{"id":"https://openalex.org/W1886622508","doi":"https://doi.org/10.1137/0404005","title":"A Simple Proof of the $O( \\sqrt{n} \\log^{3 / 4} n )$ Upright Matching Bound","display_name":"A Simple Proof of the $O( \\sqrt{n} \\log^{3 / 4} n )$ Upright Matching Bound","publication_year":1991,"publication_date":"1991-02-01","ids":{"openalex":"https://openalex.org/W1886622508","doi":"https://doi.org/10.1137/0404005","mag":"1886622508"},"language":"en","primary_location":{"id":"doi:10.1137/0404005","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0404005","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"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 Discrete Mathematics","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/A5110463438","display_name":"E. G. Coffman","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"E. G. Coffman, Jr.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5020744800","display_name":"Peter W. Shor","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"P. W. Shor","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.3345,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.53580455,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"4","issue":"1","first_page":"48","last_page":"57"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9991999864578247,"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"}},"topics":[{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9991999864578247,"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/T12176","display_name":"Optimization and Packing Problems","score":0.9991000294685364,"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/T12288","display_name":"Optimization and Search Problems","score":0.9962999820709229,"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/mathematics","display_name":"Mathematics","score":0.8726931810379028},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8045554757118225},{"id":"https://openalex.org/keywords/matching","display_name":"Matching (statistics)","score":0.6985214948654175},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.6156670451164246},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.5324697494506836},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.48932451009750366},{"id":"https://openalex.org/keywords/unit-square","display_name":"Unit square","score":0.4642096161842346},{"id":"https://openalex.org/keywords/binary-logarithm","display_name":"Binary logarithm","score":0.456726610660553},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.43425580859184265},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.41611456871032715},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.12911689281463623},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.12888765335083008},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.11142176389694214}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8726931810379028},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8045554757118225},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.6985214948654175},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.6156670451164246},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.5324697494506836},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.48932451009750366},{"id":"https://openalex.org/C7356347","wikidata":"https://www.wikidata.org/wiki/Q1307838","display_name":"Unit square","level":2,"score":0.4642096161842346},{"id":"https://openalex.org/C63553672","wikidata":"https://www.wikidata.org/wiki/Q581168","display_name":"Binary logarithm","level":2,"score":0.456726610660553},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.43425580859184265},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.41611456871032715},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.12911689281463623},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.12888765335083008},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.11142176389694214},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/0404005","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0404005","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"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 Discrete Mathematics","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":5,"referenced_works":["https://openalex.org/W1973285346","https://openalex.org/W2009931551","https://openalex.org/W2610893972","https://openalex.org/W4214939319","https://openalex.org/W4238472918"],"related_works":["https://openalex.org/W2808944898","https://openalex.org/W4254119641","https://openalex.org/W3196207352","https://openalex.org/W1983915440","https://openalex.org/W3095925971","https://openalex.org/W2963750720","https://openalex.org/W2802142240","https://openalex.org/W2157063282","https://openalex.org/W4301950763","https://openalex.org/W1992337616"],"abstract_inverted_index":{"The":[0,37,97],"stochastic":[1],"upright":[2,112],"matching":[3,61,66,113],"problem":[4,21,98],"has":[5],"had":[6],"many":[7],"important":[8],"applications,":[9],"most":[10],"notably":[11],"in":[12,33,109],"statistics":[13],"and":[14,48,94,155,165],"the":[15,34,43,85,102,125,144,173,177],"average-case":[16],"analysis":[17],"of":[18,26,62,67,105,114,127,143,172,179],"algorithms.":[19],"A":[20,169],"instance":[22],"is":[23,50,64,79,99,117,176],"a":[24,55,65,80,110,162],"set":[25],"n":[27,139,150],"points":[28,38,69,72,106],"chosen":[29,46],"uniformly":[30],"at":[31],"random":[32],"unit":[35],"square.":[36],"are":[39,45,152],"labeled":[40],"with":[41],"signs;":[42],"signs":[44],"independently":[47],"each":[49],"equally":[51],"likely":[52],"to":[53,70,84,100,157],"be":[54],"plus":[56,71,86],"or":[57],"minus.":[58],"An":[59],"up-right":[60],"S":[63],"minus":[68,81],"such":[73],"that":[74,120],"if":[75,121],"$(":[76,88],"x,y":[77],")$":[78,151],"point":[82,87],"matched":[83],"x',y'":[89],")$,":[90],"then":[91,130],"$x\\leqq":[92],"x'$":[93],"$y\\leqq":[95],"y'$.":[96],"estimate":[101],"expected":[103],"number":[104,126],"left":[107],"unmatched":[108,128],"maximum":[111],"S.":[115],"It":[116],"well":[118],"known":[119],"$U_n":[122],"$":[123],"denotes":[124],"points,":[129],"$E[":[131],"U_n":[132],"]":[133],"=":[134],"\\Theta":[135],"(":[136],"\\sqrt{n}":[137,148],"\\log^{3/4}":[138,149],")$.":[140],"Existing":[141],"proofs":[142],"upper":[145],"bound":[146],"$O(":[147],"quite":[153],"long":[154],"difficult":[156],"follow.":[158],"This":[159],"paper":[160],"presents":[161],"much":[163],"simpler":[164],"more":[166],"compact":[167],"proof.":[168],"distinctive":[170],"feature":[171],"new":[174],"proof":[175],"use":[178],"Fourier":[180],"expansions.":[181]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":3}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
