{"id":"https://openalex.org/W1979605020","doi":"https://doi.org/10.1137/0218063","title":"The Complete Convergence of Best Fit Decreasing","display_name":"The Complete Convergence of Best Fit Decreasing","publication_year":1989,"publication_date":"1989-10-01","ids":{"openalex":"https://openalex.org/W1979605020","doi":"https://doi.org/10.1137/0218063","mag":"1979605020"},"language":"en","primary_location":{"id":"doi:10.1137/0218063","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0218063","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/A5029436995","display_name":"Wansoo T. Rhee","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Wansoo T. Rhee","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5077443351","display_name":"Michel Talagrand","orcid":"https://orcid.org/0000-0003-4956-3966"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Michel Talagrand","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5029436995"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.0853,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.77383796,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"18","issue":"5","first_page":"909","last_page":"918"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12176","display_name":"Optimization and Packing Problems","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2209","display_name":"Industrial and Manufacturing Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12176","display_name":"Optimization and Packing Problems","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2209","display_name":"Industrial and Manufacturing Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9970999956130981,"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/T12288","display_name":"Optimization and Search Problems","score":0.9944999814033508,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7502342462539673},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7225021719932556},{"id":"https://openalex.org/keywords/random-variable","display_name":"Random variable","score":0.5473303198814392},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.5378125905990601},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.5350080132484436},{"id":"https://openalex.org/keywords/unit","display_name":"Unit (ring theory)","score":0.5186880826950073},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.48401781916618347},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.46306318044662476},{"id":"https://openalex.org/keywords/probability-measure","display_name":"Probability measure","score":0.41865071654319763},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3327335715293884},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.3051968216896057},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.06623691320419312}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7502342462539673},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7225021719932556},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.5473303198814392},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.5378125905990601},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.5350080132484436},{"id":"https://openalex.org/C122637931","wikidata":"https://www.wikidata.org/wiki/Q118084","display_name":"Unit (ring theory)","level":2,"score":0.5186880826950073},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.48401781916618347},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.46306318044662476},{"id":"https://openalex.org/C21031990","wikidata":"https://www.wikidata.org/wiki/Q355020","display_name":"Probability measure","level":2,"score":0.41865071654319763},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3327335715293884},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.3051968216896057},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.06623691320419312},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C145420912","wikidata":"https://www.wikidata.org/wiki/Q853077","display_name":"Mathematics education","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/0218063","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0218063","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":8,"referenced_works":["https://openalex.org/W1985246949","https://openalex.org/W2009931551","https://openalex.org/W2017540210","https://openalex.org/W2021170159","https://openalex.org/W2043862089","https://openalex.org/W2044587680","https://openalex.org/W4242879336","https://openalex.org/W4243869382"],"related_works":["https://openalex.org/W611386996","https://openalex.org/W2371343292","https://openalex.org/W629290331","https://openalex.org/W617685022","https://openalex.org/W1509983653","https://openalex.org/W3215563689","https://openalex.org/W610590827","https://openalex.org/W591599671","https://openalex.org/W1556748146","https://openalex.org/W3199594174"],"abstract_inverted_index":{"Consider":[0],"a":[1,67],"probability":[2],"measure":[3],"$\\mu":[4,25,33],"$":[5,21],"on":[6,32],"$[0,1]$":[7],"and":[8],"an":[9],"independent":[10],"sequence":[11],"of":[12,44,57,66],"random":[13],"variables":[14],"$X_1":[15,59],",":[16,19,38,60,89],"\\cdots":[17,20,39,61,90],",X_n":[18,40,62],"distributed":[22],"according":[23],"to":[24,54],"$.":[26,34,63],"No":[27],"regularity":[28],"assumptions":[29],"are":[30,48],"made":[31],"Denote":[35],"by":[36,50],"$B(X_1":[37],")$":[41,70],"the":[42],"number":[43],"unit-size":[45],"bins":[46],"that":[47,74],"used":[49],"Best":[51],"Fit":[52],"Decreasing":[53],"pack":[55],"items":[56],"size":[58],"The":[64],"existence":[65],"constant":[68],"$b(\\mu":[69],"is":[71],"proven":[72],"such":[73],"for":[75],"each":[76],"$\\varepsilon":[77],">":[78],"0,$\\[":[79],"\\sum\\limits_{n":[80],"\\geqq":[81,97],"1}":[82,86],"{P(":[83],"\\left|n^{":[84],"-":[85,93],"B":[87],"\\left(X_1":[88],"X_n":[91],"\\right)":[92],"b(\\mu":[94],")":[95],"\\right|":[96],"\\varepsilon":[98],")}":[99],"<":[100],"\\infty":[101],".":[102],"\\]":[103]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
