{"id":"https://openalex.org/W3209836283","doi":"https://doi.org/10.1007/s00453-021-00880-1","title":"Approximate Minimum Selection with Unreliable Comparisons","display_name":"Approximate Minimum Selection with Unreliable Comparisons","publication_year":2021,"publication_date":"2021-11-01","ids":{"openalex":"https://openalex.org/W3209836283","doi":"https://doi.org/10.1007/s00453-021-00880-1","mag":"3209836283","pmid":"https://pubmed.ncbi.nlm.nih.gov/35125579"},"language":"en","primary_location":{"id":"doi:10.1007/s00453-021-00880-1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00453-021-00880-1","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00453-021-00880-1.pdf","source":{"id":"https://openalex.org/S89324355","display_name":"Algorithmica","issn_l":"0178-4617","issn":["0178-4617","1432-0541"],"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":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithmica","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","datacite","pubmed"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00453-021-00880-1.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5028702811","display_name":"Stefano Leucci","orcid":"https://orcid.org/0000-0002-8848-7006"},"institutions":[{"id":"https://openalex.org/I26415053","display_name":"University of L'Aquila","ror":"https://ror.org/01j9p1r26","country_code":"IT","type":"education","lineage":["https://openalex.org/I26415053"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Stefano Leucci","raw_affiliation_strings":["Department of Information Engineering, Computer Science and Mathematics, University of L'Aquila, L'Aquila, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Information Engineering, Computer Science and Mathematics, University of L'Aquila, L'Aquila, Italy","institution_ids":["https://openalex.org/I26415053"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5008771140","display_name":"Chih-Hung Liu","orcid":"https://orcid.org/0000-0001-9683-5982"},"institutions":[{"id":"https://openalex.org/I35440088","display_name":"ETH Zurich","ror":"https://ror.org/05a28rw58","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088"]}],"countries":["CH"],"is_corresponding":true,"raw_author_name":"Chih-Hung Liu","raw_affiliation_strings":["Department of Computer Science, ETH Z\u00fcrich, Z\u00fcrich, Switzerland"],"raw_orcid":"https://orcid.org/0000-0001-9683-5982","affiliations":[{"raw_affiliation_string":"Department of Computer Science, ETH Z\u00fcrich, Z\u00fcrich, Switzerland","institution_ids":["https://openalex.org/I35440088"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5008771140"],"corresponding_institution_ids":["https://openalex.org/I35440088"],"apc_list":{"value":2890,"currency":"USD","value_usd":2890},"apc_paid":{"value":2890,"currency":"USD","value_usd":2890},"fwci":0.521,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.73570906,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"84","issue":"1","first_page":"60","last_page":"84"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12072","display_name":"Machine Learning and Algorithms","score":0.9969000220298767,"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"}},"topics":[{"id":"https://openalex.org/T12072","display_name":"Machine Learning and Algorithms","score":0.9969000220298767,"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/T12288","display_name":"Optimization and Search Problems","score":0.9955999851226807,"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":0.994700014591217,"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/mathematics","display_name":"Mathematics","score":0.7163827419281006},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6819886565208435},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.6790194511413574},{"id":"https://openalex.org/keywords/selection","display_name":"Selection (genetic algorithm)","score":0.5628040432929993},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.5610933899879456},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.533218264579773},{"id":"https://openalex.org/keywords/pairwise-comparison","display_name":"Pairwise comparison","score":0.5258132815361023},{"id":"https://openalex.org/keywords/randomized-algorithm","display_name":"Randomized algorithm","score":0.5099726915359497},{"id":"https://openalex.org/keywords/outcome","display_name":"Outcome (game theory)","score":0.48171454668045044},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4552612900733948},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.2573665976524353},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.24483737349510193},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.17174112796783447}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7163827419281006},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6819886565208435},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6790194511413574},{"id":"https://openalex.org/C81917197","wikidata":"https://www.wikidata.org/wiki/Q628760","display_name":"Selection (genetic algorithm)","level":2,"score":0.5628040432929993},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.5610933899879456},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.533218264579773},{"id":"https://openalex.org/C184898388","wikidata":"https://www.wikidata.org/wiki/Q1435712","display_name":"Pairwise comparison","level":2,"score":0.5258132815361023},{"id":"https://openalex.org/C128669082","wikidata":"https://www.wikidata.org/wiki/Q583461","display_name":"Randomized algorithm","level":2,"score":0.5099726915359497},{"id":"https://openalex.org/C148220186","wikidata":"https://www.wikidata.org/wiki/Q7111912","display_name":"Outcome (game theory)","level":2,"score":0.48171454668045044},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4552612900733948},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.2573665976524353},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.24483737349510193},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.17174112796783447},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1007/s00453-021-00880-1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00453-021-00880-1","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00453-021-00880-1.pdf","source":{"id":"https://openalex.org/S89324355","display_name":"Algorithmica","issn_l":"0178-4617","issn":["0178-4617","1432-0541"],"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":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithmica","raw_type":"journal-article"},{"id":"pmid:35125579","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/35125579","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithmica","raw_type":null},{"id":"pmh:oai:pubmedcentral.nih.gov:8786813","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/8786813","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"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":"Algorithmica","raw_type":"Text"},{"id":"pmh:oai:www.research-collection.ethz.ch:20.500.11850/515018","is_oa":true,"landing_page_url":"http://hdl.handle.net/20.500.11850/515018","pdf_url":null,"source":{"id":"https://openalex.org/S4306402302","display_name":"Repository for Publications and Research Data (ETH Zurich)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I35440088","host_organization_name":"ETH Zurich","host_organization_lineage":["https://openalex.org/I35440088"],"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":"Algorithmica, 84","raw_type":"info:eu-repo/semantics/article"},{"id":"doi:10.3929/ethz-b-000515018","is_oa":true,"landing_page_url":"https://doi.org/10.3929/ethz-b-000515018","pdf_url":null,"source":{"id":"https://openalex.org/S7407051236","display_name":"ETH Z\u00fcrich Research Collection","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Other"}],"best_oa_location":{"id":"doi:10.1007/s00453-021-00880-1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00453-021-00880-1","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00453-021-00880-1.pdf","source":{"id":"https://openalex.org/S89324355","display_name":"Algorithmica","issn_l":"0178-4617","issn":["0178-4617","1432-0541"],"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":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithmica","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3454722278","display_name":null,"funder_award_id":"200021_165524","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"},{"id":"https://openalex.org/G412114378","display_name":null,"funder_award_id":"SNF 200021_165524","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"},{"id":"https://openalex.org/G4579184819","display_name":"Energy-Tunable Combinatorial Algorithms","funder_award_id":"165524","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"},{"id":"https://openalex.org/G993971353","display_name":null,"funder_award_id":"200021","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"}],"funders":[{"id":"https://openalex.org/F4320320924","display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung","ror":"https://ror.org/00yjd3n13"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3209836283.pdf","grobid_xml":"https://content.openalex.org/works/W3209836283.grobid-xml"},"referenced_works_count":32,"referenced_works":["https://openalex.org/W569232627","https://openalex.org/W588799346","https://openalex.org/W1956210933","https://openalex.org/W1974184113","https://openalex.org/W1986978101","https://openalex.org/W2000072121","https://openalex.org/W2022085444","https://openalex.org/W2038435918","https://openalex.org/W2041395308","https://openalex.org/W2044712489","https://openalex.org/W2048175848","https://openalex.org/W2051299691","https://openalex.org/W2058699483","https://openalex.org/W2060990051","https://openalex.org/W2062563944","https://openalex.org/W2072122809","https://openalex.org/W2099569658","https://openalex.org/W2105220030","https://openalex.org/W2131306093","https://openalex.org/W2132967058","https://openalex.org/W2301054524","https://openalex.org/W2362096638","https://openalex.org/W2478356874","https://openalex.org/W2760612480","https://openalex.org/W2912254316","https://openalex.org/W2964047785","https://openalex.org/W2977256954","https://openalex.org/W2977528225","https://openalex.org/W2990360522","https://openalex.org/W2993963457","https://openalex.org/W3149410719","https://openalex.org/W4245454025"],"related_works":["https://openalex.org/W2487162673","https://openalex.org/W2942366970","https://openalex.org/W2793211469","https://openalex.org/W2949152769","https://openalex.org/W4372354731","https://openalex.org/W2562400057","https://openalex.org/W1692008701","https://openalex.org/W2597588799","https://openalex.org/W2003502867","https://openalex.org/W1994184712"],"abstract_inverted_index":{"Abstract":[0],"We":[1,57],"consider":[2],"the":[3,23,51,199,207,275,294,341],"approximate":[4,295],"minimum":[5,296],"selection":[6,297],"problem":[7,17,65,200,298],"in":[8,27,166,287,340],"presence":[9],"of":[10,22,31,70,210,278],"independent":[11],"random":[12],"comparison":[13,53],"faults":[14],".":[15,400],"This":[16],"asks":[18],"to":[19],"select":[20],"one":[21],"smallest":[24],"k":[25],"elements":[26,33,42],"a":[28,47,59,67],"linearly-ordered":[29],"collection":[30],"n":[32],"by":[34,213,281],"only":[35],"performing":[36],"unreliable":[37],"pairwise":[38],"comparisons:":[39],"whenever":[40,253],"two":[41],"are":[43],"compared,":[44],"there":[45],"is":[46,55,255,284,346,350],"small":[48],"probability":[49,69,219],"that":[50,62,206,216,274,293],"wrong":[52],"outcome":[54],"observed.":[56],"design":[58],"randomized":[60],"algorithm":[61,215,283],"solves":[63],"this":[64,288],"with":[66,218],"success":[68],"at":[71,220],"least":[72,221],"$$1-q$$":[73,222],"<mml:math":[74,87,112,138,172,184,223,236,260,311,355,375],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[75,88,113,139,173,185,224,237,261,312,356,376],"<mml:mrow>":[76,89,96,114,140,142,149,157,160,174,186,190,225,238,263,313,316,358,377,381,386,395],"<mml:mn>1</mml:mn>":[77,118,122,154,226,247,326,333,390],"<mml:mo>-</mml:mo>":[78,98,121,192,227,265,360],"<mml:mi>q</mml:mi>":[79,90,155,187,228,248,327,334,391],"</mml:mrow>":[80,100,104,124,144,151,159,162,163,178,194,197,229,251,267,330,337,362,383,393,397,398],"</mml:math>":[81,105,125,164,179,198,230,252,270,338,365,399],"for":[82],"$$q":[83,181],"\\in":[84,109],"(0,":[85],"\\frac{n-k}{n})$$":[86],"<mml:mo>\u2208</mml:mo>":[91,116],"<mml:mo>(</mml:mo>":[92,143,240,315,317,382],"<mml:mn>0</mml:mn>":[93],"<mml:mo>,</mml:mo>":[94,119],"<mml:mfrac>":[95,145,153,189,241,246,262,318,325,332,357,384,389],"<mml:mi>n</mml:mi>":[97,101,120,146,177,191,195,242,264,268,319,359,363,385],"<mml:mi>k</mml:mi>":[99,115,147,175,193,243,266,320,361,378],"</mml:mfrac>":[102,148,156,196,244,249,269,321,328,335,364,392,394],"<mml:mo>)</mml:mo>":[103,161,250,329,336,396],"and":[106,366],"any":[107,214],"$$k":[108,169,367],"[1,":[110],"n-1]$$":[111],"<mml:mo>[</mml:mo>":[117],"<mml:mo>]</mml:mo>":[123],"using":[126,302],"$$O\\big":[127],"(":[128,370],"\\frac{n}{k}":[129],"\\big":[130,134,136],"\\lceil":[131],"\\log":[132,306,307,309,372],"\\frac{1}{q}":[133],"\\rceil":[135],")$$":[137,374],"<mml:mi>O</mml:mi>":[141,314,380],"<mml:mo>\u2308</mml:mo>":[150],"<mml:mo>log</mml:mo>":[152,245,323,324,331,387,388],"<mml:mo>\u2309</mml:mo>":[158],"comparisons":[165,211,279,339],"expectation":[167],"(if":[168],"\\ge":[170,182],"n$$":[171],"<mml:mo>\u2265</mml:mo>":[176,188],"or":[180],"\\frac{n-k}{n}$$":[183],"becomes":[201],"trivial).":[202],"Then,":[203],"we":[204,291],"prove":[205],"expected":[208,276],"number":[209,277],"needed":[212],"succeeds":[217],"must":[231],"be":[232,300],"$${\\varOmega":[233],"}(\\frac{n}{k}\\log":[234],"\\frac{1}{q})$$":[235,310],"<mml:mi>\u03a9</mml:mi>":[239],"q":[254,349],"bounded":[256,351],"away":[257,352],"from":[258,353],"$$\\frac{n-k}{n}$$":[259,354],",":[271,344],"thus":[272],"implying":[273],"performed":[280],"our":[282],"asymptotically":[285],"optimal":[286,347],"range.":[289],"Moreover,":[290],"show":[292],"can":[299],"solved":[301],"$$O(":[303],"(\\frac{n}{k}":[304],"+":[305],"\\frac{1}{q})":[308],"<mml:mo>+</mml:mo>":[322],"worst":[342],"case":[343],"which":[345],"when":[348],"=":[368],"O\\big":[369],"\\frac{n}{\\log":[371],"\\frac{1}{q}}\\big":[373],"<mml:mo>=</mml:mo>":[379]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3}],"updated_date":"2026-07-31T08:31:51.225901","created_date":"2025-10-10T00:00:00"}