{"id":"https://openalex.org/W3179877719","doi":"https://doi.org/10.37190/ord210206","title":"Computing power indices for weighted voting games via dynamic programming","display_name":"Computing power indices for weighted voting games via dynamic programming","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3179877719","doi":"https://doi.org/10.37190/ord210206","mag":"3179877719"},"language":"en","primary_location":{"id":"doi:10.37190/ord210206","is_oa":true,"landing_page_url":"http://doi.org/10.37190/ord210206","pdf_url":"https://doi.org/10.37190/ord210206","source":{"id":"https://openalex.org/S2739399646","display_name":"Badania Operacyjne i Decyzje/Operations Research and Decisions","issn_l":"1230-1868","issn":["1230-1868","2081-8858","2391-6060"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317492","host_organization_name":"Wroc\u0142aw University of Science and Technology","host_organization_lineage":["https://openalex.org/P4310317492"],"host_organization_lineage_names":["Wroc\u0142aw University of Science and Technology"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Operations Research and Decisions","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://doi.org/10.37190/ord210206","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5020381550","display_name":"Jochen Staudacher","orcid":"https://orcid.org/0000-0002-0619-4606"},"institutions":[{"id":"https://openalex.org/I2802623092","display_name":"Kempten University of Applied Sciences","ror":"https://ror.org/02m4p8096","country_code":"DE","type":"education","lineage":["https://openalex.org/I2802623092"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Jochen Staudacher","raw_affiliation_strings":["Fakultt Informatik, Hochschule Kempten, Bahnhofstr. 61, 87435 Kempten, Germany","Fakult\u00e4t Informatik, Hochschule Kempten, Bahnhofstr. 61, 87435 Kempten, Germany"],"affiliations":[{"raw_affiliation_string":"Fakultt Informatik, Hochschule Kempten, Bahnhofstr. 61, 87435 Kempten, Germany","institution_ids":["https://openalex.org/I2802623092"]},{"raw_affiliation_string":"Fakult\u00e4t Informatik, Hochschule Kempten, Bahnhofstr. 61, 87435 Kempten, Germany","institution_ids":["https://openalex.org/I2802623092"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5027677214","display_name":"L\u00e1szl\u00f3 \u00c1. K\u00f3czy","orcid":"https://orcid.org/0000-0002-8588-6140"},"institutions":[{"id":"https://openalex.org/I29770179","display_name":"Budapest University of Technology and Economics","ror":"https://ror.org/02w42ss30","country_code":"HU","type":"education","lineage":["https://openalex.org/I29770179"]},{"id":"https://openalex.org/I4210147073","display_name":"Institute of Economics","ror":"https://ror.org/05ng8e884","country_code":"HU","type":"facility","lineage":["https://openalex.org/I106118109","https://openalex.org/I4210147073","https://openalex.org/I4210155320"]},{"id":"https://openalex.org/I4210155320","display_name":"ELTE Centre for Economic and Regional Studies","ror":"https://ror.org/051ea1411","country_code":"HU","type":"facility","lineage":["https://openalex.org/I106118109","https://openalex.org/I4210155320"]}],"countries":["HU"],"is_corresponding":false,"raw_author_name":"L\u00e1szl\u00f3 \u00c1. K\u00f3czy","raw_affiliation_strings":["Department of Finance, Budapest University of Technology and Economics, Magyar tud\u00f3sok k\u00f6r\u00fatja 2, H-1112 Budapest, Hungary","Institute of Economics, Centre for Economic and Regional Studies, T\u00f3th K\u00e1lm\u00e1n u. 4, H-1097 Budapest, Hungary"],"affiliations":[{"raw_affiliation_string":"Department of Finance, Budapest University of Technology and Economics, Magyar tud\u00f3sok k\u00f6r\u00fatja 2, H-1112 Budapest, Hungary","institution_ids":["https://openalex.org/I29770179"]},{"raw_affiliation_string":"Institute of Economics, Centre for Economic and Regional Studies, T\u00f3th K\u00e1lm\u00e1n u. 4, H-1097 Budapest, Hungary","institution_ids":["https://openalex.org/I4210155320","https://openalex.org/I4210147073"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5020772626","display_name":"Izabella Stach","orcid":"https://orcid.org/0000-0002-9243-8653"},"institutions":[{"id":"https://openalex.org/I686019","display_name":"AGH University of Krakow","ror":"https://ror.org/00bas1c41","country_code":"PL","type":"education","lineage":["https://openalex.org/I686019"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Izabella Stach","raw_affiliation_strings":["AGH University of Science and Technology, al. Mickiewicza 30, 30-059 Krakw, Poland","AGH University of Science and Technology, al. Mickiewicza 30, 30-059 Krak\u00f3w, Poland"],"affiliations":[{"raw_affiliation_string":"AGH University of Science and Technology, al. Mickiewicza 30, 30-059 Krakw, Poland","institution_ids":["https://openalex.org/I686019"]},{"raw_affiliation_string":"AGH University of Science and Technology, al. Mickiewicza 30, 30-059 Krak\u00f3w, Poland","institution_ids":["https://openalex.org/I686019"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5042436730","display_name":"Jan Filipp","orcid":null},"institutions":[{"id":"https://openalex.org/I2802623092","display_name":"Kempten University of Applied Sciences","ror":"https://ror.org/02m4p8096","country_code":"DE","type":"education","lineage":["https://openalex.org/I2802623092"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Jan Filipp","raw_affiliation_strings":["Fakultt Informatik, Hochschule Kempten, Bahnhofstr. 61, 87435 Kempten, Germany","Fakult\u00e4t Informatik, Hochschule Kempten, Bahnhofstr. 61, 87435 Kempten, Germany"],"affiliations":[{"raw_affiliation_string":"Fakultt Informatik, Hochschule Kempten, Bahnhofstr. 61, 87435 Kempten, Germany","institution_ids":["https://openalex.org/I2802623092"]},{"raw_affiliation_string":"Fakult\u00e4t Informatik, Hochschule Kempten, Bahnhofstr. 61, 87435 Kempten, Germany","institution_ids":["https://openalex.org/I2802623092"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5028153839","display_name":"Marcus Kramer","orcid":null},"institutions":[{"id":"https://openalex.org/I2802623092","display_name":"Kempten University of Applied Sciences","ror":"https://ror.org/02m4p8096","country_code":"DE","type":"education","lineage":["https://openalex.org/I2802623092"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Marcus Kramer","raw_affiliation_strings":["Fakultt Informatik, Hochschule Kempten, Bahnhofstr. 61, 87435 Kempten, Germany","Fakult\u00e4t Informatik, Hochschule Kempten, Bahnhofstr. 61, 87435 Kempten, Germany"],"affiliations":[{"raw_affiliation_string":"Fakultt Informatik, Hochschule Kempten, Bahnhofstr. 61, 87435 Kempten, Germany","institution_ids":["https://openalex.org/I2802623092"]},{"raw_affiliation_string":"Fakult\u00e4t Informatik, Hochschule Kempten, Bahnhofstr. 61, 87435 Kempten, Germany","institution_ids":["https://openalex.org/I2802623092"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5064647279","display_name":"Till Noffke","orcid":null},"institutions":[{"id":"https://openalex.org/I2802623092","display_name":"Kempten University of Applied Sciences","ror":"https://ror.org/02m4p8096","country_code":"DE","type":"education","lineage":["https://openalex.org/I2802623092"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Till Noffke","raw_affiliation_strings":["Fakultt Informatik, Hochschule Kempten, Bahnhofstr. 61, 87435 Kempten, Germany","Fakult\u00e4t Informatik, Hochschule Kempten, Bahnhofstr. 61, 87435 Kempten, Germany"],"affiliations":[{"raw_affiliation_string":"Fakultt Informatik, Hochschule Kempten, Bahnhofstr. 61, 87435 Kempten, Germany","institution_ids":["https://openalex.org/I2802623092"]},{"raw_affiliation_string":"Fakult\u00e4t Informatik, Hochschule Kempten, Bahnhofstr. 61, 87435 Kempten, Germany","institution_ids":["https://openalex.org/I2802623092"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5015284431","display_name":"Linus Olsson","orcid":null},"institutions":[{"id":"https://openalex.org/I2802623092","display_name":"Kempten University of Applied Sciences","ror":"https://ror.org/02m4p8096","country_code":"DE","type":"education","lineage":["https://openalex.org/I2802623092"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Linus Olsson","raw_affiliation_strings":["Fakultt Informatik, Hochschule Kempten, Bahnhofstr. 61, 87435 Kempten, Germany","Fakult\u00e4t Informatik, Hochschule Kempten, Bahnhofstr. 61, 87435 Kempten, Germany"],"affiliations":[{"raw_affiliation_string":"Fakultt Informatik, Hochschule Kempten, Bahnhofstr. 61, 87435 Kempten, Germany","institution_ids":["https://openalex.org/I2802623092"]},{"raw_affiliation_string":"Fakult\u00e4t Informatik, Hochschule Kempten, Bahnhofstr. 61, 87435 Kempten, Germany","institution_ids":["https://openalex.org/I2802623092"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5026309758","display_name":"Jonas Pichler","orcid":null},"institutions":[{"id":"https://openalex.org/I2802623092","display_name":"Kempten University of Applied Sciences","ror":"https://ror.org/02m4p8096","country_code":"DE","type":"education","lineage":["https://openalex.org/I2802623092"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Jonas Pichler","raw_affiliation_strings":["Fakultt Informatik, Hochschule Kempten, Bahnhofstr. 61, 87435 Kempten, Germany","Fakult\u00e4t Informatik, Hochschule Kempten, Bahnhofstr. 61, 87435 Kempten, Germany"],"affiliations":[{"raw_affiliation_string":"Fakultt Informatik, Hochschule Kempten, Bahnhofstr. 61, 87435 Kempten, Germany","institution_ids":["https://openalex.org/I2802623092"]},{"raw_affiliation_string":"Fakult\u00e4t Informatik, Hochschule Kempten, Bahnhofstr. 61, 87435 Kempten, Germany","institution_ids":["https://openalex.org/I2802623092"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5023674106","display_name":"Tobias Singer","orcid":null},"institutions":[{"id":"https://openalex.org/I2802623092","display_name":"Kempten University of Applied Sciences","ror":"https://ror.org/02m4p8096","country_code":"DE","type":"education","lineage":["https://openalex.org/I2802623092"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Tobias Singer","raw_affiliation_strings":["Fakultt Informatik, Hochschule Kempten, Bahnhofstr. 61, 87435 Kempten, Germany","Fakult\u00e4t Informatik, Hochschule Kempten, Bahnhofstr. 61, 87435 Kempten, Germany"],"affiliations":[{"raw_affiliation_string":"Fakultt Informatik, Hochschule Kempten, Bahnhofstr. 61, 87435 Kempten, Germany","institution_ids":["https://openalex.org/I2802623092"]},{"raw_affiliation_string":"Fakult\u00e4t Informatik, Hochschule Kempten, Bahnhofstr. 61, 87435 Kempten, Germany","institution_ids":["https://openalex.org/I2802623092"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":9,"corresponding_author_ids":["https://openalex.org/A5020381550"],"corresponding_institution_ids":["https://openalex.org/I2802623092"],"apc_list":null,"apc_paid":null,"fwci":2.6631,"has_fulltext":true,"cited_by_count":10,"citation_normalized_percentile":{"value":0.92470927,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"31","issue":"2","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10991","display_name":"Game Theory and Voting Systems","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10991","display_name":"Game Theory and Voting Systems","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11182","display_name":"Auction Theory and Applications","score":0.9922999739646912,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9628999829292297,"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/computer-science","display_name":"Computer science","score":0.747185230255127},{"id":"https://openalex.org/keywords/voting","display_name":"Voting","score":0.7306308746337891},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5613219141960144},{"id":"https://openalex.org/keywords/index","display_name":"Index (typography)","score":0.5609003305435181},{"id":"https://openalex.org/keywords/weighted-voting","display_name":"Weighted voting","score":0.5454434156417847},{"id":"https://openalex.org/keywords/implementation","display_name":"Implementation","score":0.5348089933395386},{"id":"https://openalex.org/keywords/dynamic-programming","display_name":"Dynamic programming","score":0.533251941204071},{"id":"https://openalex.org/keywords/power","display_name":"Power (physics)","score":0.5254596471786499},{"id":"https://openalex.org/keywords/power-index","display_name":"Power index","score":0.5012650489807129},{"id":"https://openalex.org/keywords/software","display_name":"Software","score":0.4811350405216217},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.4504120349884033},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.44249558448791504},{"id":"https://openalex.org/keywords/software-implementation","display_name":"Software implementation","score":0.4245496988296509},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.41469791531562805},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3324359059333801},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2332741916179657},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.1499788463115692},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.14354398846626282},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.09176009893417358}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.747185230255127},{"id":"https://openalex.org/C520049643","wikidata":"https://www.wikidata.org/wiki/Q189760","display_name":"Voting","level":3,"score":0.7306308746337891},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5613219141960144},{"id":"https://openalex.org/C2777382242","wikidata":"https://www.wikidata.org/wiki/Q6017816","display_name":"Index (typography)","level":2,"score":0.5609003305435181},{"id":"https://openalex.org/C132778050","wikidata":"https://www.wikidata.org/wiki/Q2065430","display_name":"Weighted voting","level":4,"score":0.5454434156417847},{"id":"https://openalex.org/C26713055","wikidata":"https://www.wikidata.org/wiki/Q245962","display_name":"Implementation","level":2,"score":0.5348089933395386},{"id":"https://openalex.org/C37404715","wikidata":"https://www.wikidata.org/wiki/Q380679","display_name":"Dynamic programming","level":2,"score":0.533251941204071},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.5254596471786499},{"id":"https://openalex.org/C3018596841","wikidata":"https://www.wikidata.org/wiki/Q7236523","display_name":"Power index","level":2,"score":0.5012650489807129},{"id":"https://openalex.org/C2777904410","wikidata":"https://www.wikidata.org/wiki/Q7397","display_name":"Software","level":2,"score":0.4811350405216217},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.4504120349884033},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.44249558448791504},{"id":"https://openalex.org/C2983609787","wikidata":"https://www.wikidata.org/wiki/Q10534782","display_name":"Software implementation","level":3,"score":0.4245496988296509},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.41469791531562805},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3324359059333801},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2332741916179657},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.1499788463115692},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.14354398846626282},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.09176009893417358},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","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},{"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/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37190/ord210206","is_oa":true,"landing_page_url":"http://doi.org/10.37190/ord210206","pdf_url":"https://doi.org/10.37190/ord210206","source":{"id":"https://openalex.org/S2739399646","display_name":"Badania Operacyjne i Decyzje/Operations Research and Decisions","issn_l":"1230-1868","issn":["1230-1868","2081-8858","2391-6060"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317492","host_organization_name":"Wroc\u0142aw University of Science and Technology","host_organization_lineage":["https://openalex.org/P4310317492"],"host_organization_lineage_names":["Wroc\u0142aw University of Science and Technology"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Operations Research and Decisions","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.37190/ord210206","is_oa":true,"landing_page_url":"http://doi.org/10.37190/ord210206","pdf_url":"https://doi.org/10.37190/ord210206","source":{"id":"https://openalex.org/S2739399646","display_name":"Badania Operacyjne i Decyzje/Operations Research and Decisions","issn_l":"1230-1868","issn":["1230-1868","2081-8858","2391-6060"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317492","host_organization_name":"Wroc\u0142aw University of Science and Technology","host_organization_lineage":["https://openalex.org/P4310317492"],"host_organization_lineage_names":["Wroc\u0142aw University of Science and Technology"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Operations Research and Decisions","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G8016395303","display_name":null,"funder_award_id":"K-128573","funder_id":"https://openalex.org/F4320326762","funder_display_name":"Nemzeti Kutat\u00e1si Fejleszt\u00e9si \u00e9s Innov\u00e1ci\u00f3s Hivatal"}],"funders":[{"id":"https://openalex.org/F4320326762","display_name":"Nemzeti Kutat\u00e1si Fejleszt\u00e9si \u00e9s Innov\u00e1ci\u00f3s Hivatal","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3179877719.pdf","grobid_xml":"https://content.openalex.org/works/W3179877719.grobid-xml"},"referenced_works_count":34,"referenced_works":["https://openalex.org/W64854507","https://openalex.org/W70367913","https://openalex.org/W119581101","https://openalex.org/W309690565","https://openalex.org/W1505028449","https://openalex.org/W1532736630","https://openalex.org/W1976399866","https://openalex.org/W1976402990","https://openalex.org/W1977911709","https://openalex.org/W1985941874","https://openalex.org/W1999646672","https://openalex.org/W2002616065","https://openalex.org/W2015247315","https://openalex.org/W2016424092","https://openalex.org/W2038127015","https://openalex.org/W2045122596","https://openalex.org/W2061507419","https://openalex.org/W2070901016","https://openalex.org/W2076786454","https://openalex.org/W2081183270","https://openalex.org/W2084225608","https://openalex.org/W2144872768","https://openalex.org/W2246041435","https://openalex.org/W2274539560","https://openalex.org/W2296415298","https://openalex.org/W2492569205","https://openalex.org/W2536000384","https://openalex.org/W2562832900","https://openalex.org/W2595887776","https://openalex.org/W2908480179","https://openalex.org/W2982882216","https://openalex.org/W3121916341","https://openalex.org/W3125880702","https://openalex.org/W6630917469"],"related_works":["https://openalex.org/W2741776607","https://openalex.org/W62555423","https://openalex.org/W2028171644","https://openalex.org/W150283939","https://openalex.org/W3124070457","https://openalex.org/W2953316694","https://openalex.org/W2380651582","https://openalex.org/W1662636095","https://openalex.org/W623781850","https://openalex.org/W1872937274"],"abstract_inverted_index":{"We":[0,18,86],"study":[1],"the":[2,13,20,25,52,97],"efficient":[3,49],"computation":[4],"of":[5,15,67,95],"power":[6,40,60,98],"indices":[7,29,80,99],"for":[8,23,51,77,81],"weighted":[9,82],"voting":[10,83],"games":[11,84],"using":[12],"paradigm":[14],"dynamic":[16],"programming.":[17],"survey":[19],"state-of-the-art":[21],"algorithms":[22,50],"computing":[24,78,105],"Banzhaf":[26],"and":[27,30,56],"Shapley-Shubik":[28],"point":[31],"out":[32],"how":[33],"these":[34],"approaches":[35],"carry":[36],"over":[37],"to":[38],"related":[39],"indices.":[41],"Within":[42],"a":[43,57,73,88],"unified":[44],"framework,":[45],"we":[46],"present":[47],"new":[48],"Public":[53],"Good":[54],"index":[55,61],"recently":[58],"proposed":[59],"based":[62],"on":[63],"minimal":[64],"winning":[65],"coalitions":[66],"smallest":[68],"size,":[69],"as":[70,72,107,109],"well":[71,108],"very":[74],"first":[75],"method":[76],"Johnston":[79],"efficiently.":[85],"introduce":[87],"software":[89],"package":[90],"providing":[91],"fast":[92],"C++":[93],"implementations":[94],"all":[96],"mentioned":[100],"in":[101],"this":[102],"article,":[103],"discuss":[104],"times,":[106],"storage":[110],"requirements.":[111]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}