{"id":"https://openalex.org/W7133516221","doi":"https://doi.org/10.48550/arxiv.2603.02636","title":"Undecided State Dynamics with Many Opinions","display_name":"Undecided State Dynamics with Many Opinions","publication_year":2026,"publication_date":"2026-03-03","ids":{"openalex":"https://openalex.org/W7133516221","doi":"https://doi.org/10.48550/arxiv.2603.02636"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2603.02636","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.02636","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,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2603.02636","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5128083508","display_name":"Colin Cooper","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Cooper, Colin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5128063604","display_name":"Frederik Mallmann-Trenn","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mallmann-Trenn, Frederik","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5128041637","display_name":"Tomasz Radzik","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Radzik, Tomasz","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103108401","display_name":"Nobutaka Shimizu","orcid":"https://orcid.org/0000-0001-5448-6761"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Shimizu, Nobutaka","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5067826040","display_name":"Takeharu Shiraga","orcid":"https://orcid.org/0000-0003-1236-9756"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Shiraga, Takeharu","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10772","display_name":"Distributed systems and fault tolerance","score":0.8256000280380249,"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/T10772","display_name":"Distributed systems and fault tolerance","score":0.8256000280380249,"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/T12592","display_name":"Opinion Dynamics and Social Influence","score":0.03830000013113022,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12029","display_name":"DNA and Biological Computing","score":0.016200000420212746,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/gossip","display_name":"Gossip","score":0.9174000024795532},{"id":"https://openalex.org/keywords/gossip-protocol","display_name":"Gossip protocol","score":0.7567999958992004},{"id":"https://openalex.org/keywords/population","display_name":"Population","score":0.6827999949455261},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5733000040054321},{"id":"https://openalex.org/keywords/protocol","display_name":"Protocol (science)","score":0.5351999998092651},{"id":"https://openalex.org/keywords/asynchronous-communication","display_name":"Asynchronous communication","score":0.5072000026702881},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.435699999332428},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.4332999885082245}],"concepts":[{"id":"https://openalex.org/C62989814","wikidata":"https://www.wikidata.org/wiki/Q854648","display_name":"Gossip","level":2,"score":0.9174000024795532},{"id":"https://openalex.org/C145928361","wikidata":"https://www.wikidata.org/wiki/Q5587504","display_name":"Gossip protocol","level":3,"score":0.7567999958992004},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"score":0.6827999949455261},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5733000040054321},{"id":"https://openalex.org/C2780385302","wikidata":"https://www.wikidata.org/wiki/Q367158","display_name":"Protocol (science)","level":3,"score":0.5351999998092651},{"id":"https://openalex.org/C151319957","wikidata":"https://www.wikidata.org/wiki/Q752739","display_name":"Asynchronous communication","level":2,"score":0.5072000026702881},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4950999915599823},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.435699999332428},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.4332999885082245},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4262000024318695},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.3418999910354614},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.31130000948905945},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.30550000071525574},{"id":"https://openalex.org/C52079815","wikidata":"https://www.wikidata.org/wiki/Q7229808","display_name":"Population model","level":3,"score":0.30079999566078186},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.30059999227523804},{"id":"https://openalex.org/C107107730","wikidata":"https://www.wikidata.org/wiki/Q2994424","display_name":"Consensus","level":3,"score":0.2815999984741211},{"id":"https://openalex.org/C148220186","wikidata":"https://www.wikidata.org/wiki/Q7111912","display_name":"Outcome (game theory)","level":2,"score":0.27469998598098755},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.26499998569488525},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.2614000141620636},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.26100000739097595},{"id":"https://openalex.org/C145912823","wikidata":"https://www.wikidata.org/wiki/Q113558","display_name":"Dynamics (music)","level":2,"score":0.2572999894618988},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.2549000084400177},{"id":"https://openalex.org/C169733012","wikidata":"https://www.wikidata.org/wiki/Q1613416","display_name":"Population size","level":3,"score":0.25119999051094055},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.25099998712539673}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2603.02636","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.02636","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,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2603.02636","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.02636","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,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","score":0.5565483570098877,"id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0,24,158],"study":[1],"the":[2,21,27,31,41,49,56,66,74,82,102,106,111,129,135,139,143,165],"Undecided-State":[3],"Dynamics":[4],"(USD),":[5],"a":[6,173],"fundamental":[7],"consensus":[8,42,116,149],"process":[9,46],"in":[10,100,138],"which":[11],"each":[12],"vertex":[13],"holds":[14],"one":[15],"of":[16,44,132],"$k$":[17],"decided":[18],"opinions":[19],"or":[20],"undecided":[22],"state.":[23],"consider":[25],"both":[26,101],"gossip":[28,67,103,112],"model":[29,104],"and":[30,60,95,105,177],"population":[32,57,107,144],"protocol":[33,58,108,145],"model.":[34,109],"Prior":[35],"work":[36],"established":[37],"tight":[38],"bounds":[39,162,167,182],"on":[40,73],"time":[43],"this":[45,78],"only":[47],"for":[48,86,90,96,172],"regime":[50],"$k":[51,61],"=":[52,62],"O(\\sqrt{n}/(\\log":[53],"n)^2)$":[54],"(for":[55,65],"model)":[59],"O((n/\\log":[63],"n)^{1/3})$":[64],"model),":[68],"often":[69],"under":[70],"restrictive":[71],"assumptions":[72],"initial":[75,98,175],"configuration.":[76],"In":[77,110,142],"paper,":[79],"we":[80],"obtain":[81],"first":[83,140],"consensus-time":[84],"guarantees":[85],"USD":[87,114,147],"that":[88,163,179],"hold":[89],"\\emph{arbitrary}":[91,97],"$2\\le":[92],"k\\le":[93],"n$":[94],"configurations":[99],"model,":[113,146],"reaches":[115,148],"within":[117,150],"$\\widetilde":[118,151],"O(\\min\\{k,\\sqrt":[119],"n\\})$":[120],"synchronous":[121],"rounds":[122],"with":[123,155],"probability":[124,131],"$1-p_{\\bot}-n^{-c}$,":[125],"where":[126],"$p_{\\bot}$":[127],"is":[128],"gossip-specific":[130],"collapsing":[133],"to":[134,169],"all-undecided":[136],"state":[137],"round.":[141],"O(\\min\\{kn,n^{3/2}\\})$":[152],"asynchronous":[153],"interactions":[154],"high":[156],"probability.":[157],"also":[159],"present":[160],"lower":[161],"match":[164],"upper":[166,181],"up":[168],"polylogarithmic":[170],"factors":[171],"specific":[174],"configuration":[176],"show":[178],"our":[180],"are":[183],"essentially":[184],"optimal.":[185]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-03-05T00:00:00"}
