{"id":"https://openalex.org/W2079994531","doi":"https://doi.org/10.1145/1497290.1497293","title":"Average-case analysis of some plurality algorithms","display_name":"Average-case analysis of some plurality algorithms","publication_year":2009,"publication_date":"2009-03-01","ids":{"openalex":"https://openalex.org/W2079994531","doi":"https://doi.org/10.1145/1497290.1497293","mag":"2079994531"},"language":"en","primary_location":{"id":"doi:10.1145/1497290.1497293","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1497290.1497293","pdf_url":null,"source":{"id":"https://openalex.org/S137348503","display_name":"ACM Transactions on Algorithms","issn_l":"1549-6325","issn":["1549-6325","1549-6333"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Algorithms","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/A5036013554","display_name":"Laurent Alonso","orcid":null},"institutions":[{"id":"https://openalex.org/I1326498283","display_name":"Institut national de recherche en sciences et technologies du num\u00e9rique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"government","lineage":["https://openalex.org/I1326498283"]},{"id":"https://openalex.org/I4210121838","display_name":"Laboratoire Lorrain de Recherche en Informatique et ses Applications","ror":"https://ror.org/02vnf0c38","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I277688954","https://openalex.org/I4210107720","https://openalex.org/I4210121838","https://openalex.org/I4210159245","https://openalex.org/I90183372"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Laurent Alonso","raw_affiliation_strings":["INRIA-Lorraine, Vandoeuvre-l\u00e8s-Nancy, France","INRIA Lorraine, Vandoeuvre-les-Nancy, France#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"INRIA-Lorraine, Vandoeuvre-l\u00e8s-Nancy, France","institution_ids":["https://openalex.org/I1326498283","https://openalex.org/I4210121838"]},{"raw_affiliation_string":"INRIA Lorraine, Vandoeuvre-les-Nancy, France#TAB#","institution_ids":["https://openalex.org/I1326498283"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5073186573","display_name":"Edward M. Reingold","orcid":null},"institutions":[{"id":"https://openalex.org/I180949307","display_name":"Illinois Institute of Technology","ror":"https://ror.org/037t3ry66","country_code":"US","type":"education","lineage":["https://openalex.org/I180949307"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Edward M. Reingold","raw_affiliation_strings":["Illinois Institute of Technology, Chicago, IL",", Illinois Institute of Technology, Chicago, IL"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Illinois Institute of Technology, Chicago, IL","institution_ids":["https://openalex.org/I180949307"]},{"raw_affiliation_string":", Illinois Institute of Technology, Chicago, IL","institution_ids":["https://openalex.org/I180949307"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.14967041,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"5","issue":"2","first_page":"1","last_page":"36"},"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":0.9993000030517578,"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"}},"topics":[{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","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"}},{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9991999864578247,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9976999759674072,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6522107124328613},{"id":"https://openalex.org/keywords/binary-logarithm","display_name":"Binary logarithm","score":0.62488853931427},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5891760587692261},{"id":"https://openalex.org/keywords/colored","display_name":"Colored","score":0.5479316115379333},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5001609325408936},{"id":"https://openalex.org/keywords/pairwise-comparison","display_name":"Pairwise comparison","score":0.47360682487487793},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.46494120359420776},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.410094678401947},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.24214178323745728},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.2012399137020111}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6522107124328613},{"id":"https://openalex.org/C63553672","wikidata":"https://www.wikidata.org/wiki/Q581168","display_name":"Binary logarithm","level":2,"score":0.62488853931427},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5891760587692261},{"id":"https://openalex.org/C2778307483","wikidata":"https://www.wikidata.org/wiki/Q5149038","display_name":"Colored","level":2,"score":0.5479316115379333},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5001609325408936},{"id":"https://openalex.org/C184898388","wikidata":"https://www.wikidata.org/wiki/Q1435712","display_name":"Pairwise comparison","level":2,"score":0.47360682487487793},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.46494120359420776},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.410094678401947},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.24214178323745728},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.2012399137020111},{"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/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1145/1497290.1497293","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1497290.1497293","pdf_url":null,"source":{"id":"https://openalex.org/S137348503","display_name":"ACM Transactions on Algorithms","issn_l":"1549-6325","issn":["1549-6325","1549-6333"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Algorithms","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.304.8347","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.304.8347","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://emr.cs.uiuc.edu/~reingold/avg-case.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.77.5209","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.77.5209","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://emr.cs.uiuc.edu/~reingold/avg-case.pdf","raw_type":"text"},{"id":"pmh:oai:HAL:inria-00325044v1","is_oa":false,"landing_page_url":"https://inria.hal.science/inria-00325044","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://portal.acm.org/ft_gateway.cfm?id=1497293&type=pdf&coll=GUIDE&dl=GUIDE&CFID=68819978&CFTOKEN=54725410","raw_type":"info:eu-repo/semantics/article"}],"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/W100509257","https://openalex.org/W1506965906","https://openalex.org/W1524959429","https://openalex.org/W1915338595","https://openalex.org/W1966180611","https://openalex.org/W1971578319","https://openalex.org/W1972715414","https://openalex.org/W1981663184","https://openalex.org/W1993449345","https://openalex.org/W2000986517","https://openalex.org/W2033652300","https://openalex.org/W2065801535","https://openalex.org/W2071164269","https://openalex.org/W2072153301","https://openalex.org/W2078702411","https://openalex.org/W2293538051","https://openalex.org/W2326587081","https://openalex.org/W2752853835","https://openalex.org/W3198160809","https://openalex.org/W4249611616","https://openalex.org/W4255296275"],"related_works":["https://openalex.org/W2140509105","https://openalex.org/W3146178872","https://openalex.org/W4235907447","https://openalex.org/W4205128724","https://openalex.org/W2040849466","https://openalex.org/W346008744","https://openalex.org/W2072835713","https://openalex.org/W4284887816","https://openalex.org/W891964471","https://openalex.org/W2484916042"],"abstract_inverted_index":{"Given":[0],"a":[1,145],"set":[2],"of":[3,7,12,20,32,40,139,195],"n":[4,46,69,81,102,108,112,116,120,129,135,158,164,168,172,176,185,191],"elements,":[5],"each":[6],"which":[8],"is":[9,61,106,162],"colored":[10],"one":[11],"c":[13,45,62,65,68,73,79,92,149],"colors,":[14],"we":[15],"must":[16],"determine":[17],"an":[18,53,87],"element":[19],"the":[21,37,44,90,100,125,140,156,181,196],"plurality":[22],"(most":[23],"frequently":[24],"occurring)":[25],"color":[26,30,41],"by":[27],"pairwise":[28],"equal/unequal":[29],"comparisons":[31,42],"elements.":[33],"We":[34,51,83,143],"focus":[35],"on":[36,99,155],"expected":[38,59,126,182],"number":[39],"when":[43],"colorings":[47],"are":[48],"equally":[49,103,159],"probable.":[50],"analyze":[52,86],"obvious":[54,141,197],"algorithm,":[55],"showing":[56],"that":[57],"its":[58],"performance":[60],"2":[63,74,80],"+":[64,109,117,130,136,165,173,186,192],"\u2212":[66,70],"2/2":[67],"O":[71,110,118,131,137,166,174,187,193],"(":[72],"),":[75,121,177],"with":[76],"variance":[77],"\u0398(":[78],").":[82],"present":[84],"and":[85],"algorithm":[88,147],"for":[89,148],"case":[91],"=":[93,114,133,170,189],"3":[94,101],"colors":[95,151],"whose":[96,152],"average":[97,153],"complexity":[98,127,154,183],"probable":[104,160],"inputs":[105,161],"7083/5425":[107],"(\u221a":[111,119],")":[113,169],"1.3056\u2026":[115],"substantially":[122,178],"better":[123,179],"than":[124,180],"5/3":[128],"(1)":[132,138,188,194],"1.6666\u2026":[134],"algorithm.":[142,198],"describe":[144],"similar":[146],"=4":[150],"4":[157],"761311/402850":[163],"(log":[167,175],"1.8898\u2026":[171],"9/4":[184],"2.25":[190]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":2}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}