{"id":"https://openalex.org/W4234574620","doi":"https://doi.org/10.1137/1.9781611973105.35","title":"Generalized Perron\u2013Frobenius Theorem for Multiple Choice Matrices, and Applications","display_name":"Generalized Perron\u2013Frobenius Theorem for Multiple Choice Matrices, and Applications","publication_year":2013,"publication_date":"2013-01-06","ids":{"openalex":"https://openalex.org/W4234574620","doi":"https://doi.org/10.1137/1.9781611973105.35"},"language":"en","primary_location":{"id":"doi:10.1137/1.9781611973105.35","is_oa":false,"landing_page_url":"https://doi.org/10.1137/1.9781611973105.35","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the Twenty-Fourth Annual ACM-SIAM Symposium on Discrete Algorithms","raw_type":"proceedings-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/A5010846539","display_name":"Chen Avin","orcid":"https://orcid.org/0000-0002-6647-8002"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Chen Avin","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5058032712","display_name":"Michael Borokhovich","orcid":"https://orcid.org/0000-0002-3367-0401"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Michael Borokhovich","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5070817036","display_name":"Yoram Haddad","orcid":"https://orcid.org/0000-0002-4118-2141"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yoram Haddad","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5109108206","display_name":"Erez Kantor","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Erez Kantor","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5016606156","display_name":"Zvi Lotker","orcid":"https://orcid.org/0000-0002-3759-5584"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zvi Lotker","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5022875077","display_name":"Merav Parter","orcid":"https://orcid.org/0000-0002-2357-2445"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Merav Parter","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5056419022","display_name":"David Peleg","orcid":"https://orcid.org/0000-0003-1590-0506"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"David Peleg","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":7,"corresponding_author_ids":["https://openalex.org/A5010846539"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.0876,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.80849798,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"478","last_page":"497"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9966999888420105,"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"}},"topics":[{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9966999888420105,"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/T11797","display_name":"graph theory and CDMA systems","score":0.992900013923645,"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/T12516","display_name":"Advanced Mathematical Theories and Applications","score":0.9693999886512756,"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/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.6376338601112366},{"id":"https://openalex.org/keywords/server","display_name":"Server","score":0.6354915499687195},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.6332815885543823},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5206822156906128},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.39955466985702515},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3710678815841675},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.35891222953796387}],"concepts":[{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.6376338601112366},{"id":"https://openalex.org/C93996380","wikidata":"https://www.wikidata.org/wiki/Q44127","display_name":"Server","level":2,"score":0.6354915499687195},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.6332815885543823},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5206822156906128},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.39955466985702515},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3710678815841675},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.35891222953796387},{"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C136764020","wikidata":"https://www.wikidata.org/wiki/Q466","display_name":"World Wide Web","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/1.9781611973105.35","is_oa":false,"landing_page_url":"https://doi.org/10.1137/1.9781611973105.35","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the Twenty-Fourth Annual ACM-SIAM Symposium on Discrete Algorithms","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.5699999928474426,"id":"https://metadata.un.org/sdg/17","display_name":"Partnerships for the goals"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2388464034","https://openalex.org/W2140460949","https://openalex.org/W2105580438","https://openalex.org/W2533125852","https://openalex.org/W2057435755","https://openalex.org/W2949620858","https://openalex.org/W2018782216","https://openalex.org/W1994111466","https://openalex.org/W1989375655","https://openalex.org/W2911113383"],"abstract_inverted_index":{"The":[0,22,119,251],"celebrated":[1],"Perron\u2013Frobenius":[2],"(PF)":[3],"theorem":[4,26,319],"is":[5,81,89,155,204],"stated":[6],"for":[7,69,174,269,277,316],"irreducible":[8],"nonnegative":[9,70,355],"square":[10,297],"matrices,":[11,71],"and":[12,20,43,51,166,206,234,273,293,305,314,347,357],"provides":[13,107],"a":[14,86,102,108,260,270,303,331],"simple":[15],"characterization":[16,359],"of":[17,24,41,66,74,110,130,169,177,187,220,255,291,296,334,343,354,360],"their":[18],"eigenvectors":[19],"eigenvalues.":[21],"importance":[23],"this":[25],"stems":[27],"from":[28,330],"the":[29,63,72,91,111,175,178,185,192,195,199,217,230,238,241,256,266,279,289,324,338],"fact":[30],"that":[31,141,184,197,264],"eigenvalue":[32,295],"problems":[33,80],"on":[34],"such":[35,75,350],"matrices":[36,298,356],"arise":[37],"in":[38,144,162,194,198,243,282,302],"many":[39,54],"fields":[40],"science":[42],"engineering,":[44],"including":[45],"dynamical":[46],"systems":[47,126],"theory,":[48],"economics,":[49],"statistics":[50],"optimization.":[52],"However,":[53],"real-life":[55],"scenarios":[56],"give":[57],"rise":[58],"to":[59,77,101,114,159,214,299,311,320],"nonsquare":[60,103,115,300],"matrices.":[61,118],"Despite":[62],"extensive":[64],"development":[65],"spectral":[67,352],"theories":[68,76],"applicability":[73],"non-convex":[78,271],"optimization":[79],"not":[82,190,235],"clear.":[83],"In":[84,285,336],"particular,":[85,337],"natural":[87],"question":[88],"whether":[90],"PF":[92,112,180,262],"Theorem":[93,113,263],"(along":[94],"with":[95,127,150],"its":[96],"applications)":[97],"can":[98,121,142],"be":[99,122,312],"generalized":[100,261,318],"setting.":[104],"Our":[105],"paper":[106,257],"generalization":[109],"multiple":[116,139],"choice":[117],"extension":[120],"interpreted":[123],"as":[124,246,351],"representing":[125],"additional":[128,218],"degrees":[129],"freedom,":[131],"where":[132],"each":[133],"client":[134,211,226],"entity":[135,212],"may":[136],"choose":[137],"between":[138,240],"servers":[140,224,242],"cooperate":[143],"serving":[145],"it":[146],"(while":[147],"potentially":[148],"interfering":[149],"other":[151],"clients).":[152],"This":[153],"formulation":[154],"motivated":[156],"by":[157],"applications":[158],"power":[160,219],"control":[161],"wireless":[163],"networks,":[164],"economics":[165],"others,":[167],"all":[168],"which":[170,308],"extend":[171,288],"known":[172],"examples":[173],"use":[176,328],"original":[179],"Theorem.":[181],"We":[182],"show":[183],"option":[186],"cooperation":[188,203],"does":[189],"improve":[191],"situation,":[193],"sense":[196],"optimum":[200],"solution,":[201,326],"no":[202],"needed,":[205],"only":[207],"one":[208,247],"server":[209,233],"per":[210,225],"needs":[213],"work.":[215],"Hence,":[216],"having":[221],"several":[222],"potential":[223],"translates":[227],"into":[228,236],"choosing":[229],"\u201cbest\u201d":[231],"single":[232],"sharing":[237],"load":[239],"some":[244],"way,":[245,307],"might":[248],"have":[249],"expected.":[250],"two":[252],"main":[253],"contributions":[254],"are":[258],"(i)":[259],"characterizes":[265],"optimal":[267,280,325],"solution":[268,281],"problem,":[272],"(ii)":[274],"an":[275],"algorithm":[276],"finding":[278],"polynomial":[283],"time.":[284],"addition,":[286],"we":[287,327],"definitions":[290],"irreducibility":[292],"largest":[294],"ones":[301],"novel":[304],"non-trivial":[306],"turns":[309],"out":[310],"necessary":[313],"sufficient":[315],"our":[317],"hold.":[321],"To":[322],"characterize":[323],"techniques":[329,346],"wide":[332],"range":[333],"areas.":[335],"analysis":[339],"exploits":[340],"combinatorial":[341],"properties":[342,353],"polytopes,":[344],"graph-theoretic":[345],"analytic":[348],"tools":[349],"root":[358],"integer":[361],"polynomials.":[362]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
