{"id":"https://openalex.org/W1489392556","doi":"https://doi.org/10.37236/472","title":"Random Subnetworks of Random Sorting Networks","display_name":"Random Subnetworks of Random Sorting Networks","publication_year":2010,"publication_date":"2010-04-19","ids":{"openalex":"https://openalex.org/W1489392556","doi":"https://doi.org/10.37236/472","mag":"1489392556"},"language":"en","primary_location":{"id":"doi:10.37236/472","is_oa":true,"landing_page_url":"https://doi.org/10.37236/472","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v17i1n23/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v17i1n23/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5067501882","display_name":"Omer Angel","orcid":"https://orcid.org/0000-0002-6451-8242"},"institutions":[{"id":"https://openalex.org/I1290206253","display_name":"Microsoft (United States)","ror":"https://ror.org/00d0nc645","country_code":"US","type":"company","lineage":["https://openalex.org/I1290206253"]},{"id":"https://openalex.org/I141945490","display_name":"University of British Columbia","ror":"https://ror.org/03rmrcq20","country_code":"CA","type":"education","lineage":["https://openalex.org/I141945490"]}],"countries":["CA","US"],"is_corresponding":true,"raw_author_name":"Omer Angel","raw_affiliation_strings":["Department of Mathematics, University of British Columbia, 121-1984 Mathematics Road, Vancouver, BC V6T 1Z2, Canada. and","Department of Mathematics, University of British Columbia, 121-1984 Mathematics Road, Vancouver, BC V6T 1Z2, Canada","Microsoft Research, 1 Microsoft Way, Redmond, WA 98052, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of British Columbia, 121-1984 Mathematics Road, Vancouver, BC V6T 1Z2, Canada. and","institution_ids":["https://openalex.org/I141945490"]},{"raw_affiliation_string":"Department of Mathematics, University of British Columbia, 121-1984 Mathematics Road, Vancouver, BC V6T 1Z2, Canada","institution_ids":["https://openalex.org/I141945490"]},{"raw_affiliation_string":"Microsoft Research, 1 Microsoft Way, Redmond, WA 98052, USA","institution_ids":["https://openalex.org/I1290206253"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5009362592","display_name":"Alexander E. Holroyd","orcid":"https://orcid.org/0000-0002-3364-641X"},"institutions":[{"id":"https://openalex.org/I141945490","display_name":"University of British Columbia","ror":"https://ror.org/03rmrcq20","country_code":"CA","type":"education","lineage":["https://openalex.org/I141945490"]},{"id":"https://openalex.org/I1290206253","display_name":"Microsoft (United States)","ror":"https://ror.org/00d0nc645","country_code":"US","type":"company","lineage":["https://openalex.org/I1290206253"]}],"countries":["CA","US"],"is_corresponding":false,"raw_author_name":"Alexander E. Holroyd","raw_affiliation_strings":["Department of Mathematics, University of British Columbia, 121-1984 Mathematics Road, Vancouver, BC V6T 1Z2, Canada. and","Department of Mathematics, University of British Columbia, 121-1984 Mathematics Road, Vancouver, BC V6T 1Z2, Canada","Microsoft Research, 1 Microsoft Way, Redmond, WA 98052, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of British Columbia, 121-1984 Mathematics Road, Vancouver, BC V6T 1Z2, Canada. and","institution_ids":["https://openalex.org/I141945490"]},{"raw_affiliation_string":"Department of Mathematics, University of British Columbia, 121-1984 Mathematics Road, Vancouver, BC V6T 1Z2, Canada","institution_ids":["https://openalex.org/I141945490"]},{"raw_affiliation_string":"Microsoft Research, 1 Microsoft Way, Redmond, WA 98052, USA","institution_ids":["https://openalex.org/I1290206253"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5067501882"],"corresponding_institution_ids":["https://openalex.org/I1290206253","https://openalex.org/I141945490"],"apc_list":null,"apc_paid":null,"fwci":1.1929,"has_fulltext":true,"cited_by_count":12,"citation_normalized_percentile":{"value":0.72891396,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"17","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9959999918937683,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T10064","display_name":"Complex Network Analysis Techniques","score":0.9908999800682068,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7522504329681396},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7385234236717224},{"id":"https://openalex.org/keywords/subnetwork","display_name":"Subnetwork","score":0.6832853555679321},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.680394172668457},{"id":"https://openalex.org/keywords/random-graph","display_name":"Random graph","score":0.6395014524459839},{"id":"https://openalex.org/keywords/sorting","display_name":"Sorting","score":0.5858149528503418},{"id":"https://openalex.org/keywords/sorting-network","display_name":"Sorting network","score":0.49750521779060364},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4564116597175598},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.33560705184936523},{"id":"https://openalex.org/keywords/sorting-algorithm","display_name":"Sorting algorithm","score":0.2431798279285431},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.1402778923511505},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1254483461380005}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7522504329681396},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7385234236717224},{"id":"https://openalex.org/C2780186347","wikidata":"https://www.wikidata.org/wiki/Q11414","display_name":"Subnetwork","level":2,"score":0.6832853555679321},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.680394172668457},{"id":"https://openalex.org/C47458327","wikidata":"https://www.wikidata.org/wiki/Q910404","display_name":"Random graph","level":3,"score":0.6395014524459839},{"id":"https://openalex.org/C111696304","wikidata":"https://www.wikidata.org/wiki/Q2303697","display_name":"Sorting","level":2,"score":0.5858149528503418},{"id":"https://openalex.org/C64540648","wikidata":"https://www.wikidata.org/wiki/Q646477","display_name":"Sorting network","level":4,"score":0.49750521779060364},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4564116597175598},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.33560705184936523},{"id":"https://openalex.org/C108094655","wikidata":"https://www.wikidata.org/wiki/Q181593","display_name":"Sorting algorithm","level":3,"score":0.2431798279285431},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.1402778923511505},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1254483461380005},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.37236/472","is_oa":true,"landing_page_url":"https://doi.org/10.37236/472","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v17i1n23/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.177.9130","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.177.9130","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.combinatorics.org/Volume_17/PDF/v17i1n23.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.187.9380","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.187.9380","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://research.microsoft.com/%7Eholroyd/papers/ssn.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.746.7721","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.746.7721","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/0911.2519.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.37236/472","is_oa":true,"landing_page_url":"https://doi.org/10.37236/472","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v17i1n23/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","score":0.6100000143051147,"display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1489392556.pdf","grobid_xml":"https://content.openalex.org/works/W1489392556.grobid-xml"},"referenced_works_count":24,"referenced_works":["https://openalex.org/W188357332","https://openalex.org/W630423399","https://openalex.org/W1606180716","https://openalex.org/W1980441549","https://openalex.org/W1981176128","https://openalex.org/W2023212718","https://openalex.org/W2024332750","https://openalex.org/W2029907394","https://openalex.org/W2040246814","https://openalex.org/W2074065886","https://openalex.org/W2083750870","https://openalex.org/W2106822743","https://openalex.org/W2107382982","https://openalex.org/W2110562284","https://openalex.org/W2123146927","https://openalex.org/W2134810677","https://openalex.org/W2155525982","https://openalex.org/W2165064763","https://openalex.org/W2290127356","https://openalex.org/W2314376244","https://openalex.org/W2322524800","https://openalex.org/W6675839136","https://openalex.org/W6676583277","https://openalex.org/W6679988009"],"related_works":["https://openalex.org/W2164888609","https://openalex.org/W2365998105","https://openalex.org/W2131956217","https://openalex.org/W1521404434","https://openalex.org/W2168577286","https://openalex.org/W2208979138","https://openalex.org/W2017461851","https://openalex.org/W2094179388","https://openalex.org/W2122685942","https://openalex.org/W2950876273"],"abstract_inverted_index":{"A":[0],"sorting":[1,29,36],"network":[2,30,37],"is":[3,83,110],"a":[4,77,87,101,104,113],"shortest":[5],"path":[6],"from":[7],"$12\\cdots":[8],"n$":[9],"to":[10],"$n\\cdots21$":[11],"in":[12,63,66],"the":[13,26,45,58,67,96,118,124],"Cayley":[14],"graph":[15],"of":[16,48,61,93,103,106,117,128],"$S_n$":[17],"generated":[18],"by":[19,32,123],"nearest-neighbor":[20],"swaps.":[21],"For":[22],"$m\\leq":[23],"n$,":[24],"consider":[25],"random":[27,40],"$m$-particle":[28],"obtained":[31],"choosing":[33],"an":[34],"$n$-particle":[35],"uniformly":[38,52],"at":[39,53],"and":[41,74,85,132],"then":[42],"observing":[43],"only":[44],"relative":[46],"order":[47],"$m$":[49],"particles":[50],"chosen":[51],"random.":[54],"We":[55],"prove":[56],"that":[57],"expected":[59],"number":[60],"swaps":[62],"location":[64],"$j$":[65],"subnetwork":[68,119],"does":[69],"not":[70],"depend":[71],"on":[72],"$n$,":[73],"we":[75,99],"provide":[76],"formula":[78],"for":[79],"it.":[80],"Our":[81,108],"proof":[82,102],"probabilistic,":[84],"involves":[86],"P\u00f3lya":[88],"urn":[89],"with":[90,112],"non-integer":[91],"numbers":[92],"balls.":[94],"From":[95],"case":[97],"$m=4$":[98],"obtain":[100],"conjecture":[105,127],"Warrington.":[107],"result":[109],"consistent":[111],"conjectural":[114],"limiting":[115],"law":[116],"as":[120],"$n\\to\\infty$":[121],"implied":[122],"great":[125],"circle":[126],"Angel,":[129],"Holroyd,":[130],"Romik":[131],"Vir\u00e1g.":[133]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}