{"id":"https://openalex.org/W2571496458","doi":"https://doi.org/10.1002/rsa.20341","title":"Smoothed analysis of balancing networks","display_name":"Smoothed analysis of balancing networks","publication_year":2010,"publication_date":"2010-09-15","ids":{"openalex":"https://openalex.org/W2571496458","doi":"https://doi.org/10.1002/rsa.20341","mag":"2571496458"},"language":"en","primary_location":{"id":"doi:10.1002/rsa.20341","is_oa":true,"landing_page_url":"https://doi.org/10.1002/rsa.20341","pdf_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1002/rsa.20341","source":{"id":"https://openalex.org/S59667848","display_name":"Random Structures and Algorithms","issn_l":"1042-9832","issn":["1042-9832","1098-2418"],"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":"Random Structures &amp; Algorithms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1002/rsa.20341","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5077389210","display_name":"Tobias Friedrich","orcid":"https://orcid.org/0000-0003-0076-6308"},"institutions":[{"id":"https://openalex.org/I4210109712","display_name":"Max Planck Institute for Informatics","ror":"https://ror.org/01w19ak89","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210109712"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Tobias Friedrich","raw_affiliation_strings":["Department of Algorithms and Complexity, Max-Planck-Institut fu\u0308r Informatik, Saarbru\u0308cken, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Algorithms and Complexity, Max-Planck-Institut fu\u0308r Informatik, Saarbru\u0308cken, Germany","institution_ids":["https://openalex.org/I4210109712"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5017390373","display_name":"Thomas Sauerwald","orcid":"https://orcid.org/0000-0002-0882-283X"},"institutions":[{"id":"https://openalex.org/I18014758","display_name":"Simon Fraser University","ror":"https://ror.org/0213rcc28","country_code":"CA","type":"education","lineage":["https://openalex.org/I18014758"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Thomas Sauerwald","raw_affiliation_strings":["School of Computing Science, Simon Fraser University, Burnaby, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computing Science, Simon Fraser University, Burnaby, Canada","institution_ids":["https://openalex.org/I18014758"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5067064621","display_name":"Dan Vilenchik","orcid":"https://orcid.org/0000-0002-3895-688X"},"institutions":[{"id":"https://openalex.org/I161318765","display_name":"University of California, Los Angeles","ror":"https://ror.org/046rm7j60","country_code":"US","type":"education","lineage":["https://openalex.org/I161318765"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Dan Vilenchik","raw_affiliation_strings":["Department of Mathematics, University of California, Los Angeles, California"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of California, Los Angeles, California","institution_ids":["https://openalex.org/I161318765"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5077389210"],"corresponding_institution_ids":["https://openalex.org/I4210109712"],"apc_list":{"value":4330,"currency":"USD","value_usd":4330},"apc_paid":null,"fwci":0.8536,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.78133787,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"39","issue":"1","first_page":"115","last_page":"138"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9997000098228455,"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"}},"topics":[{"id":"https://openalex.org/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9997000098228455,"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/T12404","display_name":"Mathematical Approximation and Integration","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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":0.9994000196456909,"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/security-token","display_name":"Security token","score":0.7143192887306213},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6398285627365112},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5170257687568665},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4475897550582886},{"id":"https://openalex.org/keywords/binary-logarithm","display_name":"Binary logarithm","score":0.423062264919281},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4184940457344055},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.36959969997406006},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.07251882553100586}],"concepts":[{"id":"https://openalex.org/C48145219","wikidata":"https://www.wikidata.org/wiki/Q1335365","display_name":"Security token","level":2,"score":0.7143192887306213},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6398285627365112},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5170257687568665},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4475897550582886},{"id":"https://openalex.org/C63553672","wikidata":"https://www.wikidata.org/wiki/Q581168","display_name":"Binary logarithm","level":2,"score":0.423062264919281},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4184940457344055},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.36959969997406006},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.07251882553100586},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1002/rsa.20341","is_oa":true,"landing_page_url":"https://doi.org/10.1002/rsa.20341","pdf_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1002/rsa.20341","source":{"id":"https://openalex.org/S59667848","display_name":"Random Structures and Algorithms","issn_l":"1042-9832","issn":["1042-9832","1098-2418"],"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":"Random Structures &amp; Algorithms","raw_type":"journal-article"},{"id":"pmh:oai:edoc.mpg.de:536803","is_oa":false,"landing_page_url":"http://edoc.mpg.de/536803","pdf_url":null,"source":{"id":"https://openalex.org/S4406922265","display_name":"Max Planck Institute for Plasma Physics","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":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Random Structures and Algorithms, v.Early View, 1-24 (2010)","raw_type":"Article"},{"id":"pmh:oai:edoc.mpg.de:618748","is_oa":false,"landing_page_url":"http://edoc.mpg.de/618748","pdf_url":null,"source":{"id":"https://openalex.org/S4406922265","display_name":"Max Planck Institute for Plasma Physics","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":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Random Structures &amp; Algorithms, v.39, 115-138 (2011)","raw_type":"Article"}],"best_oa_location":{"id":"doi:10.1002/rsa.20341","is_oa":true,"landing_page_url":"https://doi.org/10.1002/rsa.20341","pdf_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1002/rsa.20341","source":{"id":"https://openalex.org/S59667848","display_name":"Random Structures and Algorithms","issn_l":"1042-9832","issn":["1042-9832","1098-2418"],"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":"Random Structures &amp; Algorithms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W2571496458.pdf"},"referenced_works_count":25,"referenced_works":["https://openalex.org/W1495051890","https://openalex.org/W1603765807","https://openalex.org/W1695073853","https://openalex.org/W1909387666","https://openalex.org/W1969080501","https://openalex.org/W1983572666","https://openalex.org/W2006605460","https://openalex.org/W2023434464","https://openalex.org/W2029013046","https://openalex.org/W2034053794","https://openalex.org/W2036176451","https://openalex.org/W2050761777","https://openalex.org/W2088859845","https://openalex.org/W2096006817","https://openalex.org/W2096567392","https://openalex.org/W2113600113","https://openalex.org/W2122140789","https://openalex.org/W2157661221","https://openalex.org/W2170959740","https://openalex.org/W2295944892","https://openalex.org/W2639104656","https://openalex.org/W2987042746","https://openalex.org/W4237527233","https://openalex.org/W4247942259","https://openalex.org/W4293763691"],"related_works":["https://openalex.org/W2970530566","https://openalex.org/W2967478618","https://openalex.org/W2997152889","https://openalex.org/W4385572700","https://openalex.org/W4388335561","https://openalex.org/W4307309205","https://openalex.org/W4288261899","https://openalex.org/W4385009901","https://openalex.org/W1983915440","https://openalex.org/W3095925971"],"abstract_inverted_index":{"Abstract":[0],"In":[1,57],"a":[2,62,70,105,158],"balancing":[3,109],"network":[4,160],"each":[5,17,98],"processor":[6],"has":[7],"an":[8,89],"initial":[9],"collection":[10],"of":[11,20,54,84,92,108],"unit\u2010size":[12],"jobs":[13],"(tokens)":[14],"and":[15,77,95,141,150],"in":[16],"round,":[18],"pairs":[19],"processors":[21],"connected":[22],"by":[23],"balancers":[24],"split":[25],"their":[26],"load":[27],"as":[28,30],"evenly":[29],"possible.":[31],"An":[32],"excess":[33],"token":[34],"(if":[35],"any)":[36],"is":[37,124],"placed":[38],"according":[39],"to":[40],"some":[41],"predefined":[42],"rule.":[43],"As":[44],"it":[45],"turns":[46],"out,":[47],"this":[48,58,66],"rule":[49],"crucially":[50],"affects":[51],"the":[52,55,73,78,82,122,162],"performance":[53],"network.":[56],"work":[59],"we":[60],"propose":[61],"model":[63,71],"that":[64,114,157],"studies":[65],"effect.":[67],"We":[68,86,154],"suggest":[69],"bridging":[72],"uniformly\u2010random":[74],"assignment":[75,91,99],"rule,":[76],"arbitrary":[79,90],"one":[80],"(in":[81],"spirit":[83],"smoothed\u2010analysis).":[85],"start":[87],"with":[88,100,136],"balancer":[93],"directions":[94],"then":[96],"flip":[97],"probability":[101],"\u03b1":[102,147,151],"independently.":[103],"For":[104],"large":[106],"class":[107],"networks":[110],"our":[111],"result":[112],"implies":[113],"after":[115],"\\documentclass{article}":[116,125],"\\usepackage{amsmath,amsfonts,mathrsfs}\\pagestyle{empty}\\begin{document}":[117,126],"$\\mathcal{O}(\\log":[118],"n)$":[119,134],"\\end{document}":[120,135],"rounds":[121],"discrepancy":[123],"$\\mathcal{O}(":[127],"(1/2-\\alpha)":[128],"\\log":[129,132,133],"n":[130],"+":[131],"high":[137],"probability.":[138],"This":[139],"matches":[140,161],"generalizes":[142],"known":[143],"upper":[144,163],"bounds":[145],"for":[146,165],"=":[148,152],"0":[149],"1/2.":[153],"also":[155],"show":[156],"natural":[159],"bound":[164],"any":[166],"\u03b1.":[167],"\u00a9":[168],"2010":[169],"Wiley":[170],"Periodicals,":[171],"Inc.":[172],"Random":[173],"Struct.":[174],"Alg.,":[175],"39,":[176],"115\u2013138,":[177],"2011":[178]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
