{"id":"https://openalex.org/W1761820742","doi":"https://doi.org/10.1137/090753115","title":"Belief Propagation for Weighted b-Matchings on Arbitrary Graphs and its Relation to Linear Programs with Integer Solutions","display_name":"Belief Propagation for Weighted b-Matchings on Arbitrary Graphs and its Relation to Linear Programs with Integer Solutions","publication_year":2011,"publication_date":"2011-01-01","ids":{"openalex":"https://openalex.org/W1761820742","doi":"https://doi.org/10.1137/090753115","mag":"1761820742"},"language":"en","primary_location":{"id":"doi:10.1137/090753115","doi":"https://doi.org/10.1137/090753115","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090753115","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","ccf-c","cwts-core","dongbi-b","jufo-2","norway-1","poland-100","russia-white-list-2","vabb-shw"],"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/0709.1190","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5091599934","display_name":"Mohsen Bayati","orcid":"https://orcid.org/0000-0002-7280-912X","observed_orcids":["https://orcid.org/0000-0002-7280-912X"]},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Mohsen Bayati","raw_affiliation_strings":["Stanford University, Stanford CA 94305"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Stanford University, Stanford CA 94305","institution_ids":["https://openalex.org/I97018004"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5007082382","display_name":"Christian Borgs","orcid":"https://orcid.org/0000-0001-5653-0498","observed_orcids":["https://orcid.org/0000-0001-5653-0498"]},"institutions":[{"id":"https://openalex.org/I1290206253","display_name":"Microsoft (United States)","ror":"https://ror.org/00d0nc645","country_code":"US","type":"company","lineage":["https://openalex.org/I1290206253"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Christian Borgs","raw_affiliation_strings":["Microsoft Research, Cambridge MA 02142"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Microsoft Research, Cambridge MA 02142","institution_ids":["https://openalex.org/I1290206253"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5038662431","display_name":"Jennifer Chayes","orcid":"https://orcid.org/0000-0003-4020-8618","observed_orcids":["https://orcid.org/0000-0003-4020-8618"]},"institutions":[{"id":"https://openalex.org/I1290206253","display_name":"Microsoft (United States)","ror":"https://ror.org/00d0nc645","country_code":"US","type":"company","lineage":["https://openalex.org/I1290206253"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jennifer Chayes","raw_affiliation_strings":["Microsoft Research, Cambridge MA 02142"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Microsoft Research, Cambridge MA 02142","institution_ids":["https://openalex.org/I1290206253"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5041685522","display_name":"Riccardo Zecchina","orcid":"https://orcid.org/0000-0002-1221-5207","observed_orcids":["https://orcid.org/0000-0002-1221-5207"]},"institutions":[{"id":"https://openalex.org/I177477856","display_name":"Politecnico di Torino","ror":"https://ror.org/00bgk9508","country_code":"IT","type":"education","lineage":["https://openalex.org/I177477856"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Riccardo Zecchina","raw_affiliation_strings":["Politecnico Di Torino, Torino Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Politecnico Di Torino, Torino Italy","institution_ids":["https://openalex.org/I177477856"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":8.0666,"has_fulltext":false,"cited_by_count":71,"citation_normalized_percentile":{"value":0.98127451,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"25","issue":"2","first_page":"989","last_page":"1011"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9063000082969666,"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"}},"topics":[{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9063000082969666,"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/T11596","display_name":"Constraint Satisfaction and Optimization","score":0.03220000118017197,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.009200000204145908,"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/belief-propagation","display_name":"belief propagation","score":0.9980000257492065},{"id":"https://openalex.org/keywords/minimum-weight-matching","display_name":"minimum weight matching","score":0.8650000095367432},{"id":"https://openalex.org/keywords/linear-programming-relaxation","display_name":"linear programming relaxation","score":0.7979999780654907},{"id":"https://openalex.org/keywords/integer-linear-programming","display_name":"integer linear programming","score":0.6200000047683716},{"id":"https://openalex.org/keywords/graph-covers","display_name":"graph covering","score":0.7490000128746033},{"id":"https://openalex.org/keywords/combinatorial-optimization","display_name":"combinatorial optimization","score":0.9210000038146973},{"id":"https://openalex.org/keywords/fractional-solutions","display_name":"fractional solutions","score":0.3240000009536743}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.741639256477356},{"id":"https://openalex.org/C55439883","wikidata":"https://www.wikidata.org/wiki/Q360812","display_name":"Correctness","level":2,"score":0.7316654920578003},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.6121615767478943},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.5878437757492065},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5541992783546448},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.515300989151001},{"id":"https://openalex.org/C152948882","wikidata":"https://www.wikidata.org/wiki/Q4060686","display_name":"Belief propagation","level":3,"score":0.5004787445068359},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.45981699228286743},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.45096734166145325},{"id":"https://openalex.org/C151319957","wikidata":"https://www.wikidata.org/wiki/Q752739","display_name":"Asynchronous communication","level":2,"score":0.42994725704193115},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.4276791512966156},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.27794167399406433},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.15718498826026917},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"score":0.0}],"mesh":[],"locations_count":8,"locations":[{"id":"doi:10.1137/090753115","doi":"https://doi.org/10.1137/090753115","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090753115","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","ccf-c","cwts-core","dongbi-b","jufo-2","norway-1","poland-100","russia-white-list-2","vabb-shw"],"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:0709.1190","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/0709.1190","pdf_url":"https://arxiv.org/pdf/0709.1190","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.244.9210","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.244.9210","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/0709.1190v2.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.245.1151","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.245.1151","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/0709.1190v1.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.307.1006","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.307.1006","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://research.microsoft.com/pubs/101958/8-b-matching SIDMA.pdf","raw_type":"text"},{"id":"pmh:oai:iris.polito.it:11583/2439001","doi":null,"is_oa":false,"landing_page_url":"http://hdl.handle.net/11583/2439001","pdf_url":null,"source":{"id":"https://openalex.org/S7407055329","display_name":"PORTO@Iris","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:porto.polito.it:2439001","doi":null,"is_oa":false,"landing_page_url":"http://porto.polito.it/2439001/","pdf_url":null,"source":{"id":"https://openalex.org/S4306402038","display_name":"PORTO Publications Open Repository TOrino (Politecnico di Torino)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I177477856","host_organization_name":"Politecnico di Torino","host_organization_lineage":["https://openalex.org/I177477856"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ISSN:0895-4801","raw_type":"info:eu-repo/semantics/article"},{"id":"doi:10.48550/arxiv.0709.1190","doi":"https://doi.org/10.48550/arxiv.0709.1190","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.0709.1190","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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-journal"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:0709.1190","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/0709.1190","pdf_url":"https://arxiv.org/pdf/0709.1190","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":71,"referenced_works":["https://openalex.org/W7241855","https://openalex.org/W177280531","https://openalex.org/W193818406","https://openalex.org/W222437202","https://openalex.org/W1504317671","https://openalex.org/W1528845765","https://openalex.org/W1545381479","https://openalex.org/W1584102736","https://openalex.org/W1588943481","https://openalex.org/W1627947145","https://openalex.org/W1640741887","https://openalex.org/W1761820742","https://openalex.org/W1963712368","https://openalex.org/W1967786343","https://openalex.org/W1979483474","https://openalex.org/W1980130379","https://openalex.org/W1980276492","https://openalex.org/W1983289383","https://openalex.org/W1986705527","https://openalex.org/W1993433103","https://openalex.org/W1997998268","https://openalex.org/W2008310023","https://openalex.org/W2009070933","https://openalex.org/W2019599312","https://openalex.org/W2033718639","https://openalex.org/W2058408846","https://openalex.org/W2081642252","https://openalex.org/W2089770904","https://openalex.org/W2098387242","https://openalex.org/W2099091355","https://openalex.org/W2099515224","https://openalex.org/W2100034662","https://openalex.org/W2100326972","https://openalex.org/W2105546154","https://openalex.org/W2107750985","https://openalex.org/W2108619558","https://openalex.org/W2110886826","https://openalex.org/W2117371776","https://openalex.org/W2125631472","https://openalex.org/W2128765501","https://openalex.org/W2134074092","https://openalex.org/W2134995722","https://openalex.org/W2135094946","https://openalex.org/W2139919528","https://openalex.org/W2149342630","https://openalex.org/W2151173657","https://openalex.org/W2158122241","https://openalex.org/W2159080219","https://openalex.org/W2165232124","https://openalex.org/W2169134868","https://openalex.org/W2169732368","https://openalex.org/W2170484108","https://openalex.org/W2170987079","https://openalex.org/W2175160295","https://openalex.org/W2295244470","https://openalex.org/W2296319761","https://openalex.org/W2340149117","https://openalex.org/W2547794491","https://openalex.org/W2740348893","https://openalex.org/W2807232057","https://openalex.org/W2950654313","https://openalex.org/W2951682774","https://openalex.org/W2963217435","https://openalex.org/W3100131557","https://openalex.org/W3105479371","https://openalex.org/W3140660692","https://openalex.org/W4236872582","https://openalex.org/W4239977398","https://openalex.org/W4285719527","https://openalex.org/W4298212823","https://openalex.org/W4300188436"],"related_works":["https://openalex.org/W1667647204","https://openalex.org/W2404647514","https://openalex.org/W4247536566","https://openalex.org/W2018477250","https://openalex.org/W3119814709","https://openalex.org/W4241418540","https://openalex.org/W1508895727","https://openalex.org/W2725786787","https://openalex.org/W4283160672","https://openalex.org/W55831818"],"abstract_inverted_index":{"We":[0,16,43],"consider":[1],"the":[2,7,20,26,33,40,48,56,64,72,79,92,108,123,145,151,162],"general":[3],"problem":[4,27],"of":[5,25,74,81,91,107,130,135,139,150,165,169],"finding":[6],"minimum":[8],"weight":[9],"[Formula:":[10],"see":[11],"text]-matching":[12],"on":[13,71,112,144],"arbitrary":[14],"graphs.":[15],"prove":[17],"that,":[18],"whenever":[19],"linear":[21],"programming":[22],"(LP)":[23],"relaxation":[24,50],"has":[28,51],"no":[29],"fractional":[30,53],"solutions,":[31],"then":[32,55],"belief":[34],"propagation":[35],"(BP)":[36],"algorithm":[37,58,173],"converges":[38],"to":[39,62],"correct":[41],"solution.":[42],"also":[44],"show":[45],"that":[46],"when":[47],"LP":[49,65],"a":[52,131,175],"solution":[54],"BP":[57,140,172],"can":[59],"be":[60],"used":[61],"solve":[63],"relaxation.":[66],"Our":[67],"proof":[68,152,164],"is":[69,120,128,161],"based":[70],"notion":[73],"graph":[75,146],"covers":[76],"and":[77,86,99,102,115,157,167],"extends":[78],"analyses":[80],"[M.":[82],"Bayati,":[83],"D.":[84],"Shah":[85],"M.":[87],"Sharma,":[88],"in":[89,105,122],"Proceedings":[90,106],"IEEE":[93],"Int.":[94],"Symp.":[95],"Information":[96],"Theory,":[97],"2005]":[98],"[B.":[100],"Huang":[101],"T.":[103],"Jebara,":[104],"Eleventh":[109],"International":[110],"Conference":[111],"Artificial":[113],"Intelligence":[114],"Statistics,":[116],"2007].":[117],"The":[118],"result":[119],"notable":[121],"following":[124],"regards:":[125],"(1)":[126],"It":[127],"one":[129],"very":[132],"small":[133],"number":[134],"proofs":[136],"showing":[137],"correctness":[138,168],"without":[141],"any":[142],"constraint":[143],"structure;":[147],"(2)":[148],"Variants":[149],"work":[153],"for":[154,174],"both":[155],"synchronous":[156],"asynchronous":[158,171],"BP;":[159],"it":[160],"first":[163],"convergence":[166],"an":[170],"combinatorial":[176],"optimization":[177],"problem.":[178]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":10},{"year":2013,"cited_by_count":6},{"year":2012,"cited_by_count":6}],"updated_date":"2026-10-14T16:39:01.820549","created_date":"2025-10-10T00:00:00"}
