{"id":"https://openalex.org/W2025189987","doi":"https://doi.org/10.1109/tac.2014.2322942","title":"Fastest Mixing Reversible Markov Chains on Graphs With Degree Proportional Stationary Distributions","display_name":"Fastest Mixing Reversible Markov Chains on Graphs With Degree Proportional Stationary Distributions","publication_year":2014,"publication_date":"2014-05-09","ids":{"openalex":"https://openalex.org/W2025189987","doi":"https://doi.org/10.1109/tac.2014.2322942","mag":"2025189987"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2014.2322942","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2014.2322942","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","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/A5023284112","display_name":"Onur Cihan","orcid":"https://orcid.org/0000-0002-5729-2417"},"institutions":[{"id":"https://openalex.org/I4405392","display_name":"Bo\u011fazi\u00e7i University","ror":"https://ror.org/03z9tma90","country_code":"TR","type":"education","lineage":["https://openalex.org/I4405392"]}],"countries":["TR"],"is_corresponding":true,"raw_author_name":"Onur Cihan","raw_affiliation_strings":["Department of Electrical and Electronic Engineering, Bo\u011fazi\u00e7i University, \u0130stanbul, Turkey","Dept. of Electr. & Electron. Eng., Bogazici Univ., I\u0301stanbul, Turkey"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Electronic Engineering, Bo\u011fazi\u00e7i University, \u0130stanbul, Turkey","institution_ids":["https://openalex.org/I4405392"]},{"raw_affiliation_string":"Dept. of Electr. & Electron. Eng., Bogazici Univ., I\u0301stanbul, Turkey","institution_ids":["https://openalex.org/I4405392"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5102998562","display_name":"Mehmet Akar","orcid":"https://orcid.org/0000-0002-0166-9932"},"institutions":[{"id":"https://openalex.org/I4405392","display_name":"Bo\u011fazi\u00e7i University","ror":"https://ror.org/03z9tma90","country_code":"TR","type":"education","lineage":["https://openalex.org/I4405392"]}],"countries":["TR"],"is_corresponding":false,"raw_author_name":"Mehmet Akar","raw_affiliation_strings":["Department of Electrical and Electronic Engineering, Bo\u011fazi\u00e7i University, \u0130stanbul, Turkey","Dept. of Electr. & Electron. Eng., Bogazici Univ., I\u0301stanbul, Turkey"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Electronic Engineering, Bo\u011fazi\u00e7i University, \u0130stanbul, Turkey","institution_ids":["https://openalex.org/I4405392"]},{"raw_affiliation_string":"Dept. of Electr. & Electron. Eng., Bogazici Univ., I\u0301stanbul, Turkey","institution_ids":["https://openalex.org/I4405392"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5023284112"],"corresponding_institution_ids":["https://openalex.org/I4405392"],"apc_list":null,"apc_paid":null,"fwci":2.321,"has_fulltext":false,"cited_by_count":20,"citation_normalized_percentile":{"value":0.86744281,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"60","issue":"1","first_page":"227","last_page":"232"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":0.9980999827384949,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T11476","display_name":"Graph theory and applications","score":0.9980999827384949,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9972000122070312,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.996399998664856,"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/markov-chain","display_name":"Markov chain","score":0.8336856365203857},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.679283618927002},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6571096181869507},{"id":"https://openalex.org/keywords/stationary-distribution","display_name":"Stationary distribution","score":0.6416212320327759},{"id":"https://openalex.org/keywords/markov-chain-mixing-time","display_name":"Markov chain mixing time","score":0.6386141180992126},{"id":"https://openalex.org/keywords/mixing","display_name":"Mixing (physics)","score":0.6334306597709656},{"id":"https://openalex.org/keywords/markov-process","display_name":"Markov process","score":0.5164209008216858},{"id":"https://openalex.org/keywords/balance-equation","display_name":"Balance equation","score":0.49790048599243164},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.46956562995910645},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.455234557390213},{"id":"https://openalex.org/keywords/transition-rate-matrix","display_name":"Transition rate matrix","score":0.44192585349082947},{"id":"https://openalex.org/keywords/probability-distribution","display_name":"Probability distribution","score":0.44167229533195496},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4293319284915924},{"id":"https://openalex.org/keywords/continuous-time-markov-chain","display_name":"Continuous-time Markov chain","score":0.4232880771160126},{"id":"https://openalex.org/keywords/markov-model","display_name":"Markov model","score":0.3861282765865326},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.375765323638916},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3696414828300476},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.1825467348098755},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.1742282509803772},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07916802167892456}],"concepts":[{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.8336856365203857},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.679283618927002},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6571096181869507},{"id":"https://openalex.org/C98951983","wikidata":"https://www.wikidata.org/wiki/Q7604341","display_name":"Stationary distribution","level":3,"score":0.6416212320327759},{"id":"https://openalex.org/C97074811","wikidata":"https://www.wikidata.org/wiki/Q6771322","display_name":"Markov chain mixing time","level":5,"score":0.6386141180992126},{"id":"https://openalex.org/C138777275","wikidata":"https://www.wikidata.org/wiki/Q6884054","display_name":"Mixing (physics)","level":2,"score":0.6334306597709656},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.5164209008216858},{"id":"https://openalex.org/C158917313","wikidata":"https://www.wikidata.org/wiki/Q4849964","display_name":"Balance equation","level":4,"score":0.49790048599243164},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.46956562995910645},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.455234557390213},{"id":"https://openalex.org/C70557757","wikidata":"https://www.wikidata.org/wiki/Q7834432","display_name":"Transition rate matrix","level":2,"score":0.44192585349082947},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.44167229533195496},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4293319284915924},{"id":"https://openalex.org/C147080032","wikidata":"https://www.wikidata.org/wiki/Q176720","display_name":"Continuous-time Markov chain","level":5,"score":0.4232880771160126},{"id":"https://openalex.org/C163836022","wikidata":"https://www.wikidata.org/wiki/Q6771326","display_name":"Markov model","level":3,"score":0.3861282765865326},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.375765323638916},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3696414828300476},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.1825467348098755},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.1742282509803772},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07916802167892456},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tac.2014.2322942","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2014.2322942","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W1992780816","https://openalex.org/W2074400367","https://openalex.org/W2120204400","https://openalex.org/W2123056045","https://openalex.org/W2134711723","https://openalex.org/W2138187596","https://openalex.org/W3105329945","https://openalex.org/W4236352634"],"related_works":["https://openalex.org/W4388292411","https://openalex.org/W2159877461","https://openalex.org/W4244281465","https://openalex.org/W2127370188","https://openalex.org/W1523345375","https://openalex.org/W2032212734","https://openalex.org/W2336740323","https://openalex.org/W2585248738","https://openalex.org/W2366075589","https://openalex.org/W2781998744"],"abstract_inverted_index":{"In":[0,26],"this":[1],"technical":[2],"note,":[3],"we":[4],"study":[5],"two":[6],"semi-definite":[7],"programming":[8],"(SDP)":[9],"methods":[10],"of":[11,44,74],"assigning":[12],"transition":[13,35],"probabilities":[14],"to":[15,21,38,48,55,64,71,97],"a":[16,33,65],"Markov":[17,60],"chain":[18,61],"in":[19],"order":[20],"optimize":[22],"its":[23],"mixing":[24],"rate.":[25],"the":[27,56,72,86,90,102],"first":[28],"SDP":[29,104],"formulation,":[30],"there":[31],"is":[32,69,82],"single":[34,87],"probability":[36,43],"parameter":[37,88],"be":[39],"optimized":[40],"(the":[41],"holding":[42],"vertices)":[45],"which":[46],"leads":[47],"easier":[49],"and":[50,89],"faster":[51],"computation":[52],"as":[53],"opposed":[54],"more":[57],"general":[58],"reversible":[59,93],"formulation":[62,105],"corresponding":[63],"stationary":[66],"distribution":[67],"that":[68,84],"proportional":[70,92],"degree":[73,91],"vertices.":[75],"By":[76],"deriving":[77],"exact":[78],"analytical":[79],"results,":[80],"it":[81],"shown":[83],"both":[85],"FMMC":[94],"formulations":[95],"tend":[96],"yield":[98],"better":[99],"results":[100],"than":[101],"symmetric":[103],"for":[106],"some":[107],"well-known":[108],"graphs.":[109]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}