{"id":"https://openalex.org/W4289822360","doi":"https://doi.org/10.1109/tnsm.2022.3195292","title":"Tree Representation, Growth Rate of Blockchain and Reward Allocation in Ethereum With Multiple Mining Pools","display_name":"Tree Representation, Growth Rate of Blockchain and Reward Allocation in Ethereum With Multiple Mining Pools","publication_year":2022,"publication_date":"2022-08-05","ids":{"openalex":"https://openalex.org/W4289822360","doi":"https://doi.org/10.1109/tnsm.2022.3195292"},"language":"en","primary_location":{"id":"doi:10.1109/tnsm.2022.3195292","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnsm.2022.3195292","pdf_url":null,"source":{"id":"https://openalex.org/S173527311","display_name":"IEEE Transactions on Network and Service Management","issn_l":"1932-4537","issn":["1932-4537","2373-7379"],"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 Network and Service Management","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/A5101938734","display_name":"Quan\u2010Lin Li","orcid":"https://orcid.org/0000-0002-6400-1059"},"institutions":[{"id":"https://openalex.org/I37796252","display_name":"Beijing University of Technology","ror":"https://ror.org/037b1pp87","country_code":"CN","type":"education","lineage":["https://openalex.org/I37796252"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Quan-Lin Li","raw_affiliation_strings":["School of Economics and Management, Beijing University of Technology, Beijing, China"],"affiliations":[{"raw_affiliation_string":"School of Economics and Management, Beijing University of Technology, Beijing, China","institution_ids":["https://openalex.org/I37796252"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5063230011","display_name":"Yan-Xia Chang","orcid":"https://orcid.org/0000-0001-7601-6998"},"institutions":[{"id":"https://openalex.org/I37796252","display_name":"Beijing University of Technology","ror":"https://ror.org/037b1pp87","country_code":"CN","type":"education","lineage":["https://openalex.org/I37796252"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yan-Xia Chang","raw_affiliation_strings":["School of Economics and Management, Beijing University of Technology, Beijing, China"],"affiliations":[{"raw_affiliation_string":"School of Economics and Management, Beijing University of Technology, Beijing, China","institution_ids":["https://openalex.org/I37796252"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100458229","display_name":"Chi Zhang","orcid":"https://orcid.org/0000-0003-1475-333X"},"institutions":[{"id":"https://openalex.org/I37796252","display_name":"Beijing University of Technology","ror":"https://ror.org/037b1pp87","country_code":"CN","type":"education","lineage":["https://openalex.org/I37796252"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chi Zhang","raw_affiliation_strings":["School of Economics and Management, Beijing University of Technology, Beijing, China"],"affiliations":[{"raw_affiliation_string":"School of Economics and Management, Beijing University of Technology, Beijing, China","institution_ids":["https://openalex.org/I37796252"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5101938734"],"corresponding_institution_ids":["https://openalex.org/I37796252"],"apc_list":null,"apc_paid":null,"fwci":3.6389,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.93855729,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":98},"biblio":{"volume":"20","issue":"1","first_page":"182","last_page":"200"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10270","display_name":"Blockchain Technology Applications and Security","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1710","display_name":"Information Systems"},"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/T10270","display_name":"Blockchain Technology Applications and Security","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1710","display_name":"Information Systems"},"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/computer-science","display_name":"Computer science","score":0.7875736951828003},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.6243185997009277},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.5515970587730408},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.5490730404853821},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.5460801124572754},{"id":"https://openalex.org/keywords/key","display_name":"Key (lock)","score":0.5077697038650513},{"id":"https://openalex.org/keywords/blockchain","display_name":"Blockchain","score":0.4972884953022003},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.32507598400115967},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.1542903482913971}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7875736951828003},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.6243185997009277},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.5515970587730408},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.5490730404853821},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.5460801124572754},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.5077697038650513},{"id":"https://openalex.org/C2779687700","wikidata":"https://www.wikidata.org/wiki/Q20514253","display_name":"Blockchain","level":2,"score":0.4972884953022003},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.32507598400115967},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.1542903482913971},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tnsm.2022.3195292","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnsm.2022.3195292","pdf_url":null,"source":{"id":"https://openalex.org/S173527311","display_name":"IEEE Transactions on Network and Service Management","issn_l":"1932-4537","issn":["1932-4537","2373-7379"],"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 Network and Service Management","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G152187440","display_name":null,"funder_award_id":"71932002","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2625577841","display_name":null,"funder_award_id":"71671158","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":43,"referenced_works":["https://openalex.org/W2103863878","https://openalex.org/W2295940006","https://openalex.org/W2397661077","https://openalex.org/W2557090183","https://openalex.org/W2604844934","https://openalex.org/W2798711290","https://openalex.org/W2803238698","https://openalex.org/W2805943963","https://openalex.org/W2897525439","https://openalex.org/W2901425049","https://openalex.org/W2901509724","https://openalex.org/W2916837475","https://openalex.org/W2942565834","https://openalex.org/W2943740904","https://openalex.org/W2947589355","https://openalex.org/W2949029756","https://openalex.org/W2952214479","https://openalex.org/W2963594166","https://openalex.org/W2963822137","https://openalex.org/W2966761660","https://openalex.org/W2978321937","https://openalex.org/W2981886215","https://openalex.org/W2982544778","https://openalex.org/W3001603089","https://openalex.org/W3017676959","https://openalex.org/W3034459010","https://openalex.org/W3077087723","https://openalex.org/W3091755869","https://openalex.org/W3098407052","https://openalex.org/W3103292315","https://openalex.org/W3110928664","https://openalex.org/W3113438726","https://openalex.org/W3156382242","https://openalex.org/W3176708559","https://openalex.org/W3201477816","https://openalex.org/W3214711012","https://openalex.org/W4248175462","https://openalex.org/W4288257480","https://openalex.org/W4295178704","https://openalex.org/W4302377426","https://openalex.org/W6712179443","https://openalex.org/W6747952709","https://openalex.org/W6767115310"],"related_works":["https://openalex.org/W4210406818","https://openalex.org/W4306779889","https://openalex.org/W3048554917","https://openalex.org/W3211706803","https://openalex.org/W4382775358","https://openalex.org/W4246942721","https://openalex.org/W3209862047","https://openalex.org/W4386732777","https://openalex.org/W4304136894","https://openalex.org/W2989851257"],"abstract_inverted_index":{"It":[0],"is":[1],"interesting":[2],"but":[3,42],"difficult":[4],"and":[5,98,101,106,133,159,172,180,204,227],"challenging":[6],"to":[7,24,37,45,52,154],"study":[8,238],"Ethereum":[9,217,240],"with":[10,30,74,218,241],"multiple":[11,31,39,58,75,139,188,219,242],"mining":[12,40,54,59,140,189,211,220,243],"pools.":[13,60,221],"One":[14],"of":[15,84,108,113,119,131,178,208,216,239,249],"the":[16,38,53,57,72,89,110,117,128,134,138,144,162,169,174,181,187,206,209,214,225,237],"main":[17,90],"difficulties":[18],"comes":[19],"from":[20],"not":[21],"only":[22],"how":[23,44],"represent":[25],"such":[26,167,245],"a":[27,47,68,81,193,199,247],"general":[28],"tree":[29,73],"block":[32,76,82],"branches":[33],"(or":[34],"sub-chains)":[35],"related":[36],"pools,":[41,190,244],"also":[43],"analyze":[46],"multi-dimensional":[48],"stochastic":[49],"system":[50],"due":[51],"competition":[55],"among":[56,137,186],"In":[61],"this":[62,231],"paper,":[63],"we":[64,79,125,149,197],"first":[65],"set":[66],"up":[67],"mathematical":[69],"representation":[70],"for":[71,202],"branches.":[77],"Then":[78],"provide":[80,198],"classification":[83],"Ethereum:":[85],"Regular":[86],"blocks":[87,114],"(in":[88],"chain),":[91],"orphan":[92],"blocks,":[93,95,97,100],"uncle":[94],"stale":[96],"nephew":[99],"give":[102],"some":[103,151],"key":[104,170],"ratios":[105,171],"probabilities":[107],"generating":[109],"different":[111],"types":[112],"by":[115],"applying":[116,143],"law":[118],"large":[120],"numbers.":[121],"Based":[122],"on":[123,213,236],"this,":[124],"further":[126],"discuss":[127],"growth":[129,176],"rate":[130,177],"blockchain":[132],"reward":[135,146,183],"allocation":[136,184],"pools":[141],"through":[142],"renewal":[145],"theorem.":[147],"Finally,":[148],"use":[150],"simulation":[152],"experiments":[153],"verify":[155],"our":[156],"theoretical":[157],"results,":[158],"show":[160],"that":[161,224,246],"approximate":[163],"computation":[164],"approaches":[165],"developed,":[166],"as":[168],"probabilities,":[173],"long-term":[175,182],"blockchain,":[179],"(rate)":[185],"can":[191,252],"have":[192],"faster":[194],"convergence.":[195],"Therefore,":[196],"powerful":[200],"tool":[201],"observing":[203],"understanding":[205],"influence":[207],"selfish":[210],"attacks":[212],"performance":[215],"We":[222],"believe":[223],"methodology":[226],"results":[228],"developed":[229],"in":[230],"paper":[232],"will":[233],"shed":[234],"light":[235],"series":[248],"promising":[250],"research":[251],"be":[253],"inspired":[254],"potentially.":[255]},"counts_by_year":[{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}