{"id":"https://openalex.org/W2075620352","doi":"https://doi.org/10.1137/0205001","title":"Sorting and Searching in Multisets","display_name":"Sorting and Searching in Multisets","publication_year":1976,"publication_date":"1976-03-01","ids":{"openalex":"https://openalex.org/W2075620352","doi":"https://doi.org/10.1137/0205001","mag":"2075620352"},"language":"en","primary_location":{"id":"doi:10.1137/0205001","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0205001","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/A5061696421","display_name":"Ian Munro","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Ian Munro","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5041813088","display_name":"Philip M. Spira","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Philip M. Spira","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5061696421"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.8429,"has_fulltext":false,"cited_by_count":79,"citation_normalized_percentile":{"value":0.93930636,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"5","issue":"1","first_page":"1","last_page":"8"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9889000058174133,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9889000058174133,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9850000143051147,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic 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/T11476","display_name":"Graph theory and applications","score":0.9632999897003174,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/multiset","display_name":"Multiset","score":0.9708257913589478},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.7028719186782837},{"id":"https://openalex.org/keywords/multiplicative-function","display_name":"Multiplicative function","score":0.6915726065635681},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6731866002082825},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6549460291862488},{"id":"https://openalex.org/keywords/intersection","display_name":"Intersection (aeronautics)","score":0.6031491160392761},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.5803406238555908},{"id":"https://openalex.org/keywords/multiplicity","display_name":"Multiplicity (mathematics)","score":0.5627139806747437},{"id":"https://openalex.org/keywords/sorting","display_name":"Sorting","score":0.5511113405227661},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.4632953405380249},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.42130279541015625},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.41711822152137756},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4104786515235901},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.1781643033027649},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.17645934224128723}],"concepts":[{"id":"https://openalex.org/C2779623528","wikidata":"https://www.wikidata.org/wiki/Q864377","display_name":"Multiset","level":2,"score":0.9708257913589478},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.7028719186782837},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.6915726065635681},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6731866002082825},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6549460291862488},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.6031491160392761},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.5803406238555908},{"id":"https://openalex.org/C156004811","wikidata":"https://www.wikidata.org/wiki/Q2228257","display_name":"Multiplicity (mathematics)","level":2,"score":0.5627139806747437},{"id":"https://openalex.org/C111696304","wikidata":"https://www.wikidata.org/wiki/Q2303697","display_name":"Sorting","level":2,"score":0.5511113405227661},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.4632953405380249},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.42130279541015625},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.41711822152137756},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4104786515235901},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.1781643033027649},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.17645934224128723},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","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/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","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},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/0205001","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0205001","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":4,"referenced_works":["https://openalex.org/W1991983920","https://openalex.org/W2051283794","https://openalex.org/W2082045536","https://openalex.org/W4240200084"],"related_works":["https://openalex.org/W2731160740","https://openalex.org/W1526131532","https://openalex.org/W4286972003","https://openalex.org/W3199969630","https://openalex.org/W3208948601","https://openalex.org/W3034333085","https://openalex.org/W2955482447","https://openalex.org/W3197609398","https://openalex.org/W1985114981","https://openalex.org/W4221162730"],"abstract_inverted_index":{"In":[0],"this":[1,29],"paper":[2],"the":[3,16,38,50,56,63,72,82,95],"problem":[4],"of":[5,18,40,65,71,94,97,109],"sorting":[6],"multisets":[7,99],"is":[8,22,26,31,35,53,75,79,100],"considered.":[9],"An":[10],"information":[11],"theoretic":[12],"lower":[13,59],"bound":[14,30,60,83],"on":[15,61],"number":[17],"three":[19],"branch":[20],"comparisons":[21,48],"obtained,":[23],"and":[24,77,103],"it":[25,78],"shown":[27,36],"that":[28,37,81],"asymptotically":[32],"attainable.":[33],"It":[34],"multiplicities":[39],"a":[41,66,69,89,107,120],"set":[42],"can":[43,84],"only":[44],"be":[45,85],"obtained":[46],"by":[47],"if":[49],"total":[51],"order":[52],"discovered":[54],"in":[55],"process.":[57],"A":[58],"finding":[62],"mode":[64],"multiset":[67],"as":[68],"function":[70],"actual":[73],"multiplicity":[74],"given,":[76],"demonstrated":[80],"achieved":[86],"to":[87],"within":[88],"multiplicative":[90],"constant.":[91],"The":[92],"determination":[93],"intersection":[96],"two":[98,117],"also":[101],"discussed,":[102],"partial":[104],"results,":[105],"including":[106],"generalization":[108],"Reingold\u2019s":[110],"result":[111],"for":[112],"determining":[113],"whether":[114],"or":[115],"not":[116],"sets":[118],"have":[119],"nonempty":[121],"intersection,":[122],"are":[123],"obtained.":[124]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
