{"id":"https://openalex.org/W3004379270","doi":"https://doi.org/10.37236/9445","title":"A Randomly Weighted Minimum Spanning Tree with a Random Cost Constraint","display_name":"A Randomly Weighted Minimum Spanning Tree with a Random Cost Constraint","publication_year":2021,"publication_date":"2021-01-29","ids":{"openalex":"https://openalex.org/W3004379270","doi":"https://doi.org/10.37236/9445","mag":"3004379270"},"language":"en","primary_location":{"id":"doi:10.37236/9445","is_oa":true,"landing_page_url":"https://doi.org/10.37236/9445","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v28i1p22/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v28i1p22/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5056950019","display_name":"Alan Frieze","orcid":"https://orcid.org/0000-0002-8481-5615"},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Alan Frieze","raw_affiliation_strings":["Carnegie Mellon University"],"affiliations":[{"raw_affiliation_string":"Carnegie Mellon University","institution_ids":["https://openalex.org/I74973139"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5062557622","display_name":"Tomasz Tkocz","orcid":"https://orcid.org/0000-0002-4317-3900"},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Tomasz Tkocz","raw_affiliation_strings":["Carnegie Mellon University"],"affiliations":[{"raw_affiliation_string":"Carnegie Mellon University","institution_ids":["https://openalex.org/I74973139"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5056950019"],"corresponding_institution_ids":["https://openalex.org/I74973139"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.01419921,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"28","issue":"1","first_page":"670","last_page":"689"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9977999925613403,"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"}},"topics":[{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9977999925613403,"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9959999918937683,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9919999837875366,"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/minimum-spanning-tree","display_name":"Minimum spanning tree","score":0.7669824361801147},{"id":"https://openalex.org/keywords/spanning-tree","display_name":"Spanning tree","score":0.7504584789276123},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.697974681854248},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6879262924194336},{"id":"https://openalex.org/keywords/minimum-weight","display_name":"Minimum weight","score":0.6800130605697632},{"id":"https://openalex.org/keywords/digraph","display_name":"Digraph","score":0.6637145280838013},{"id":"https://openalex.org/keywords/constructive-proof","display_name":"Constructive proof","score":0.5778285264968872},{"id":"https://openalex.org/keywords/minimum-degree-spanning-tree","display_name":"Minimum degree spanning tree","score":0.5690195560455322},{"id":"https://openalex.org/keywords/constructive","display_name":"Constructive","score":0.5440523028373718},{"id":"https://openalex.org/keywords/connected-dominating-set","display_name":"Connected dominating set","score":0.5075420141220093},{"id":"https://openalex.org/keywords/steiner-tree-problem","display_name":"Steiner tree problem","score":0.5059275031089783},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.48664411902427673},{"id":"https://openalex.org/keywords/k-minimum-spanning-tree","display_name":"k-minimum spanning tree","score":0.44588884711265564},{"id":"https://openalex.org/keywords/kruskals-algorithm","display_name":"Kruskal's algorithm","score":0.4367560148239136},{"id":"https://openalex.org/keywords/random-graph","display_name":"Random graph","score":0.43510696291923523},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.43508657813072205},{"id":"https://openalex.org/keywords/distributed-minimum-spanning-tree","display_name":"Distributed minimum spanning tree","score":0.4281699061393738},{"id":"https://openalex.org/keywords/enhanced-data-rates-for-gsm-evolution","display_name":"Enhanced Data Rates for GSM Evolution","score":0.41559216380119324},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.3821970820426941},{"id":"https://openalex.org/keywords/k-ary-tree","display_name":"K-ary tree","score":0.24888291954994202},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.16568389534950256},{"id":"https://openalex.org/keywords/binary-tree","display_name":"Binary tree","score":0.1563045084476471},{"id":"https://openalex.org/keywords/tree-structure","display_name":"Tree structure","score":0.14110028743743896}],"concepts":[{"id":"https://openalex.org/C13743678","wikidata":"https://www.wikidata.org/wiki/Q240464","display_name":"Minimum spanning tree","level":2,"score":0.7669824361801147},{"id":"https://openalex.org/C64331007","wikidata":"https://www.wikidata.org/wiki/Q831672","display_name":"Spanning tree","level":2,"score":0.7504584789276123},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.697974681854248},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6879262924194336},{"id":"https://openalex.org/C2778945305","wikidata":"https://www.wikidata.org/wiki/Q6865502","display_name":"Minimum weight","level":2,"score":0.6800130605697632},{"id":"https://openalex.org/C2779145032","wikidata":"https://www.wikidata.org/wiki/Q191494","display_name":"Digraph","level":2,"score":0.6637145280838013},{"id":"https://openalex.org/C202854965","wikidata":"https://www.wikidata.org/wiki/Q3044470","display_name":"Constructive proof","level":2,"score":0.5778285264968872},{"id":"https://openalex.org/C64271015","wikidata":"https://www.wikidata.org/wiki/Q6865444","display_name":"Minimum degree spanning tree","level":3,"score":0.5690195560455322},{"id":"https://openalex.org/C2778701210","wikidata":"https://www.wikidata.org/wiki/Q28130034","display_name":"Constructive","level":3,"score":0.5440523028373718},{"id":"https://openalex.org/C37810922","wikidata":"https://www.wikidata.org/wiki/Q5161409","display_name":"Connected dominating set","level":3,"score":0.5075420141220093},{"id":"https://openalex.org/C76220878","wikidata":"https://www.wikidata.org/wiki/Q1764144","display_name":"Steiner tree problem","level":2,"score":0.5059275031089783},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.48664411902427673},{"id":"https://openalex.org/C202750272","wikidata":"https://www.wikidata.org/wiki/Q6322849","display_name":"k-minimum spanning tree","level":5,"score":0.44588884711265564},{"id":"https://openalex.org/C63645285","wikidata":"https://www.wikidata.org/wiki/Q797860","display_name":"Kruskal's algorithm","level":3,"score":0.4367560148239136},{"id":"https://openalex.org/C47458327","wikidata":"https://www.wikidata.org/wiki/Q910404","display_name":"Random graph","level":3,"score":0.43510696291923523},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.43508657813072205},{"id":"https://openalex.org/C65949645","wikidata":"https://www.wikidata.org/wiki/Q5283163","display_name":"Distributed minimum spanning tree","level":3,"score":0.4281699061393738},{"id":"https://openalex.org/C162307627","wikidata":"https://www.wikidata.org/wiki/Q204833","display_name":"Enhanced Data Rates for GSM Evolution","level":2,"score":0.41559216380119324},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.3821970820426941},{"id":"https://openalex.org/C100560664","wikidata":"https://www.wikidata.org/wiki/Q3608019","display_name":"K-ary tree","level":4,"score":0.24888291954994202},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.16568389534950256},{"id":"https://openalex.org/C197855036","wikidata":"https://www.wikidata.org/wiki/Q380172","display_name":"Binary tree","level":2,"score":0.1563045084476471},{"id":"https://openalex.org/C163797641","wikidata":"https://www.wikidata.org/wiki/Q2067937","display_name":"Tree structure","level":3,"score":0.14110028743743896},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.0},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.37236/9445","is_oa":true,"landing_page_url":"https://doi.org/10.37236/9445","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v28i1p22/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1905.01229","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1905.01229","pdf_url":"https://arxiv.org/pdf/1905.01229","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":"","raw_type":null},{"id":"doi:10.48550/arxiv.1905.01229","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1905.01229","pdf_url":null,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"},{"id":"mag:3004379270","is_oa":false,"landing_page_url":"https://dblp.uni-trier.de/db/conf/soda/soda2020.html#FriezeT20","pdf_url":null,"source":{"id":"https://openalex.org/S4306420974","display_name":"Symposium on Discrete Algorithms","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"conference"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":"Symposium on Discrete Algorithms","raw_type":null}],"best_oa_location":{"id":"doi:10.37236/9445","is_oa":true,"landing_page_url":"https://doi.org/10.37236/9445","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v28i1p22/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3077003604","display_name":null,"funder_award_id":"DMS1955175","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G445480892","display_name":null,"funder_award_id":"DMS1661063","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8139251166","display_name":"Random Structures and Algorithms","funder_award_id":"1661063","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320306164","display_name":"Simons Foundation","ror":"https://ror.org/01cmst727"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3004379270.pdf","grobid_xml":"https://content.openalex.org/works/W3004379270.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W3130835883","https://openalex.org/W1965702747","https://openalex.org/W3010374802","https://openalex.org/W1576317141","https://openalex.org/W2617647927","https://openalex.org/W2349424300","https://openalex.org/W2396379829","https://openalex.org/W1977567299","https://openalex.org/W2092979316","https://openalex.org/W2059559155","https://openalex.org/W1965810411","https://openalex.org/W2066266916","https://openalex.org/W1491195793","https://openalex.org/W2354042733","https://openalex.org/W2014324934","https://openalex.org/W88291963","https://openalex.org/W1484903242","https://openalex.org/W2095963760","https://openalex.org/W2809830069","https://openalex.org/W2005675714"],"abstract_inverted_index":{"We":[0,61],"study":[1],"the":[2,8,32,42,53,70,74,78],"minimum":[3],"spanning":[4,54],"tree":[5,55],"problem":[6],"on":[7],"complete":[9],"graph":[10],"$K_n$":[11],"where":[12,36],"an":[13,28],"edge":[14],"$e$":[15],"has":[16],"a":[17,21,50,64,81],"weight":[18,76],"$W_e$":[19],"and":[20,39],"cost":[22],"$C_e$,":[23],"each":[24],"of":[25,31,66,73,80],"which":[26],"is":[27,41,48],"independent":[29],"copy":[30],"random":[33,45],"variable":[34],"$U^\\gamma$":[35],"$\\gamma\\leq":[37],"1$":[38],"$U$":[40],"uniform":[43],"$[0,1]$":[44],"variable.":[46],"There":[47],"also":[49],"constraint":[51],"that":[52],"$T$":[56],"must":[57],"satisfy":[58],"$C(T)\\leq":[59],"c_0$.":[60],"establish,":[62],"for":[63,68],"range":[65],"values":[67],"$c_0,\\gamma$,":[69],"asymptotic":[71],"value":[72],"optimum":[75],"via":[77],"consideration":[79],"dual":[82],"problem.":[83]},"counts_by_year":[],"updated_date":"2026-04-21T08:09:41.155169","created_date":"2025-10-10T00:00:00"}