{"id":"https://openalex.org/W1986428580","doi":"https://doi.org/10.1137/0218079","title":"Solution of a Divide-and-Conquer Maximin Recurrence","display_name":"Solution of a Divide-and-Conquer Maximin Recurrence","publication_year":1989,"publication_date":"1989-12-01","ids":{"openalex":"https://openalex.org/W1986428580","doi":"https://doi.org/10.1137/0218079","mag":"1986428580"},"language":"en","primary_location":{"id":"doi:10.1137/0218079","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0218079","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/A5100337917","display_name":"Zhiyuan Li","orcid":"https://orcid.org/0000-0001-5364-1598"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Zhiyuan Li","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5073186573","display_name":"Edward M. Reingold","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Edward M. Reingold","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5100337917"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.9636,"has_fulltext":false,"cited_by_count":20,"citation_normalized_percentile":{"value":0.79208328,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"18","issue":"6","first_page":"1188","last_page":"1200"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11269","display_name":"Algorithms and Data Compression","score":0.9984999895095825,"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":0.9984999895095825,"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9948999881744385,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9945999979972839,"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/combinatorics","display_name":"Combinatorics","score":0.8459442853927612},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7862776517868042},{"id":"https://openalex.org/keywords/divide-and-conquer-algorithms","display_name":"Divide and conquer algorithms","score":0.5960809588432312},{"id":"https://openalex.org/keywords/minimax","display_name":"Minimax","score":0.5047718286514282},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.43682989478111267},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3397918939590454},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.15049362182617188},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.11363101005554199}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8459442853927612},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7862776517868042},{"id":"https://openalex.org/C71559656","wikidata":"https://www.wikidata.org/wiki/Q671298","display_name":"Divide and conquer algorithms","level":2,"score":0.5960809588432312},{"id":"https://openalex.org/C149728462","wikidata":"https://www.wikidata.org/wiki/Q751319","display_name":"Minimax","level":2,"score":0.5047718286514282},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.43682989478111267},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3397918939590454},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.15049362182617188},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.11363101005554199},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/0218079","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0218079","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":17,"referenced_works":["https://openalex.org/W41435888","https://openalex.org/W1550546692","https://openalex.org/W1971842242","https://openalex.org/W1972793839","https://openalex.org/W1985286232","https://openalex.org/W1986022261","https://openalex.org/W1993216012","https://openalex.org/W2011999472","https://openalex.org/W2030527372","https://openalex.org/W2043819676","https://openalex.org/W2045012623","https://openalex.org/W2106596127","https://openalex.org/W2132339863","https://openalex.org/W2143603891","https://openalex.org/W2152813177","https://openalex.org/W2475478067","https://openalex.org/W3148461011"],"related_works":["https://openalex.org/W1978042415","https://openalex.org/W2726819869","https://openalex.org/W2033963897","https://openalex.org/W1995061222","https://openalex.org/W1966276700","https://openalex.org/W2042743612","https://openalex.org/W2005314516","https://openalex.org/W2042041813","https://openalex.org/W2050500926","https://openalex.org/W2065052396"],"abstract_inverted_index":{"The":[0],"solution":[1,89,127],"of":[2,28,45,110,116],"the":[3,42,59,76,88,108,113,126],"divide-and-conquer":[4],"recurrence\\[":[5],"M(n)\\mathop":[6],"{\\max":[7],"}\\limits_{1":[8],"\\leqq":[9],"k":[10],"<":[11],"n}":[12,99,137,162],"(M(k)":[13],"+":[14,18,94,132,148,157],"M(n":[15],"-":[16,21,96,101,134,139,159,164,167],"k)":[17],"\\min":[19],"(f(k),f(n":[20],"k)))":[22],"\\]is":[23],"found":[24,36],"for":[25,37,49,142],"a":[26,56],"variety":[27],"functions":[29],"f.":[30],"Asymptotic":[31],"bounds":[32],"on":[33],"$M(n)$":[34,46,66],"are":[35],"arbitrary":[38],"nondecreasing":[39,51],"f,":[40],"and":[41,52],"exact":[43,77],"form":[44],"is":[47,63,72,90,107,128,153],"determined":[48],"f":[50,71],"weakly":[53],"concave.":[54],"As":[55],"corollary":[57],"to":[58],"asymptotic":[60],"bounds,":[61],"it":[62],"shown":[64],"that":[65],"remains":[67],"linear":[68],"even":[69],"when":[70],"almost":[73],"linear.":[74],"Among":[75],"forms":[78],"determined:":[79],"For":[80,118],"$f(x)":[81,119,143],"=":[82,92,120,130,144,155],"\\lfloor":[83,97,121,160],"{\\lg":[84,98,122,136,146,161],"x}":[85,123],"\\rfloor":[86,100,124,163],"$,":[87,125,151],"$M(n)":[91,129,154],"(M(1)":[93,131,156],"1)n":[95,133],"\\nu":[102,165],"(n)$":[103,106],"where":[104],"$\\nu":[105],"number":[109],"1-bits":[111],"in":[112],"binary":[114],"representation":[115],"n.":[117],"\\lceil":[135,145],"\\rceil":[138,150],"1$,":[140],"while":[141],"(x":[147],"1)}":[149],"thesolution":[152],"2)n":[158],"(n)":[166],"1$.":[168]},"counts_by_year":[{"year":2017,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}