{"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"],"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"],"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":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":0.5599,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.73952591,"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":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":"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/publishedVersion"},{"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":[],"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":"article-journal"}],"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/G4836148144","display_name":"Immunologie des Typ-1 Diabetes.","funder_award_id":"20002","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":{"We":[0,55],"consider":[1],"the":[2,21,49,135,143,192,211,239],"<i>approximate":[3],"minimum":[4,213],"selection</i>":[5],"problem":[6,15,63,136,215],"in":[7,25,117,204],"presence":[8],"of":[9,20,29,68,146,195],"<i>independent":[10],"random":[11],"comparison":[12,51],"faults</i>.":[13],"This":[14],"asks":[16],"to":[17],"select":[18],"one":[19],"smallest":[22],"<i>k</i>":[23],"elements":[24,31,40],"a":[26,45,57,65],"linearly-ordered":[27],"collection":[28],"<i>n</i>":[30],"by":[32,149,198],"only":[33],"performing":[34],"<i>unreliable</i>":[35],"pairwise":[36],"comparisons:":[37],"whenever":[38,175],"two":[39],"are":[41],"compared,":[42],"there":[43],"is":[44,53,177,201,243,247],"small":[46],"probability":[47,67,155],"that":[48,60,142,152,191,210],"wrong":[50],"outcome":[52],"observed.":[54],"design":[56],"randomized":[58],"algorithm":[59,151,200],"solves":[61],"this":[62,205],"with":[64,154],"success":[66],"at":[69,156],"least":[70,157],"<mml:math":[71,77,91,103,120,126,158,165,181,220,251,259],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mrow><mml:mn>1</mml:mn>":[72,159],"<mml:mo>-</mml:mo>":[73,84,98,130,160,184,254],"<mml:mi>q</mml:mi></mml:mrow>":[74,161],"</mml:math>":[75,88,101,115,124,134,162,174,187,236,257,273],"for":[76],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mrow><mml:mi>q</mml:mi>":[78,127],"<mml:mo>\u2208</mml:mo>":[79,93],"<mml:mo>(</mml:mo>":[80,167,222],"<mml:mn>0</mml:mn>":[81],"<mml:mo>,</mml:mo>":[82,96],"<mml:mfrac><mml:mrow><mml:mi>n</mml:mi>":[83,129,183,253],"<mml:mi>k</mml:mi></mml:mrow>":[85,131,185,255],"<mml:mi>n</mml:mi></mml:mfrac>":[86,132,186,256],"<mml:mo>)</mml:mo></mml:mrow>":[87,173,231,235],"and":[89,258],"any":[90,150],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mrow><mml:mi>k</mml:mi>":[92,121,260],"<mml:mo>[</mml:mo>":[94],"<mml:mn>1</mml:mn>":[95,99],"<mml:mi>n</mml:mi>":[97],"<mml:mo>]</mml:mo></mml:mrow>":[100],"using":[102,219],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mrow><mml:mi>O</mml:mi>":[104,221],"<mml:mrow><mml:mo>(</mml:mo></mml:mrow>":[105,263],"<mml:mfrac><mml:mi>n</mml:mi>":[106,168,224,264],"<mml:mi>k</mml:mi></mml:mfrac>":[107,169,225],"<mml:mrow><mml:mo>\u2308</mml:mo></mml:mrow>":[108],"<mml:mo>log</mml:mo>":[109,170,227,228,232,266],"<mml:mfrac><mml:mn>1</mml:mn>":[110,171,229,233,267],"<mml:mi>q</mml:mi></mml:mfrac>":[111,172,230,234,268],"<mml:mrow><mml:mo>\u2309</mml:mo></mml:mrow>":[112],"<mml:mrow><mml:mo>)</mml:mo></mml:mrow>":[113,271],"</mml:mrow>":[114,133,269,272],"comparisons":[116,147,196,237],"expectation":[118],"(if":[119],"<mml:mo>\u2265</mml:mo>":[122,128],"<mml:mi>n</mml:mi></mml:mrow>":[123],"or":[125],"becomes":[137],"trivial).":[138],"Then,":[139],"we":[140,208],"prove":[141],"expected":[144,193],"number":[145,194],"needed":[148],"succeeds":[153],"must":[163],"be":[164,217],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mrow><mml:mi>\u03a9</mml:mi>":[166],"<i>q</i>":[176,246],"bounded":[178,248],"away":[179,249],"from":[180,250],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[182,252],",":[188],"thus":[189],"implying":[190],"performed":[197],"our":[199],"asymptotically":[202],"optimal":[203,244],"range.":[206],"Moreover,":[207],"show":[209],"approximate":[212],"selection":[214],"can":[216],"solved":[218],"<mml:mrow><mml:mo>(</mml:mo>":[223],"<mml:mo>+</mml:mo>":[226],"<i>in":[238],"worst":[240],"case</i>,":[241],"which":[242],"when":[245],"<mml:mo>=</mml:mo>":[261],"<mml:mi>O</mml:mi>":[262],"<mml:mrow><mml:mo>log</mml:mo>":[265],"</mml:mfrac>":[270],".":[274]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}
