{"id":"https://openalex.org/W2078711343","doi":"https://doi.org/10.1002/jgt.3190140505","title":"Extremal cover times for random walks on trees","display_name":"Extremal cover times for random walks on trees","publication_year":1990,"publication_date":"1990-11-01","ids":{"openalex":"https://openalex.org/W2078711343","doi":"https://doi.org/10.1002/jgt.3190140505","mag":"2078711343"},"language":"en","primary_location":{"id":"doi:10.1002/jgt.3190140505","is_oa":false,"landing_page_url":"https://doi.org/10.1002/jgt.3190140505","pdf_url":null,"source":{"id":"https://openalex.org/S193368155","display_name":"Journal of Graph Theory","issn_l":"0364-9024","issn":["0364-9024","1097-0118"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Graph Theory","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/A5039259953","display_name":"Graham Brightwell","orcid":"https://orcid.org/0000-0001-5955-3628"},"institutions":[{"id":"https://openalex.org/I909854389","display_name":"London School of Economics and Political Science","ror":"https://ror.org/0090zs177","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I909854389"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Graham Brightwell","raw_affiliation_strings":["London School of Economics","\ufeffLondon School of Economics"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"London School of Economics","institution_ids":["https://openalex.org/I909854389"]},{"raw_affiliation_string":"\ufeffLondon School of Economics","institution_ids":["https://openalex.org/I909854389"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5056680757","display_name":"Peter Winkler","orcid":"https://orcid.org/0000-0002-1259-3574"},"institutions":[{"id":"https://openalex.org/I150468666","display_name":"Emory University","ror":"https://ror.org/03czfpz43","country_code":"US","type":"education","lineage":["https://openalex.org/I150468666"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Peter Winkler","raw_affiliation_strings":["Emory University and Bellcore"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Emory University and Bellcore","institution_ids":["https://openalex.org/I150468666"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":3760,"currency":"USD","value_usd":3760},"apc_paid":null,"fwci":1.1197,"has_fulltext":false,"cited_by_count":35,"citation_normalized_percentile":{"value":0.76759259,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"14","issue":"5","first_page":"547","last_page":"554"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9998999834060669,"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.996999979019165,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T11269","display_name":"Algorithms and Data Compression","score":0.9901999831199646,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/combinatorics","display_name":"Combinatorics","score":0.8826148509979248},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8115009069442749},{"id":"https://openalex.org/keywords/cover","display_name":"Cover (algebra)","score":0.7057256102561951},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.687770664691925},{"id":"https://openalex.org/keywords/path","display_name":"Path (computing)","score":0.5552576780319214},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.5132874846458435},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5123847126960754},{"id":"https://openalex.org/keywords/random-walk","display_name":"Random walk","score":0.5010218620300293},{"id":"https://openalex.org/keywords/star","display_name":"Star (game theory)","score":0.48797911405563354},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.38534122705459595},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.23151648044586182},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.09067824482917786},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.07553285360336304}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8826148509979248},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8115009069442749},{"id":"https://openalex.org/C2780428219","wikidata":"https://www.wikidata.org/wiki/Q16952335","display_name":"Cover (algebra)","level":2,"score":0.7057256102561951},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.687770664691925},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.5552576780319214},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.5132874846458435},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5123847126960754},{"id":"https://openalex.org/C121194460","wikidata":"https://www.wikidata.org/wiki/Q856741","display_name":"Random walk","level":2,"score":0.5010218620300293},{"id":"https://openalex.org/C2780897414","wikidata":"https://www.wikidata.org/wiki/Q7600592","display_name":"Star (game theory)","level":2,"score":0.48797911405563354},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.38534122705459595},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.23151648044586182},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.09067824482917786},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.07553285360336304},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/jgt.3190140505","is_oa":false,"landing_page_url":"https://doi.org/10.1002/jgt.3190140505","pdf_url":null,"source":{"id":"https://openalex.org/S193368155","display_name":"Journal of Graph Theory","issn_l":"0364-9024","issn":["0364-9024","1097-0118"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Graph Theory","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320337345","display_name":"Office of Naval Research","ror":"https://ror.org/00rk2pe57"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W1968695868","https://openalex.org/W2034975570","https://openalex.org/W2036762370","https://openalex.org/W2047435800","https://openalex.org/W2049587783","https://openalex.org/W2067012168","https://openalex.org/W2084768526","https://openalex.org/W2156184725"],"related_works":["https://openalex.org/W1597743604","https://openalex.org/W2038723108","https://openalex.org/W2033630974","https://openalex.org/W2325737604","https://openalex.org/W4245069437","https://openalex.org/W2042537860","https://openalex.org/W4297449606","https://openalex.org/W2382333285","https://openalex.org/W2076621518","https://openalex.org/W1528607006"],"abstract_inverted_index":{"Abstract":[0],"Let":[1],"C":[2,43,86],"\u03bd":[3,44,87],"(":[4,45,88],"T":[5,14,46,49,89,94],")":[6,47,82,90],"denote":[7],"the":[8,12,16,22,73,110,120,130,141],"\u201ccover":[9],"time\u201d":[10],"of":[11,25,37,102,140],"tree":[13,51],"from":[15],"vertex":[17,36],"v":[18,33,99],",":[19],"that":[20,85,109],"is,":[21],"expected":[23],"number":[24],"steps":[26],"before":[27],"a":[28,50,96,126,135],"random":[29],"walk":[30],"starting":[31,121],"at":[32,129,138],"hits":[34],"every":[35],"T.":[38],"Asymptotic":[39],"lower":[40,75],"bounds":[41],"for":[42],"(for":[48],"on":[52],"n":[53,79,81],"vertices)":[54],"have":[55],"been":[56],"obtained":[57],"recently":[58],"by":[59,66,83,125,134],"Kahn,":[60],"Linial,":[61],"Nisan":[62],"and":[63,65,68,98,116,132],"Saks,":[64],"Devroye":[67],"Sbihi;":[69],"here,":[70],"we":[71,107],"obtain":[72],"exact":[74],"bound":[76],"(approximately":[77],"2":[78],"In":[80,105],"showing":[84],"is":[91,95,100,123],"minimized":[92,124],"when":[93],"star":[97,127],"one":[101,139],"its":[103],"leaves.":[104],"addition,":[106],"show":[108],"time":[111],"to":[112,119],"cover":[113],"all":[114],"vertices":[115],"then":[117],"return":[118],"point":[122],"(beginning":[128,137],"center)":[131],"maximized":[133],"path":[136],"ends).":[142]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":3},{"year":2012,"cited_by_count":1}],"updated_date":"2026-06-23T06:36:01.041984","created_date":"2025-10-10T00:00:00"}