{"id":"https://openalex.org/W2010091510","doi":"https://doi.org/10.1137/0220010","title":"More Nearly Optimal Algorithms for Unbounded Searching, Part I: The Finite Case","display_name":"More Nearly Optimal Algorithms for Unbounded Searching, Part I: The Finite Case","publication_year":1991,"publication_date":"1991-02-01","ids":{"openalex":"https://openalex.org/W2010091510","doi":"https://doi.org/10.1137/0220010","mag":"2010091510"},"language":"en","primary_location":{"id":"doi:10.1137/0220010","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0220010","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5073186573","display_name":"Edward M. Reingold","orcid":null},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Edward M. Reingold","raw_affiliation_strings":["University of Illinois at Urbana-Champaign Urbana"],"affiliations":[{"raw_affiliation_string":"University of Illinois at Urbana-Champaign Urbana","institution_ids":["https://openalex.org/I157725225"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5076110710","display_name":"Xiaojun Shen","orcid":"https://orcid.org/0000-0001-6950-3974"},"institutions":[{"id":"https://openalex.org/I75421653","display_name":"University of Missouri\u2013Kansas City","ror":"https://ror.org/01w0d5g70","country_code":"US","type":"education","lineage":["https://openalex.org/I75421653"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Xiaojun Shen","raw_affiliation_strings":["University of Missouri - Kansas City, Kansas City"],"affiliations":[{"raw_affiliation_string":"University of Missouri - Kansas City, Kansas City","institution_ids":["https://openalex.org/I75421653"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5073186573"],"corresponding_institution_ids":["https://openalex.org/I157725225"],"apc_list":null,"apc_paid":null,"fwci":0.9201,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.77292576,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"20","issue":"1","first_page":"156","last_page":"183"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12288","display_name":"Optimization and Search Problems","score":0.9994000196456909,"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"}},"topics":[{"id":"https://openalex.org/T12288","display_name":"Optimization and Search Problems","score":0.9994000196456909,"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/T12072","display_name":"Machine Learning and Algorithms","score":0.9991999864578247,"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/T11269","display_name":"Algorithms and Data Compression","score":0.9987999796867371,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6950798034667969},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6345224976539612},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.5752196311950684},{"id":"https://openalex.org/keywords/ackermann-function","display_name":"Ackermann function","score":0.5260049104690552},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.5150994658470154},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5067377686500549},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4908164441585541},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.48408734798431396},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.44859635829925537}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6950798034667969},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6345224976539612},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.5752196311950684},{"id":"https://openalex.org/C33436860","wikidata":"https://www.wikidata.org/wiki/Q341835","display_name":"Ackermann function","level":3,"score":0.5260049104690552},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.5150994658470154},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5067377686500549},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4908164441585541},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.48408734798431396},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.44859635829925537},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/0220010","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0220010","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W621941035","https://openalex.org/W1975489634","https://openalex.org/W1982998010","https://openalex.org/W1986022261","https://openalex.org/W1986428580","https://openalex.org/W1988287732","https://openalex.org/W1993742159","https://openalex.org/W2013367214","https://openalex.org/W2019176509","https://openalex.org/W2035367168","https://openalex.org/W2075188242","https://openalex.org/W2106596127","https://openalex.org/W2126590220","https://openalex.org/W2128777897","https://openalex.org/W2143603891","https://openalex.org/W2328961910","https://openalex.org/W2492935281","https://openalex.org/W3175046490","https://openalex.org/W4254091985"],"related_works":["https://openalex.org/W2076743759","https://openalex.org/W4235144492","https://openalex.org/W4388435768","https://openalex.org/W2756792282","https://openalex.org/W2756744637","https://openalex.org/W3216309640","https://openalex.org/W2759493398","https://openalex.org/W2807877113","https://openalex.org/W4254767272","https://openalex.org/W1549756090"],"abstract_inverted_index":{"Given":[0],"a":[1,56,60,85,137,214,237,290,317],"function":[2,61],"$F:N^":[3],"+":[4,226],"\\to":[5],"\\{":[6],"X,Y\\}":[7],"$":[8],"with":[9,262],"the":[10,28,37,45,53,63,70,73,90,95,99,111,141,151,157,229,251,257,263,273,282,287,294,302,313],"property":[11],"that":[12,49,110,153,217,270],"if":[13],"$F(n_0":[14],")":[15],"=":[16,20,41,51],"{\\text{Y}}$":[17,21],"then":[18],"$F(n)":[19],"for":[22,281],"all":[23],"$n":[24],">":[25],"n_0":[26],"$,":[27],"unbounded":[29],"search":[30,57,82,164,204,249],"problem":[31,83],"is":[32,59,76,98,108,126,146,155,169,183,193,210,218,236,259,308],"to":[33,43,80,104,172,311,315],"use":[34],"tests":[35,67],"of":[36,55,65,72,89,101,114,136,143,163,167,180,191,203,223,228,240,256,289,296,320],"form":[38],"\u201cis":[39],"$F(i)":[40,50],"{\\text{X}}$?\u201d":[42],"determine":[44],"smallest":[46],"n":[47,106],"such":[48,66],"{\\text{Y}}$;":[52],"\u201ccost\u201d":[54],"algorithm":[58],"$c(n)$,":[62],"number":[64,100],"used":[68,103],"when":[69],"location":[71],"first":[74],"Y":[75,291],"n.":[77],"A":[78,177],"solution":[79],"this":[81,144,201],"specifies":[84],"prefix-free,":[86,253],"binary":[87,254],"encoding":[88,255],"positive":[91],"integers":[92,258],"in":[93,150,159,213,285],"which":[94,125,168,192,209,286],"cost":[96,142,288,295],"$c(n)$":[97],"bits":[102],"encode":[105],"It":[107],"shown":[109,309],"\u201cultimate":[112],"algorithm,\u201d":[113],"Bentley":[115],"and":[116,293,324],"Yao":[117],"[Inform.":[118],"Process.":[119],"Lett.,":[120],"5":[121],"(1976),":[122],"pp.":[123],"82\u201387],":[124],"within":[127,219],"an":[128,160,207,220,297],"additive":[129,221],"$\\Theta":[130],"(\\lg":[131],"^":[132],"*":[133],"n)$":[134],"factor":[135,222],"lower":[138,181,231,274,325],"bound":[139],"on":[140,187],"problem,":[145],"\u201cfar\u201d":[147],"from":[148,272],"optimal":[149],"sense":[152],"it":[154,307],"just":[156],"second":[158],"infinite":[161],"sequence":[162,179,202,319],"algorithms,":[165],"each":[166,190,248],"much":[170,194],"closer":[171],"optimality":[173],"than":[174,196],"its":[175,197],"predecessor.":[176,198],"corresponding":[178,230,252],"bounds":[182,275],"also":[184],"given,":[185,260],"based":[186],"Kraft\u2019s":[188],"inequality,":[189],"stronger":[195],"Diagonalizing":[199],"over":[200],"algorithms":[205],"yields":[206],"algorithm,":[208,250],"given":[211],"explicitly":[212],"Pascal-like":[215],"notation,":[216],"$\\alpha":[224,234],"(n)":[225],"2$":[227],"bound,":[232],"where":[233],"(n)$":[235],"functional":[238],"inverse":[239],"Ackermann\u2019s":[241],"function\u2014an":[242],"extremely":[243],"slowly":[244],"growing":[245],"function.":[246],"For":[247],"together":[261],"decoding":[264],"algorithm.":[265],"Finally,":[266],"algorithms/encodings":[267,323],"are":[268,300],"constructed":[269],"differ":[271],"by":[276],"only":[277],"negligible":[278],"amounts":[279],"even":[280],"asymmetric":[283],"case":[284],"answer":[292,299],"X":[298],"not":[301],"same.":[303],"In":[304],"Part":[305],"II":[306],"how":[310],"continue":[312],"construction":[314],"get":[316],"transfinite":[318],"dramatically":[321],"better":[322],"bounds.":[326]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}