{"id":"https://openalex.org/W264197046","doi":"https://doi.org/10.1007/978-3-540-85238-4_38","title":"Smoothed Analysis of Binary Search Trees and Quicksort under Additive Noise","display_name":"Smoothed Analysis of Binary Search Trees and Quicksort under Additive Noise","publication_year":2008,"publication_date":"2008-08-18","ids":{"openalex":"https://openalex.org/W264197046","doi":"https://doi.org/10.1007/978-3-540-85238-4_38","mag":"264197046"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-540-85238-4_38","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-540-85238-4_38","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":"conference-paper","indexed_in":["crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.07391.3","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5002315999","display_name":"Bodo Manthey","orcid":"https://orcid.org/0000-0001-6278-5059"},"institutions":[{"id":"https://openalex.org/I91712215","display_name":"Saarland University","ror":"https://ror.org/01jdpyv68","country_code":"DE","type":"education","lineage":["https://openalex.org/I91712215"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Bodo Manthey","raw_affiliation_strings":["Computer Science, Saarland University, Postfach 151150, 66041, Saarbr\u00fccken, Germany","Computer Science, Saarland University, Saarbr\u00fccken, Germany 66041"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Computer Science, Saarland University, Postfach 151150, 66041, Saarbr\u00fccken, Germany","institution_ids":["https://openalex.org/I91712215"]},{"raw_affiliation_string":"Computer Science, Saarland University, Saarbr\u00fccken, Germany 66041","institution_ids":["https://openalex.org/I91712215"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5003607737","display_name":"Till Tantau","orcid":"https://orcid.org/0000-0002-3946-8028"},"institutions":[{"id":"https://openalex.org/I9341345","display_name":"University of L\u00fcbeck","ror":"https://ror.org/00t3r8h32","country_code":"DE","type":"education","lineage":["https://openalex.org/I9341345"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Till Tantau","raw_affiliation_strings":["Institut f\u00fcr Theoretische Informatik, Universit\u00e4t zu L\u00fcbeck, Ratzeburger Allee 160, 23538, L\u00fcbeck, Germany","Institut f\u00fcr Theoretische Informatik, Universit\u00e4t zu L\u00fcbeck, L\u00fcbeck, Germany 23538#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Theoretische Informatik, Universit\u00e4t zu L\u00fcbeck, Ratzeburger Allee 160, 23538, L\u00fcbeck, Germany","institution_ids":["https://openalex.org/I9341345"]},{"raw_affiliation_string":"Institut f\u00fcr Theoretische Informatik, Universit\u00e4t zu L\u00fcbeck, L\u00fcbeck, Germany 23538#TAB#","institution_ids":["https://openalex.org/I9341345"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.02760085,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"14","issue":null,"first_page":"467","last_page":"478"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9921000003814697,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9921000003814697,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11269","display_name":"Algorithms and Data Compression","score":0.9771999716758728,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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":0.9750999808311462,"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/binary-search-tree","display_name":"Binary search tree","score":0.798892080783844},{"id":"https://openalex.org/keywords/quicksort","display_name":"Quicksort","score":0.7767142653465271},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6422109603881836},{"id":"https://openalex.org/keywords/random-binary-tree","display_name":"Random binary tree","score":0.5844277143478394},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.5395753383636475},{"id":"https://openalex.org/keywords/binary-tree","display_name":"Binary tree","score":0.5155541896820068},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5097710490226746},{"id":"https://openalex.org/keywords/randomness","display_name":"Randomness","score":0.5086511373519897},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.47228485345840454},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.45928525924682617},{"id":"https://openalex.org/keywords/optimal-binary-search-tree","display_name":"Optimal binary search tree","score":0.4250234365463257},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.36337196826934814},{"id":"https://openalex.org/keywords/sorting","display_name":"Sorting","score":0.23145711421966553},{"id":"https://openalex.org/keywords/interval-tree","display_name":"Interval tree","score":0.19759908318519592},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.19272875785827637},{"id":"https://openalex.org/keywords/sorting-algorithm","display_name":"Sorting algorithm","score":0.1332678496837616},{"id":"https://openalex.org/keywords/tree-structure","display_name":"Tree structure","score":0.11890745162963867},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.08314096927642822}],"concepts":[{"id":"https://openalex.org/C91154448","wikidata":"https://www.wikidata.org/wiki/Q623818","display_name":"Binary search tree","level":3,"score":0.798892080783844},{"id":"https://openalex.org/C2778937211","wikidata":"https://www.wikidata.org/wiki/Q486598","display_name":"Quicksort","level":4,"score":0.7767142653465271},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6422109603881836},{"id":"https://openalex.org/C11829167","wikidata":"https://www.wikidata.org/wiki/Q751292","display_name":"Random binary tree","level":3,"score":0.5844277143478394},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.5395753383636475},{"id":"https://openalex.org/C197855036","wikidata":"https://www.wikidata.org/wiki/Q380172","display_name":"Binary tree","level":2,"score":0.5155541896820068},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5097710490226746},{"id":"https://openalex.org/C125112378","wikidata":"https://www.wikidata.org/wiki/Q176640","display_name":"Randomness","level":2,"score":0.5086511373519897},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.47228485345840454},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.45928525924682617},{"id":"https://openalex.org/C27628562","wikidata":"https://www.wikidata.org/wiki/Q17154715","display_name":"Optimal binary search tree","level":5,"score":0.4250234365463257},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.36337196826934814},{"id":"https://openalex.org/C111696304","wikidata":"https://www.wikidata.org/wiki/Q2303697","display_name":"Sorting","level":2,"score":0.23145711421966553},{"id":"https://openalex.org/C84927040","wikidata":"https://www.wikidata.org/wiki/Q6057306","display_name":"Interval tree","level":4,"score":0.19759908318519592},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.19272875785827637},{"id":"https://openalex.org/C108094655","wikidata":"https://www.wikidata.org/wiki/Q181593","display_name":"Sorting algorithm","level":3,"score":0.1332678496837616},{"id":"https://openalex.org/C163797641","wikidata":"https://www.wikidata.org/wiki/Q2067937","display_name":"Tree structure","level":3,"score":0.11890745162963867},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.08314096927642822},{"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0}],"mesh":[],"locations_count":8,"locations":[{"id":"doi:10.1007/978-3-540-85238-4_38","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-540-85238-4_38","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":"pmh:oai:CiteSeerX.psu:10.1.1.175.1349","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.175.1349","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.utwente.nl/%7Emantheyb/conferences/MFCS2008_MantheyTantau_SmoothedTrees.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.634.5208","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.634.5208","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://eccc.hpi-web.de/report/2007/039/revision/1/download/","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.84.1616","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.84.1616","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://eccc.hpi-web.de/eccc-reports/2007/TR07-039/Paper.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.89.8395","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.89.8395","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://drops.dagstuhl.de/opus/volltexte/2007/1289/pdf/07391.MantheyBodo.Paper.1289.pdf","raw_type":"text"},{"id":"pmh:oai:drops-oai.dagstuhl.de:1289","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.07391.3","pdf_url":null,"source":{"id":"https://openalex.org/S4377196569","display_name":"DROPS (Schloss Dagstuhl \u2013 Leibniz Center for Informatics)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2799853480","host_organization_name":"Schloss Dagstuhl \u2013 Leibniz Center for Informatics","host_organization_lineage":["https://openalex.org/I2799853480"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"InProceedings"},{"id":"doi:10.4230/dagsemproc.07391.3","is_oa":true,"landing_page_url":"https://doi.org/10.4230/dagsemproc.07391.3","pdf_url":null,"source":null,"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"JournalArticle"},{"id":"mag:264197046","is_oa":false,"landing_page_url":"https://dblp.uni-trier.de/db/journals/eccc/eccc14.html#MantheyT07","pdf_url":null,"source":{"id":"https://openalex.org/S4306418148","display_name":"Dagstuhl Seminar Proceedings","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":"Dagstuhl Seminar Proceedings","raw_type":null}],"best_oa_location":{"id":"pmh:oai:drops-oai.dagstuhl.de:1289","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.07391.3","pdf_url":null,"source":{"id":"https://openalex.org/S4377196569","display_name":"DROPS (Schloss Dagstuhl \u2013 Leibniz Center for Informatics)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2799853480","host_organization_name":"Schloss Dagstuhl \u2013 Leibniz Center for Informatics","host_organization_lineage":["https://openalex.org/I2799853480"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"InProceedings"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W243610207","https://openalex.org/W1443152572","https://openalex.org/W1547842568","https://openalex.org/W1553493984","https://openalex.org/W1587032893","https://openalex.org/W1981177980","https://openalex.org/W2011233451","https://openalex.org/W2034053794","https://openalex.org/W2070520587","https://openalex.org/W2076172709","https://openalex.org/W2086474457","https://openalex.org/W2157661221","https://openalex.org/W2187329374","https://openalex.org/W2295428206","https://openalex.org/W2401328023","https://openalex.org/W6669417358"],"related_works":["https://openalex.org/W1503775959","https://openalex.org/W1504119404","https://openalex.org/W2123024824","https://openalex.org/W2140003446","https://openalex.org/W1996039969","https://openalex.org/W1552012135","https://openalex.org/W1577191794","https://openalex.org/W2112729204","https://openalex.org/W1986816810","https://openalex.org/W2962954810","https://openalex.org/W3118453904","https://openalex.org/W2538291496","https://openalex.org/W2024535490","https://openalex.org/W3102736130","https://openalex.org/W2013021781","https://openalex.org/W2004158059","https://openalex.org/W2136667426","https://openalex.org/W1750154403","https://openalex.org/W1811083715","https://openalex.org/W1970473153"],"abstract_inverted_index":{"Binary":[0],"search":[1,72,101],"trees":[2,102],"are":[3,68],"a":[4,12,35,52,71,134],"fundamental":[5],"data":[6],"structure":[7],"and":[8,64,84,161],"their":[9,25],"height":[10,27,80,98],"plays":[11],"key":[13],"role":[14],"in":[15,41,133],"the":[16,42,65,77,88,96,122,127,155,158,164],"analysis":[17,75,119],"of":[18,37,61,76,90,99,125,130,157,167],"divide-and-conquer":[19],"algorithms":[20],"like":[21],"quicksort.":[22],"We":[23,93,136,149],"analyze":[24],"smoothed":[26,78,97,128,165],"under":[28],"additive":[29],"uniform":[30],"noise:":[31],"An":[32,74],"adversary":[33],"chooses":[34],"sequence":[36],"n":[38,83,176],"real":[39],"numbers":[40,67],"range":[43],"[0,1],":[44],"each":[45],"number":[46,129,166],"is":[47,103,172],"individually":[48],"perturbed":[49],"by":[50,170],"adding":[51],"value":[53],"drawn":[54],"uniformly":[55],"at":[56,87],"random":[57],"from":[58],"an":[59],"interval":[60],"size":[62],"d,":[63],"resulting":[66],"inserted":[69],"into":[70],"tree.":[73],"tree":[79],"subject":[81],"to":[82,154],"d":[85,111],"lies":[86],"heart":[89],"our":[91,152],"paper:":[92],"prove":[94,162],"that":[95,163],"binary":[100],"$\\Theta":[104,143],"(\\sqrt{n/d}":[105,144],"+":[106,145,175],"\\log":[107,146,177],"n)$":[108,147,178],",":[109],"where":[110],"\u2265":[112],"1/n":[113],"may":[114],"depend":[115],"on":[116],"n.":[117],"Our":[118],"starts":[120],"with":[121],"simpler":[123],"problem":[124],"determining":[126],"left-to-right":[131],"maxima":[132],"sequence.":[135],"establish":[137],"matching":[138],"bounds,":[139],"namely":[140],"once":[141],"more":[142],".":[148,179],"also":[150],"apply":[151],"findings":[153],"performance":[156],"quicksort":[159,171],"algorithm":[160],"comparisons":[168],"made":[169],"$\\Theta(\\frac{n}{d+1}":[173],"\\sqrt{n/d}":[174]},"counts_by_year":[],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-10T00:00:00"}