{"id":"https://openalex.org/W1489494099","doi":"https://doi.org/10.1007/3-540-61422-2_116","title":"The Randomized Complexity of Maintaining the Minimum","display_name":"The Randomized Complexity of Maintaining the Minimum","publication_year":1996,"publication_date":"1996-01-01","ids":{"openalex":"https://openalex.org/W1489494099","doi":"https://doi.org/10.1007/3-540-61422-2_116","mag":"1489494099"},"language":"en","primary_location":{"id":"doi:10.1007/3-540-61422-2_116","is_oa":false,"landing_page_url":"https://doi.org/10.1007/3-540-61422-2_116","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://tidsskrift.dk/brics/article/download/20022/17654","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5039943336","display_name":"Gerth St\u00f8lting Brodal","orcid":"https://orcid.org/0000-0001-9054-915X"},"institutions":[{"id":"https://openalex.org/I204337017","display_name":"Aarhus University","ror":"https://ror.org/01aj84f44","country_code":"DK","type":"education","lineage":["https://openalex.org/I204337017"]}],"countries":["DK"],"is_corresponding":false,"raw_author_name":"Gerth St\u00f8lting Brodal","raw_affiliation_strings":["BRICS, Department of Computer Science, University of Aarhus, Ny Munkegade, DK-8000 \u00c5rhus C, Denmark"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"BRICS, Department of Computer Science, University of Aarhus, Ny Munkegade, DK-8000 \u00c5rhus C, Denmark","institution_ids":["https://openalex.org/I204337017"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5109880876","display_name":"Shiva Chaudhuri","orcid":null},"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":false,"raw_author_name":"Shiva Chaudhuri","raw_affiliation_strings":["Max-Planck Institut f\u00fcr Informatik, Im Stadtwald, 66123 Saarbr\u00fccken, Germany#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Max-Planck Institut f\u00fcr Informatik, Im Stadtwald, 66123 Saarbr\u00fccken, Germany#TAB#","institution_ids":["https://openalex.org/I4210109712"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5080324608","display_name":"Jaikumar Radhakrishnan","orcid":"https://orcid.org/0000-0002-3875-4620"},"institutions":[{"id":"https://openalex.org/I11947397","display_name":"Tata Institute of Fundamental Research","ror":"https://ror.org/03ht1xw27","country_code":"IN","type":"education","lineage":["https://openalex.org/I11947397","https://openalex.org/I2799351866","https://openalex.org/I3149292468"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Jaikumar Radhakrishnan","raw_affiliation_strings":["Tata Institute of Fundamental Research, Mumbai, India.#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Tata Institute of Fundamental Research, Mumbai, India.#TAB#","institution_ids":["https://openalex.org/I11947397"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":{"value":5000,"currency":"EUR","value_usd":5392},"fwci":0.5166,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.60869174,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"3","issue":"40","first_page":"4","last_page":"15"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9993000030517578,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9993000030517578,"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/T12288","display_name":"Optimization and Search Problems","score":0.9980000257492065,"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/T11567","display_name":"semigroups and automata theory","score":0.9973000288009644,"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/amortized-analysis","display_name":"Amortized analysis","score":0.8462483882904053},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.7299258708953857},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6007532477378845},{"id":"https://openalex.org/keywords/randomized-algorithm","display_name":"Randomized algorithm","score":0.5709224939346313},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5386388897895813},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.44774138927459717},{"id":"https://openalex.org/keywords/deterministic-algorithm","display_name":"Deterministic algorithm","score":0.42110979557037354},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4051395654678345},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.38347017765045166},{"id":"https://openalex.org/keywords/data-structure","display_name":"Data structure","score":0.2650882601737976}],"concepts":[{"id":"https://openalex.org/C142417499","wikidata":"https://www.wikidata.org/wiki/Q331716","display_name":"Amortized analysis","level":3,"score":0.8462483882904053},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.7299258708953857},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6007532477378845},{"id":"https://openalex.org/C128669082","wikidata":"https://www.wikidata.org/wiki/Q583461","display_name":"Randomized algorithm","level":2,"score":0.5709224939346313},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5386388897895813},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.44774138927459717},{"id":"https://openalex.org/C13533509","wikidata":"https://www.wikidata.org/wiki/Q1064349","display_name":"Deterministic algorithm","level":2,"score":0.42110979557037354},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4051395654678345},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.38347017765045166},{"id":"https://openalex.org/C162319229","wikidata":"https://www.wikidata.org/wiki/Q175263","display_name":"Data structure","level":2,"score":0.2650882601737976},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":13,"locations":[{"id":"doi:10.1007/3-540-61422-2_116","is_oa":false,"landing_page_url":"https://doi.org/10.1007/3-540-61422-2_116","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},{"id":"doi:10.7146/brics.v3i40.20022","is_oa":true,"landing_page_url":"https://doi.org/10.7146/brics.v3i40.20022","pdf_url":"https://tidsskrift.dk/brics/article/download/20022/17654","source":{"id":"https://openalex.org/S2764813624","display_name":"BRICS Report Series","issn_l":"0909-0878","issn":["0909-0878","1601-5355"],"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":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"BRICS Report Series","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.38.3550","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.38.3550","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.daimi.aau.dk/~gerth/Papers/njc.swat96.ps.gz","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.43.901","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.43.901","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.daimi.aau.dk/~gerth/Papers/mpi-i-96-1-014.ps.gz","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.54.7586","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.54.7586","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.brics.dk/~gerth/Papers/swat96min.ps.gz","raw_type":"text"},{"id":"pmh:oai:edoc.mpg.de:517727","is_oa":false,"landing_page_url":"http://edoc.mpg.de/517727","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":"Karlsson, Rolf; Lingas, Andrzej: Algorithm Theory - SWAT'96: 5th Scandinavian Workshop on Algorithm Theory, Springer, 4-15 (1996)","raw_type":"Conference-Paper"},{"id":"pmh:oai:edoc.mpg.de:517827","is_oa":false,"landing_page_url":"http://edoc.mpg.de/517827","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":"Nordic Journal of Computing, v.3, 337-351 (1996)","raw_type":"Article"},{"id":"pmh:oai:pure.atira.dk:publications/248b59d3-5062-4dca-90d4-a819c06edcc7","is_oa":false,"landing_page_url":"https://pure.au.dk/portal/en/publications/248b59d3-5062-4dca-90d4-a819c06edcc7","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Brodal, G S, Chaudhuri, S & Radhakrishnan, J 1996, 'The randomized complexity of maintaining the minimum', Nordic Journal of Computing, vol. 3, no. 4, pp. 337-351.","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:pure.mpg.de:item_1331725","is_oa":false,"landing_page_url":"http://hdl.handle.net/11858/00-001M-0000-0014-ABAD-7","pdf_url":null,"source":{"id":"https://openalex.org/S4306400654","display_name":"MPG.PuRe (Max Planck Society)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I149899117","host_organization_name":"Max Planck Society","host_organization_lineage":["https://openalex.org/I149899117"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"info:eu-repo/semantics/conferenceObject"},{"id":"pmh:oai:pure.mpg.de:item_1331726","is_oa":false,"landing_page_url":"http://hdl.handle.net/11858/00-001M-0000-0014-ABAF-3","pdf_url":null,"source":{"id":"https://openalex.org/S4306400654","display_name":"MPG.PuRe (Max Planck Society)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I149899117","host_organization_name":"Max Planck Society","host_organization_lineage":["https://openalex.org/I149899117"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Nordic Journal of Computing","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:pure.mpg.de:item_1827396","is_oa":true,"landing_page_url":"http://hdl.handle.net/11858/00-001M-0000-0014-A18C-7","pdf_url":null,"source":{"id":"https://openalex.org/S4306400654","display_name":"MPG.PuRe (Max Planck Society)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I149899117","host_organization_name":"Max Planck Society","host_organization_lineage":["https://openalex.org/I149899117"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Research Report / Max-Planck-Institut f\u00fcr Informatik","raw_type":"info:eu-repo/semantics/report"},{"id":"mag:1489494099","is_oa":false,"landing_page_url":"http://pubman.mpdl.mpg.de/pubman/item/escidoc:1331726","pdf_url":null,"source":{"id":"https://openalex.org/S34876645","display_name":"Nordic journal of computing","issn_l":"1236-6064","issn":["1236-6064"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":"Nordic journal of computing","raw_type":null},{"id":"mag:1541523264","is_oa":false,"landing_page_url":"http://pubman.mpdl.mpg.de/pubman/item/escidoc:1331725","pdf_url":null,"source":{"id":"https://openalex.org/S4306533943","display_name":"Untitled Event","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":"Untitled Event","raw_type":null}],"best_oa_location":{"id":"doi:10.7146/brics.v3i40.20022","is_oa":true,"landing_page_url":"https://doi.org/10.7146/brics.v3i40.20022","pdf_url":"https://tidsskrift.dk/brics/article/download/20022/17654","source":{"id":"https://openalex.org/S2764813624","display_name":"BRICS Report Series","issn_l":"0909-0878","issn":["0909-0878","1601-5355"],"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":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"BRICS Report Series","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320320671","display_name":"National Research Foundation","ror":"https://ror.org/05s0g1g46"},{"id":"https://openalex.org/F4320320943","display_name":"Danmarks Grundforskningsfond","ror":"https://ror.org/00znyv691"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1489494099.pdf","grobid_xml":"https://content.openalex.org/works/W1489494099.grobid-xml"},"referenced_works_count":17,"referenced_works":["https://openalex.org/W1488538028","https://openalex.org/W1535027983","https://openalex.org/W1543575092","https://openalex.org/W1757811393","https://openalex.org/W1972951113","https://openalex.org/W2023146810","https://openalex.org/W2023224443","https://openalex.org/W2045183461","https://openalex.org/W2045807935","https://openalex.org/W2063301486","https://openalex.org/W2134458085","https://openalex.org/W2136598300","https://openalex.org/W2269804680","https://openalex.org/W2347079328","https://openalex.org/W3198470706","https://openalex.org/W4240200084","https://openalex.org/W6661673758"],"related_works":["https://openalex.org/W2277905681","https://openalex.org/W2045807935","https://openalex.org/W1864228528","https://openalex.org/W2950044093","https://openalex.org/W2527128860","https://openalex.org/W2750791343","https://openalex.org/W1543525280","https://openalex.org/W1989218322","https://openalex.org/W1979700875","https://openalex.org/W2096809840","https://openalex.org/W2088826026","https://openalex.org/W1975646422","https://openalex.org/W2100135702","https://openalex.org/W2989876257","https://openalex.org/W1555216065","https://openalex.org/W2246679964","https://openalex.org/W1489861152","https://openalex.org/W2114720809","https://openalex.org/W2950382589","https://openalex.org/W2084077236"],"abstract_inverted_index":{"The":[0],"complexity":[1],"of":[2,100],"maintaining":[3],"a":[4,52,61,87],"set":[5],"under":[6],"the":[7,16,101],"operations":[8],"Insert,":[9],"Delete":[10,35],"and":[11,34],"FindMin":[12,48],"is":[13,20,49,58,74,103],"considered.":[14],"In":[15],"comparison":[17],"model":[18],"it":[19,57,73],"shown":[21,59,75],"that":[22,60,76],"any":[23],"randomized":[24,62],"algorithm":[25,63,79,89],"with":[26,64,90],"expected":[27,37,66],"amortized":[28,92],"cost":[29,38,67,93],"t":[30],"comparisons":[31,44],"per":[32,68,94],"Insert":[33],"has":[36],"at":[39],"least":[40],"n/(e2^2t)":[41],"\u2212":[42],"1":[43],"for":[45,96],"FindMin.&lt;br":[46],"/&gt;If":[47],"replaced":[50],"by":[51],"weaker":[53],"operation,":[54],"FindAny,":[55],"then":[56],"constant":[65,82,91],"operation":[69,95],"exists;":[70],"in":[71],"contrast,":[72],"no":[77],"deterministic":[78,88],"can":[80],"have":[81],"cost&lt;br":[83],"/&gt;per":[84],"operation.":[85],"Finally,":[86],"an":[97],"offline":[98],"version":[99],"problem":[102],"given.":[104]},"counts_by_year":[{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2026-06-19T17:40:00.097472","created_date":"2025-10-10T00:00:00"}
