{"id":"https://openalex.org/W3175046490","doi":"https://doi.org/10.1137/0220011","title":"More Nearly Optimal Algorithms for Unbounded Searching, II:The Transfinite Case","display_name":"More Nearly Optimal Algorithms for Unbounded Searching, II:The Transfinite Case","publication_year":1991,"publication_date":"1991-02-01","ids":{"openalex":"https://openalex.org/W3175046490","doi":"https://doi.org/10.1137/0220011","mag":"3175046490"},"language":"en","primary_location":{"id":"doi:10.1137/0220011","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0220011","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":[],"countries":[],"is_corresponding":true,"raw_author_name":"Edward M. Reingold","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5076110710","display_name":"Xiaojun Shen","orcid":"https://orcid.org/0000-0001-6950-3974"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xiaojun Shen","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5073186573"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.0353,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.83021444,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"20","issue":"1","first_page":"184","last_page":"208"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11269","display_name":"Algorithms and Data Compression","score":0.9997000098228455,"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/T11269","display_name":"Algorithms and Data Compression","score":0.9997000098228455,"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":0.9983000159263611,"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/T12029","display_name":"DNA and Biological Computing","score":0.991100013256073,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/transfinite-number","display_name":"Transfinite number","score":0.8966670036315918},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.52113938331604},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.49557483196258545},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4394076466560364},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.39036282896995544},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3677770495414734},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3276943564414978},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.32558631896972656},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.17818483710289001}],"concepts":[{"id":"https://openalex.org/C147358099","wikidata":"https://www.wikidata.org/wiki/Q1069891","display_name":"Transfinite number","level":2,"score":0.8966670036315918},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.52113938331604},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.49557483196258545},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4394076466560364},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.39036282896995544},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3677770495414734},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3276943564414978},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.32558631896972656},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.17818483710289001}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/0220011","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0220011","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W1579247651","https://openalex.org/W1975489634","https://openalex.org/W1982998010","https://openalex.org/W2010091510","https://openalex.org/W2020050887","https://openalex.org/W2066527932","https://openalex.org/W2075188242","https://openalex.org/W2080021443","https://openalex.org/W2128777897","https://openalex.org/W2167003332","https://openalex.org/W2336574378","https://openalex.org/W3022666322","https://openalex.org/W4254091985"],"related_works":["https://openalex.org/W2089968568","https://openalex.org/W2048273249","https://openalex.org/W2950239705","https://openalex.org/W2261099788","https://openalex.org/W2498880115","https://openalex.org/W1663013072","https://openalex.org/W3087796271","https://openalex.org/W1864532727","https://openalex.org/W1606946808","https://openalex.org/W2086359902"],"abstract_inverted_index":{"Given":[0],"a":[1,57,61,112,149,201,216],"function":[2,62],"$F:N^":[3],"+":[4,138],"\\to":[5],"\\{":[6],"X,Y\\}":[7],"$":[8],"with":[9],"the":[10,29,38,46,54,64,71,74,122,125,141,162,197,222],"property":[11],"that":[12,50,115,190],"if":[13],"$F(n_0":[14],")":[15,20],"=":[16,21,42,52],"Y$":[17,22],"then":[18],"$F(n":[19],"for":[23,178,207,221],"all":[24],"$n":[25],">":[26],"n_0":[27],"$,":[28,185],"unbounded":[30],"search":[31,58],"problem":[32],"is":[33,60,77,86,99,116,130,148,188,191],"to":[34,44,89,102,167,194,200,212],"use":[35],"tests":[36,68],"of":[37,56,66,73,82,94,97,121,135,140,152],"form":[39],"\u201cis":[40],"$F(i)":[41],"X$?*#821;":[43],"determine":[45],"smallest":[47],"n":[48,78],"such":[49,67],"$F(n)":[51],"Y$;":[53],"\u201ccost\u201d":[55],"algorithm":[59,114,129,187,198],"$c(n)$,":[63],"number":[65],"used":[69],"when":[70],"location":[72],"first":[75],"Y":[76],"In":[79,159],"Part":[80],"I":[81],"this":[83,109,127,160],"paper":[84,161],"it":[85],"shown":[87],"how":[88],"construct":[90],"an":[91,132,186],"infinite":[92],"sequence":[93,110],"algorithms,":[95],"each":[96,179],"which":[98],"much":[100],"closer":[101,193],"optimality":[103,195],"than":[104,119,196],"its":[105],"predecessor.":[106],"Diagonalizing":[107],"over":[108],"yields":[111],"new":[113],"far":[117],"better":[118,170],"any":[120],"algorithms":[123,171,205],"in":[124,215],"sequence:":[126],"\u201comega-th\u201d":[128],"within":[131],"additive":[133],"factor":[134],"$\\alpha":[136,146],"(n)":[137],"2$":[139],"corresponding":[142,199],"lower":[143,173],"bound,":[144],"where":[145],"(n)$":[147],"functional":[150],"inverse":[151],"Ackermann\u2019s":[153],"function\u2014an":[154],"extremely":[155],"slowly":[156],"growing":[157],"function.":[158],"construction":[163],"techniques":[164],"are":[165,210,225],"generalized":[166],"get":[168],"dramatically":[169,192],"and":[172],"bounds":[174],"ad":[175],"infinitum.":[176],"Specifically,":[177],"ordinal":[180],"$\\iota":[181],"<":[182],"\\epsilon":[183],"_0":[184],"given":[189],"smaller":[202],"ordinal.":[203],"All":[204],"constructed":[206],"t":[208],"Eo":[209],"proved":[211],"be":[213],"optimal":[214],"strong":[217],"sense.":[218],"Parallel":[219],"results":[220],"asymmetric":[223],"case":[224],"also":[226],"given.":[227]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}