{"id":"https://openalex.org/W2170257531","doi":"https://doi.org/10.1109/allerton.2008.4797660","title":"Convergence of optimal values past critical threshold","display_name":"Convergence of optimal values past critical threshold","publication_year":2008,"publication_date":"2008-09-01","ids":{"openalex":"https://openalex.org/W2170257531","doi":"https://doi.org/10.1109/allerton.2008.4797660","mag":"2170257531"},"language":"en","primary_location":{"id":"doi:10.1109/allerton.2008.4797660","is_oa":false,"landing_page_url":"https://doi.org/10.1109/allerton.2008.4797660","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2008 46th Annual Allerton Conference on Communication, Control, and Computing","raw_type":"proceedings-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/A5056494635","display_name":"Steven Jaslar","orcid":null},"institutions":[{"id":"https://openalex.org/I32971472","display_name":"Yale University","ror":"https://ror.org/03v76x132","country_code":"US","type":"education","lineage":["https://openalex.org/I32971472"]},{"id":"https://openalex.org/I4210131439","display_name":"Applied Mathematics (United States)","ror":"https://ror.org/03seew607","country_code":"US","type":"company","lineage":["https://openalex.org/I4210131439"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Steven Jaslar","raw_affiliation_strings":["Program in Applied Mathematics, Yale University, New Heaven, CT, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Program in Applied Mathematics, Yale University, New Heaven, CT, USA","institution_ids":["https://openalex.org/I32971472","https://openalex.org/I4210131439"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5072765803","display_name":"Sekhar Tatikonda","orcid":"https://orcid.org/0000-0002-8956-6208"},"institutions":[{"id":"https://openalex.org/I32971472","display_name":"Yale University","ror":"https://ror.org/03v76x132","country_code":"US","type":"education","lineage":["https://openalex.org/I32971472"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Sekhar Tatikonda","raw_affiliation_strings":["Department of Electrical Engineering, Yale University, New Heaven, CT, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Yale University, New Heaven, CT, USA","institution_ids":["https://openalex.org/I32971472"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.20553926,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"945","last_page":"951"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11106","display_name":"Data Management and Algorithms","score":0.9965999722480774,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/T11106","display_name":"Data Management and Algorithms","score":0.9965999722480774,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9954000115394592,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9939000010490417,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.5782269835472107},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.5377071499824524},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.535071611404419},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.5125772356987},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.47952985763549805},{"id":"https://openalex.org/keywords/matching","display_name":"Matching (statistics)","score":0.46580249071121216},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.44789960980415344},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.42435187101364136},{"id":"https://openalex.org/keywords/expected-value","display_name":"Expected value","score":0.412821888923645},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3327638506889343},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3204108476638794},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.2413056492805481},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.11394169926643372},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.0795937180519104}],"concepts":[{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5782269835472107},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.5377071499824524},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.535071611404419},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.5125772356987},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.47952985763549805},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.46580249071121216},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.44789960980415344},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.42435187101364136},{"id":"https://openalex.org/C141042865","wikidata":"https://www.wikidata.org/wiki/Q200125","display_name":"Expected value","level":2,"score":0.412821888923645},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3327638506889343},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3204108476638794},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.2413056492805481},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.11394169926643372},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0795937180519104},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/allerton.2008.4797660","is_oa":false,"landing_page_url":"https://doi.org/10.1109/allerton.2008.4797660","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2008 46th Annual Allerton Conference on Communication, Control, and Computing","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W191748401","https://openalex.org/W1519375772","https://openalex.org/W1533148775","https://openalex.org/W1648500155","https://openalex.org/W1872905819","https://openalex.org/W1973072981","https://openalex.org/W2004216344","https://openalex.org/W2043065436","https://openalex.org/W2083116175","https://openalex.org/W2493844837","https://openalex.org/W2963332076","https://openalex.org/W4247615678"],"related_works":["https://openalex.org/W1972035260","https://openalex.org/W2794488505","https://openalex.org/W4301594054","https://openalex.org/W3125889879","https://openalex.org/W3124422538","https://openalex.org/W2295467472","https://openalex.org/W3046451053","https://openalex.org/W2097909533","https://openalex.org/W4360764540","https://openalex.org/W3125188128"],"abstract_inverted_index":{"In":[0,116],"this":[1],"paper":[2],"we":[3,53,75,138,154],"examine":[4,54],"maximum":[5,175,179],"weight":[6,176,180],"independent":[7],"sets":[8],"(MWIS)":[9],"on":[10],"branching":[11],"processes":[12],"and":[13,18,67,129,146,178],"Erdos-Renyi":[14,114],"graphs.":[15,115],"Gamarnik,":[16],"Nowicki,":[17],"Swirscsz,":[19],"showed":[20],"that,":[21,77],"if":[22],"a":[23,29,100,105],"particular":[24],"fixed":[25,64,135],"point":[26,65,136],"equation":[27],"had":[28],"unique":[30],"solution,":[31],"then":[32],"the":[33,49,63,85,93,110,117,125,134,150],"MWIS":[34,50,94,111,151],"value":[35,95,112],"converged.":[36],"This":[37],"followed":[38],"by":[39],"showing":[40],"that":[41,92],"there":[42,58,69],"was":[43],"no":[44],"long":[45,71,88],"range":[46,72,89],"dependencies":[47,90],"in":[48,97],"solution.":[51],"Here":[52],"what":[55],"happens":[56],"when":[57],"are":[59,70,160],"multiple":[60,131],"solutions":[61,132],"to":[62,99,133,142,163,166],"equation,":[66,137],"hence":[68],"dependencies.":[73],"Specifically,":[74],"show":[76,143,155],"under":[78],"surprisingly":[79],"weak":[80],"conditions":[81],"-":[82,91],"which":[83],"include":[84],"possibility":[86],"of":[87,119,149],"converges":[96],"probability":[98],"random":[101],"variable.":[102],"We":[103],"give":[104],"new":[106],"method":[107,141],"for":[108,113],"calculating":[109],"case":[118],"vertex":[120],"weights":[121],"independently":[122],"drawn":[123],"from":[124],"standard":[126],"exponential":[127],"distribution":[128],"with":[130,170],"use":[139],"our":[140,157],"improved":[144],"upper":[145],"lower":[147],"bounds":[148],"value.":[152],"Finally,":[153],"how":[156],"proof":[158],"techniques":[159],"general":[161],"enough":[162],"be":[164],"applied":[165],"other":[167],"optimization":[168],"problems":[169],"local":[171],"constraints":[172],"such":[173],"as":[174],"matching":[177],"color.":[181]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}