{"id":"https://openalex.org/W2090921949","doi":"https://doi.org/10.1137/s0097539794268406","title":"Hypercubic Sorting Networks","display_name":"Hypercubic Sorting Networks","publication_year":1998,"publication_date":"1998-02-01","ids":{"openalex":"https://openalex.org/W2090921949","doi":"https://doi.org/10.1137/s0097539794268406","mag":"2090921949"},"language":"en","primary_location":{"id":"doi:10.1137/s0097539794268406","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0097539794268406","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/A5113572159","display_name":"Tom Leighton","orcid":null},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Tom Leighton","raw_affiliation_strings":["Massachusetts Institute of Technology"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Massachusetts Institute of Technology","institution_ids":["https://openalex.org/I63966007"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5109574111","display_name":"C. Greg Plaxton","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"C. Greg Plaxton","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.6223,"has_fulltext":false,"cited_by_count":35,"citation_normalized_percentile":{"value":0.90887622,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"27","issue":"1","first_page":"1","last_page":"47"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10829","display_name":"Interconnection Networks and Systems","score":0.9997000098228455,"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"}},"topics":[{"id":"https://openalex.org/T10829","display_name":"Interconnection Networks and Systems","score":0.9997000098228455,"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"}},{"id":"https://openalex.org/T11269","display_name":"Algorithms and Data Compression","score":0.9987999796867371,"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/T11797","display_name":"graph theory and CDMA systems","score":0.998199999332428,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/tournament","display_name":"Tournament","score":0.882152795791626},{"id":"https://openalex.org/keywords/sorting","display_name":"Sorting","score":0.7795689105987549},{"id":"https://openalex.org/keywords/sorting-network","display_name":"Sorting network","score":0.7562072277069092},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6881842017173767},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.6424232721328735},{"id":"https://openalex.org/keywords/comparator","display_name":"Comparator","score":0.6303699016571045},{"id":"https://openalex.org/keywords/ranking","display_name":"Ranking (information retrieval)","score":0.5281572341918945},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.49159297347068787},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.4881618618965149},{"id":"https://openalex.org/keywords/omega","display_name":"Omega","score":0.48651570081710815},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4850448966026306},{"id":"https://openalex.org/keywords/sorting-algorithm","display_name":"Sorting algorithm","score":0.4707746207714081},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.46991080045700073},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.45821613073349},{"id":"https://openalex.org/keywords/node","display_name":"Node (physics)","score":0.41460832953453064},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.41220569610595703},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3652505874633789},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.16677090525627136},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09327974915504456}],"concepts":[{"id":"https://openalex.org/C136975688","wikidata":"https://www.wikidata.org/wiki/Q1320634","display_name":"Tournament","level":2,"score":0.882152795791626},{"id":"https://openalex.org/C111696304","wikidata":"https://www.wikidata.org/wiki/Q2303697","display_name":"Sorting","level":2,"score":0.7795689105987549},{"id":"https://openalex.org/C64540648","wikidata":"https://www.wikidata.org/wiki/Q646477","display_name":"Sorting network","level":4,"score":0.7562072277069092},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6881842017173767},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.6424232721328735},{"id":"https://openalex.org/C155745195","wikidata":"https://www.wikidata.org/wiki/Q1164179","display_name":"Comparator","level":3,"score":0.6303699016571045},{"id":"https://openalex.org/C189430467","wikidata":"https://www.wikidata.org/wiki/Q7293293","display_name":"Ranking (information retrieval)","level":2,"score":0.5281572341918945},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.49159297347068787},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.4881618618965149},{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.48651570081710815},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4850448966026306},{"id":"https://openalex.org/C108094655","wikidata":"https://www.wikidata.org/wiki/Q181593","display_name":"Sorting algorithm","level":3,"score":0.4707746207714081},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.46991080045700073},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.45821613073349},{"id":"https://openalex.org/C62611344","wikidata":"https://www.wikidata.org/wiki/Q1062658","display_name":"Node (physics)","level":2,"score":0.41460832953453064},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.41220569610595703},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3652505874633789},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.16677090525627136},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09327974915504456},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C165801399","wikidata":"https://www.wikidata.org/wiki/Q25428","display_name":"Voltage","level":2,"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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/s0097539794268406","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0097539794268406","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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.30.620","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.30.620","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.utexas.edu/users/plaxton/html/../ps/1998/sicomp.ps","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.40.9595","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.40.9595","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ftp://ftp.cs.utexas.edu/pub/techreports/tr94-18.ps.Z","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W140245995","https://openalex.org/W1587590810","https://openalex.org/W1969008575","https://openalex.org/W1971714289","https://openalex.org/W1977908721","https://openalex.org/W1988294273","https://openalex.org/W2004759812","https://openalex.org/W2007200565","https://openalex.org/W2010442238","https://openalex.org/W2034955722","https://openalex.org/W2042587503","https://openalex.org/W2075488055","https://openalex.org/W2080304917","https://openalex.org/W2097755092","https://openalex.org/W2108610799","https://openalex.org/W2114870379","https://openalex.org/W2141389982","https://openalex.org/W2155371437","https://openalex.org/W2752853835","https://openalex.org/W4241840173","https://openalex.org/W4250527476"],"related_works":["https://openalex.org/W2396743875","https://openalex.org/W2094179388","https://openalex.org/W2126436988","https://openalex.org/W2325315917","https://openalex.org/W2372558933","https://openalex.org/W2385397541","https://openalex.org/W4239051739","https://openalex.org/W2054216114","https://openalex.org/W2374324126","https://openalex.org/W2381187503"],"abstract_inverted_index":{"This":[0],"paper":[1],"provides":[2],"an":[3,65,86,127],"analysis":[4],"of":[5,29,42,48,59,76],"a":[6,21,45,78,107,118],"natural":[7],"d-round":[8],"tournament":[9,19,31],"over":[10],"n":[11],"=":[12],"2d":[13],"players":[14],"and":[15,117],"demonstrates":[16],"that":[17,54,71],"the":[18,56,60,73],"possesses":[20],"surprisingly":[22],"strong":[23],"ranking":[24,27],"property.":[25],"The":[26],"property":[28],"this":[30,104],"is":[32],"used":[33],"to":[34],"design":[35],"efficient":[36],"sorting":[37,80,90,122],"algorithms":[38,98],"for":[39,92,121],"several":[40],"models":[41],"parallel":[43],"computation:":[44],"comparator":[46,69],"network":[47,70,81],"depth":[49],"$c\\\\cdot\\lg":[50],"n$,":[51],"$c\\approx":[52],"7.44$,":[53],"sorts":[55,72],"vast":[57,74],"majority":[58,75],"n!":[61],"possible":[62],"input":[63],"permutations;":[64,77],"$O(\\lg":[66,87],"n)$-depth":[67],"hypercubic":[68,79,94],"with":[82],"nearly":[83],"logarithmic":[84],"depth;":[85],"n)$-time":[88],"randomized":[89,119],"algorithm":[91,105,120],"any":[93,113],"machine":[95,131],"(other":[96],"such":[97],"have":[99],"been":[100],"previously":[101,114],"discovered,":[102],"but":[103],"has":[106],"significantly":[108],"smaller":[109],"failure":[110],"probability":[111],"than":[112],"known":[115],"algorithm);":[116],"nO":[123],"(m)-bit":[124],"records":[125],"on":[126],"$(n\\lg":[128],"n)$-node":[129],"omega":[130],"in":[132],"$O(m+\\lg":[133],"n)$":[134],"bit":[135],"steps.":[136]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":2},{"year":2012,"cited_by_count":4}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}