{"id":"https://openalex.org/W1969935217","doi":"https://doi.org/10.1007/bf01954896","title":"On the distribution of comparisons in sorting algorithms","display_name":"On the distribution of comparisons in sorting algorithms","publication_year":1988,"publication_date":"1988-12-01","ids":{"openalex":"https://openalex.org/W1969935217","doi":"https://doi.org/10.1007/bf01954896","mag":"1969935217"},"language":"en","primary_location":{"id":"doi:10.1007/bf01954896","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf01954896","pdf_url":null,"source":{"id":"https://openalex.org/S125499977","display_name":"BIT Numerical Mathematics","issn_l":"0006-3835","issn":["0006-3835","1572-9125"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"BIT","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/A5036610989","display_name":"Dana Richards","orcid":"https://orcid.org/0000-0002-7260-4394"},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]},{"id":"https://openalex.org/I51556381","display_name":"University of Virginia","ror":"https://ror.org/0153tk833","country_code":"US","type":"education","lineage":["https://openalex.org/I51556381"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Dana Richards","raw_affiliation_strings":["Dept. of Computer Science, University of Illinois, 61801, Urbana, IL, USA","Dept. of Computer Science, University of Virginia, 22903, Charlottesville, VA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dept. of Computer Science, University of Illinois, 61801, Urbana, IL, USA","institution_ids":["https://openalex.org/I157725225"]},{"raw_affiliation_string":"Dept. of Computer Science, University of Virginia, 22903, Charlottesville, VA, USA","institution_ids":["https://openalex.org/I51556381"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5108215094","display_name":"Pravin M. Vaidya","orcid":null},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]},{"id":"https://openalex.org/I51556381","display_name":"University of Virginia","ror":"https://ror.org/0153tk833","country_code":"US","type":"education","lineage":["https://openalex.org/I51556381"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Pravin Vaidya","raw_affiliation_strings":["Dept. of Computer Science, University of Illinois, 61801, Urbana, IL, USA","Dept. of Computer Science, University of Virginia, 22903, Charlottesville, VA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dept. of Computer Science, University of Illinois, 61801, Urbana, IL, USA","institution_ids":["https://openalex.org/I157725225"]},{"raw_affiliation_string":"Dept. of Computer Science, University of Virginia, 22903, Charlottesville, VA, USA","institution_ids":["https://openalex.org/I51556381"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2990,"currency":"USD","value_usd":2990},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.09319021,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"28","issue":"4","first_page":"764","last_page":"774"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11269","display_name":"Algorithms and Data Compression","score":0.9995999932289124,"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":0.9995999932289124,"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/T11567","display_name":"semigroups and automata theory","score":0.9994999766349792,"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"}},{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9993000030517578,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/sorting","display_name":"Sorting","score":0.8441687822341919},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.7071428894996643},{"id":"https://openalex.org/keywords/sorting-algorithm","display_name":"Sorting algorithm","score":0.6371919512748718},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6181625127792358},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5760923027992249},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5748574733734131},{"id":"https://openalex.org/keywords/matching","display_name":"Matching (statistics)","score":0.5652111172676086},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.5309436321258545},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4747855067253113},{"id":"https://openalex.org/keywords/natural-number","display_name":"Natural number","score":0.45089462399482727},{"id":"https://openalex.org/keywords/distribution","display_name":"Distribution (mathematics)","score":0.4146439731121063},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.37292617559432983},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3638005256652832},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.11411184072494507}],"concepts":[{"id":"https://openalex.org/C111696304","wikidata":"https://www.wikidata.org/wiki/Q2303697","display_name":"Sorting","level":2,"score":0.8441687822341919},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.7071428894996643},{"id":"https://openalex.org/C108094655","wikidata":"https://www.wikidata.org/wiki/Q181593","display_name":"Sorting algorithm","level":3,"score":0.6371919512748718},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6181625127792358},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5760923027992249},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5748574733734131},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.5652111172676086},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.5309436321258545},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4747855067253113},{"id":"https://openalex.org/C184264201","wikidata":"https://www.wikidata.org/wiki/Q21199","display_name":"Natural number","level":2,"score":0.45089462399482727},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.4146439731121063},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.37292617559432983},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3638005256652832},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.11411184072494507},{"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/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/bf01954896","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf01954896","pdf_url":null,"source":{"id":"https://openalex.org/S125499977","display_name":"BIT Numerical Mathematics","issn_l":"0006-3835","issn":["0006-3835","1572-9125"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"BIT","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":12,"referenced_works":["https://openalex.org/W19243652","https://openalex.org/W1993449345","https://openalex.org/W2021384638","https://openalex.org/W2023047598","https://openalex.org/W2045183461","https://openalex.org/W2045807935","https://openalex.org/W2076458424","https://openalex.org/W2151407355","https://openalex.org/W2528636261","https://openalex.org/W2530214907","https://openalex.org/W2752853835","https://openalex.org/W3198160809"],"related_works":["https://openalex.org/W2809748609","https://openalex.org/W3033694952","https://openalex.org/W2372558933","https://openalex.org/W2349288944","https://openalex.org/W797244100","https://openalex.org/W4298155039","https://openalex.org/W2801186172","https://openalex.org/W2367560286","https://openalex.org/W2181812531","https://openalex.org/W961204790"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}
