,90,117],"2.":[58],"limit":[60],"conjectured":[62],"be":[64],"\u03c02/6,":[65],"while":[66],"recent":[68],"conjecture":[69,108],"for":[72],"finite":[73],"expected":[76],"cost":[77],"\u2211":[79],"1/i2.":[80],"This":[81],"paper":[82],"contains":[83],"two":[84],"principal":[85],"results.":[86],"First,":[87],"by":[88],"defining":[89],"analyzing":[91],"constructive":[93],"algorithm,":[94],"we":[95,104],"show":[96],"c*<1.94.":[102],"Second,":[103],"extend":[105],"finite-n":[107],"partial":[110],"assignments":[111],"on":[112],"m\u00d7n":[114],"graphs":[116],"prove":[118],"limited":[122],"cases.":[123],"\u00a91999":[124],"John":[125],"Wiley":[126],"&":[127],"Sons,":[128],"Inc.":[129],"Random":[130],"Struct.":[131],"Alg.,":[132],"15,":[133],"113\u2013144,":[134],"1999":[135]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":6},{"year":2013,"cited_by_count":2}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}