{"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","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,"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"},"type":"article","indexed_in":["arxiv","crossref"],"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"},"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":true,"raw_author_name":"Mohsen Bayati","raw_affiliation_strings":["Stanford University, Stanford CA 94305"],"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"},"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"],"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"},"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"],"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"},"institutions":[{"id":"https://openalex.org/I177477856","display_name":"Polytechnic University of Turin","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"],"affiliations":[{"raw_affiliation_string":"Politecnico Di Torino, Torino Italy","institution_ids":["https://openalex.org/I177477856"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5091599934"],"corresponding_institution_ids":["https://openalex.org/I97018004"],"apc_list":null,"apc_paid":null,"fwci":10.5665,"has_fulltext":false,"cited_by_count":76,"citation_normalized_percentile":{"value":0.98452143,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"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/T11321","display_name":"Error Correcting Code Techniques","score":0.9988999962806702,"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/T11321","display_name":"Error Correcting Code Techniques","score":0.9988999962806702,"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/T10796","display_name":"Cooperative Communication and Network Coding","score":0.9940000176429749,"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/T12288","display_name":"Optimization and Search Problems","score":0.9936000108718872,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.741639256477356},{"id":"https://openalex.org/keywords/correctness","display_name":"Correctness","score":0.7316654920578003},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.6121615767478943},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.5878437757492065},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5541992783546448},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.515300989151001},{"id":"https://openalex.org/keywords/belief-propagation","display_name":"Belief propagation","score":0.5004787445068359},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.45981699228286743},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.45096734166145325},{"id":"https://openalex.org/keywords/asynchronous-communication","display_name":"Asynchronous communication","score":0.42994725704193115},{"id":"https://openalex.org/keywords/matching","display_name":"Matching (statistics)","score":0.4276791512966156},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.27794167399406433},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.15718498826026917}],"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":6,"locations":[{"id":"doi: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,"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","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":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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.244.9210","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","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","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:porto.polito.it:2439001","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,"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"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:0709.1190","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":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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":72,"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/W1628621408","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/W2963332076","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/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":[0,14,41],"consider":[1],"the":[2,7,18,24,31,38,46,54,62,70,77,90,106,121,143,149,160],"general":[3],"problem":[4,25],"of":[5,23,72,79,89,105,128,133,137,148,163,167],"finding":[6],"minimum":[8],"weight":[9],"-matching":[10],"on":[11,69,110,142],"arbitrary":[12],"graphs.":[13],"prove":[15],"that,":[16],"whenever":[17],"linear":[19],"programming":[20],"(LP)":[21],"relaxation":[22,48],"has":[26,49],"no":[27],"fractional":[28,51],"solutions,":[29],"then":[30,53],"belief":[32],"propagation":[33],"(BP)":[34],"algorithm":[35,56,171],"converges":[36],"to":[37,60],"correct":[39],"solution.":[40],"also":[42],"show":[43],"that":[44],"when":[45],"LP":[47,63],"a":[50,129,173],"solution":[52],"BP":[55,138,170],"can":[57],"be":[58],"used":[59],"solve":[61],"relaxation.":[64],"Our":[65],"proof":[66,150,162],"is":[67,118,126,159],"based":[68],"notion":[71],"graph":[73,144],"covers":[74],"and":[75,84,97,100,113,155,165],"extends":[76],"analyses":[78],"[M.":[80],"Bayati,":[81],"D.":[82],"Shah":[83],"M.":[85],"Sharma,":[86],"in":[87,103,120],"Proceedings":[88,104],"IEEE":[91],"Int.":[92],"Symp.":[93],"Information":[94],"Theory,":[95],"2005]":[96],"[B.":[98],"Huang":[99],"T.":[101],"Jebara,":[102],"Eleventh":[107],"International":[108],"Conference":[109],"Artificial":[111],"Intelligence":[112],"Statistics,":[114],"2007].":[115],"The":[116],"result":[117],"notable":[119],"following":[122],"regards:":[123],"(1)":[124],"It":[125],"one":[127],"very":[130],"small":[131],"number":[132],"proofs":[134],"showing":[135],"correctness":[136,166],"without":[139],"any":[140],"constraint":[141],"structure;":[145],"(2)":[146],"Variants":[147],"work":[151],"for":[152,172],"both":[153],"synchronous":[154],"asynchronous":[156,169],"BP;":[157],"it":[158],"first":[161],"convergence":[164],"an":[168],"combinatorial":[174],"optimization":[175],"problem.":[176]},"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":5},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":11},{"year":2013,"cited_by_count":7},{"year":2012,"cited_by_count":6}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
