{"id":"https://openalex.org/W2047680997","doi":"https://doi.org/10.1137/0218015","title":"The Token Distribution Problem","display_name":"The Token Distribution Problem","publication_year":1989,"publication_date":"1989-04-01","ids":{"openalex":"https://openalex.org/W2047680997","doi":"https://doi.org/10.1137/0218015","mag":"2047680997"},"language":"en","primary_location":{"id":"doi:10.1137/0218015","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0218015","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","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/A5056419022","display_name":"David Peleg","orcid":"https://orcid.org/0000-0003-1590-0506"},"institutions":[{"id":"https://openalex.org/I53964585","display_name":"Weizmann Institute of Science","ror":"https://ror.org/0316ej306","country_code":"IL","type":"education","lineage":["https://openalex.org/I53964585"]}],"countries":["IL"],"is_corresponding":true,"raw_author_name":"David Peleg","raw_affiliation_strings":["The Weizmann Institute of Science, Rehovot, Israel"],"affiliations":[{"raw_affiliation_string":"The Weizmann Institute of Science, Rehovot, Israel","institution_ids":["https://openalex.org/I53964585"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5028869858","display_name":"Eli Upfal","orcid":"https://orcid.org/0000-0002-9321-9460"},"institutions":[{"id":"https://openalex.org/I53964585","display_name":"Weizmann Institute of Science","ror":"https://ror.org/0316ej306","country_code":"IL","type":"education","lineage":["https://openalex.org/I53964585"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Eli Upfal","raw_affiliation_strings":["The Weizmann Institute of Science, Rehovot, Israel"],"affiliations":[{"raw_affiliation_string":"The Weizmann Institute of Science, Rehovot, Israel","institution_ids":["https://openalex.org/I53964585"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5056419022"],"corresponding_institution_ids":["https://openalex.org/I53964585"],"apc_list":null,"apc_paid":null,"fwci":5.8458,"has_fulltext":false,"cited_by_count":88,"citation_normalized_percentile":{"value":0.96079198,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"18","issue":"2","first_page":"229","last_page":"243"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10772","display_name":"Distributed systems and fault tolerance","score":0.9987999796867371,"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":0.9987999796867371,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9962999820709229,"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/T11716","display_name":"Random Matrices and Applications","score":0.9944999814033508,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/expander-graph","display_name":"Expander graph","score":0.850993275642395},{"id":"https://openalex.org/keywords/security-token","display_name":"Security token","score":0.5716776251792908},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5447377562522888},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5113429427146912},{"id":"https://openalex.org/keywords/binary-logarithm","display_name":"Binary logarithm","score":0.4939118027687073},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.49226656556129456},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4348964989185333},{"id":"https://openalex.org/keywords/distribution","display_name":"Distribution (mathematics)","score":0.43223002552986145},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.43140825629234314},{"id":"https://openalex.org/keywords/probabilistic-logic","display_name":"Probabilistic logic","score":0.42906394600868225},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.35632503032684326}],"concepts":[{"id":"https://openalex.org/C154547637","wikidata":"https://www.wikidata.org/wiki/Q776602","display_name":"Expander graph","level":3,"score":0.850993275642395},{"id":"https://openalex.org/C48145219","wikidata":"https://www.wikidata.org/wiki/Q1335365","display_name":"Security token","level":2,"score":0.5716776251792908},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5447377562522888},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5113429427146912},{"id":"https://openalex.org/C63553672","wikidata":"https://www.wikidata.org/wiki/Q581168","display_name":"Binary logarithm","level":2,"score":0.4939118027687073},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.49226656556129456},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4348964989185333},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.43223002552986145},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.43140825629234314},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.42906394600868225},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.35632503032684326},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","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},{"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:10.1137/0218015","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0218015","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","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":9,"referenced_works":["https://openalex.org/W1631603072","https://openalex.org/W1994038072","https://openalex.org/W2004759812","https://openalex.org/W2042587503","https://openalex.org/W2043560882","https://openalex.org/W2058355999","https://openalex.org/W2107997203","https://openalex.org/W2121284046","https://openalex.org/W2157211828"],"related_works":["https://openalex.org/W2078123803","https://openalex.org/W4388335561","https://openalex.org/W2970530566","https://openalex.org/W1491170033","https://openalex.org/W2967478618","https://openalex.org/W2997152889","https://openalex.org/W4385009901","https://openalex.org/W2089439745","https://openalex.org/W2099601775","https://openalex.org/W1539916885"],"abstract_inverted_index":{"A":[0],"solution":[1,110,150,174],"to":[2,31,107,116,159,172],"the":[3,43,47,62,97,109,112,122,152,160,173],"following":[4],"fundamental":[5],"communication":[6,135,167],"problem":[7,29,77,115,125],"is":[8,30,52,68,104,140],"presented.":[9],"Suppose":[10],"that":[11,40,71,134],"n":[12,18],"tokens":[13,44],"are":[14],"arbitrarily":[15],"distributed":[16,179],"among":[17,46],"processors":[19],"with":[20,91],"no":[21],"processor":[22],"having":[23],"more":[24],"than":[25],"K":[26],"tokens.":[27],"The":[28,49],"specify":[32],"a":[33,53,127,141],"bounded-degree":[34],"network":[35],"topology":[36],"and":[37,165],"an":[38,72,117,137,145],"algorithm":[39,120],"can":[41,78],"distribute":[42],"uniformly":[45],"processors.":[48],"first":[50],"result":[51],"tight":[54],"$\\Theta":[55],"(K":[56],"+":[57,84,147],"\\log":[58,85,148],"n)$":[59,86,149],"bound":[60],"on":[61,87,126],"complexity":[63],"of":[64,75,100,130,151,163,175],"this":[65,76,101],"problem.":[66,153],"It":[67],"also":[69],"shown":[70,105],"approximate":[73,113],"version":[74],"be":[79],"solved":[80],"deterministically":[81],"in":[82,178],"$O(K":[83,146],"any":[88],"expander":[89,131,138],"graph":[90,139],"sufficiently":[92],"large":[93],"expansion":[94],"factor.":[95],"In":[96],"second":[98],"part":[99],"work,":[102],"it":[103],"how":[106],"extend":[108],"for":[111,121,144],"distribution":[114,124],"optimal":[118],"probabilistic":[119],"exact":[123],"similar":[128],"class":[129],"graphs.":[132],"Note":[133],"through":[136],"necessary":[142],"condition":[143],"These":[154],"results":[155],"have":[156],"direct":[157],"applications":[158],"efficient":[161],"implementation":[162],"many-to-one":[164],"one-to-many":[166],"requests,":[168],"as":[169,171],"well":[170],"load-balancing":[176],"problems":[177],"systems.":[180]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
