{"id":"https://openalex.org/W2004777406","doi":"https://doi.org/10.1142/s0218196711006674","title":"TROPICAL POLYHEDRA ARE EQUIVALENT TO MEAN PAYOFF GAMES","display_name":"TROPICAL POLYHEDRA ARE EQUIVALENT TO MEAN PAYOFF GAMES","publication_year":2011,"publication_date":"2011-06-29","ids":{"openalex":"https://openalex.org/W2004777406","doi":"https://doi.org/10.1142/s0218196711006674","mag":"2004777406"},"language":"en","primary_location":{"id":"doi:10.1142/s0218196711006674","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196711006674","pdf_url":null,"source":{"id":"https://openalex.org/S23260266","display_name":"International Journal of Algebra and Computation","issn_l":"0218-1967","issn":["0218-1967","1793-6500"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Algebra and Computation","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/0912.2462","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"MARIANNE AKIAN","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/I142476485","display_name":"\u00c9cole Polytechnique","ror":"https://ror.org/05hy3tk52","country_code":"FR","type":"education","lineage":["https://openalex.org/I142476485","https://openalex.org/I4210145102"]},{"id":"https://openalex.org/I4210126360","display_name":"Centre Inria de Saclay","ror":"https://ror.org/0315e5x55","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1326498283","https://openalex.org/I4210126360"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"MARIANNE AKIAN","raw_affiliation_strings":["CMAP, \u00c9cole Polytechnique, Route de Saclay, 91128 Palaiseau Cedex, France","INRIA Saclay\u2013\u00cele-de-France, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CMAP, \u00c9cole Polytechnique, Route de Saclay, 91128 Palaiseau Cedex, France","institution_ids":["https://openalex.org/I142476485"]},{"raw_affiliation_string":"INRIA Saclay\u2013\u00cele-de-France, France","institution_ids":["https://openalex.org/I4210126360","https://openalex.org/I1326498283"]}]},{"author_position":"middle","author":{"id":null,"display_name":"ST\u00c9PHANE GAUBERT","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/I142476485","display_name":"\u00c9cole Polytechnique","ror":"https://ror.org/05hy3tk52","country_code":"FR","type":"education","lineage":["https://openalex.org/I142476485","https://openalex.org/I4210145102"]},{"id":"https://openalex.org/I4210126360","display_name":"Centre Inria de Saclay","ror":"https://ror.org/0315e5x55","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1326498283","https://openalex.org/I4210126360"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"ST\u00c9PHANE GAUBERT","raw_affiliation_strings":["CMAP, \u00c9cole Polytechnique, Route de Saclay, 91128 Palaiseau Cedex, France","INRIA Saclay\u2013\u00cele-de-France, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CMAP, \u00c9cole Polytechnique, Route de Saclay, 91128 Palaiseau Cedex, France","institution_ids":["https://openalex.org/I142476485"]},{"raw_affiliation_string":"INRIA Saclay\u2013\u00cele-de-France, France","institution_ids":["https://openalex.org/I4210126360","https://openalex.org/I1326498283"]}]},{"author_position":"last","author":{"id":null,"display_name":"ALEXANDER GUTERMAN","orcid":null},"institutions":[{"id":"https://openalex.org/I19880235","display_name":"Lomonosov Moscow State University","ror":"https://ror.org/010pmpe69","country_code":"RU","type":"education","lineage":["https://openalex.org/I19880235"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"ALEXANDER GUTERMAN","raw_affiliation_strings":["Moscow State University, Leninskie Gory, 119991, GSP-1, Moscow, Russia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Moscow State University, Leninskie Gory, 119991, GSP-1, Moscow, Russia","institution_ids":["https://openalex.org/I19880235"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I1326498283","https://openalex.org/I142476485","https://openalex.org/I4210126360"],"apc_list":null,"apc_paid":null,"fwci":6.1955,"has_fulltext":false,"cited_by_count":93,"citation_normalized_percentile":{"value":0.96832314,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"22","issue":"01","first_page":"1250001","last_page":"1250001"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.8763999938964844,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.8763999938964844,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.021800000220537186,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.014700000174343586,"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/corollary","display_name":"Corollary","score":0.6996999979019165},{"id":"https://openalex.org/keywords/polyhedron","display_name":"Polyhedron","score":0.6676999926567078},{"id":"https://openalex.org/keywords/convexity","display_name":"Convexity","score":0.6177999973297119},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.5667999982833862},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.5005000233650208},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.4966000020503998},{"id":"https://openalex.org/keywords/stochastic-game","display_name":"Stochastic game","score":0.44350001215934753},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.39239999651908875}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9047999978065491},{"id":"https://openalex.org/C2780012671","wikidata":"https://www.wikidata.org/wiki/Q1343870","display_name":"Corollary","level":2,"score":0.6996999979019165},{"id":"https://openalex.org/C54829058","wikidata":"https://www.wikidata.org/wiki/Q172937","display_name":"Polyhedron","level":2,"score":0.6676999926567078},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.6177999973297119},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5846999883651733},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.5667999982833862},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.5005000233650208},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.4966000020503998},{"id":"https://openalex.org/C22171661","wikidata":"https://www.wikidata.org/wiki/Q1074380","display_name":"Stochastic game","level":2,"score":0.44350001215934753},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.41359999775886536},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.39239999651908875},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.35910001397132874},{"id":"https://openalex.org/C2776230367","wikidata":"https://www.wikidata.org/wiki/Q7314222","display_name":"Representation theorem","level":2,"score":0.35339999198913574},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.3465999960899353},{"id":"https://openalex.org/C104140500","wikidata":"https://www.wikidata.org/wiki/Q2088159","display_name":"Row and column spaces","level":3,"score":0.33239999413490295},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.32919999957084656},{"id":"https://openalex.org/C135598885","wikidata":"https://www.wikidata.org/wiki/Q1366302","display_name":"Row","level":2,"score":0.3215999901294708},{"id":"https://openalex.org/C110943637","wikidata":"https://www.wikidata.org/wiki/Q4129097","display_name":"Convex polytope","level":5,"score":0.29269999265670776},{"id":"https://openalex.org/C156103551","wikidata":"https://www.wikidata.org/wiki/Q130998","display_name":"Equivalence relation","level":2,"score":0.28790000081062317},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.2840000092983246},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.27880001068115234},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.27160000801086426},{"id":"https://openalex.org/C115988155","wikidata":"https://www.wikidata.org/wiki/Q3262192","display_name":"Decision problem","level":2,"score":0.2678000032901764}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1142/s0218196711006674","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196711006674","pdf_url":null,"source":{"id":"https://openalex.org/S23260266","display_name":"International Journal of Algebra and Computation","issn_l":"0218-1967","issn":["0218-1967","1793-6500"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Algebra and Computation","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:0912.2462","is_oa":true,"landing_page_url":"http://arxiv.org/abs/0912.2462","pdf_url":"https://arxiv.org/pdf/0912.2462","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:HAL:hal-00778078v1","is_oa":false,"landing_page_url":"https://inria.hal.science/hal-00778078","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":"International Journal of Algebra and Computation, 2012, 22 (1), pp.1250001, 43. &#x27E8;10.1142/S0218196711006674&#x27E9;","raw_type":"Journal articles"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:0912.2462","is_oa":true,"landing_page_url":"http://arxiv.org/abs/0912.2462","pdf_url":"https://arxiv.org/pdf/0912.2462","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":44,"referenced_works":["https://openalex.org/W1608548244","https://openalex.org/W1609080720","https://openalex.org/W1889804802","https://openalex.org/W1965663154","https://openalex.org/W1966347268","https://openalex.org/W1971499713","https://openalex.org/W1979388351","https://openalex.org/W1990398263","https://openalex.org/W1991840188","https://openalex.org/W1992852632","https://openalex.org/W1999526684","https://openalex.org/W2008582047","https://openalex.org/W2008632553","https://openalex.org/W2010548783","https://openalex.org/W2020145866","https://openalex.org/W2026128612","https://openalex.org/W2028660300","https://openalex.org/W2031196367","https://openalex.org/W2043228814","https://openalex.org/W2063809466","https://openalex.org/W2067705833","https://openalex.org/W2068571303","https://openalex.org/W2069445541","https://openalex.org/W2076358787","https://openalex.org/W2077767509","https://openalex.org/W2078268196","https://openalex.org/W2081641166","https://openalex.org/W2082820693","https://openalex.org/W2087150194","https://openalex.org/W2095082073","https://openalex.org/W2096935426","https://openalex.org/W2100439831","https://openalex.org/W2107551402","https://openalex.org/W2114657710","https://openalex.org/W2127670671","https://openalex.org/W2144755471","https://openalex.org/W2154089215","https://openalex.org/W2154682386","https://openalex.org/W2157261308","https://openalex.org/W2158437920","https://openalex.org/W2170793209","https://openalex.org/W4230398107","https://openalex.org/W4232283720","https://openalex.org/W4256361994"],"related_works":[],"abstract_inverted_index":{"We":[0,67],"show":[1,53],"that":[2,54,79],"several":[3],"decision":[4],"problems":[5],"originating":[6],"from":[7,62,129],"max-plus":[8],"or":[9],"tropical":[10,32,41,65,81,122],"convexity":[11],"are":[12,117],"equivalent":[13],"to":[14,44],"zero-sum":[15,36],"two":[16],"player":[17],"game":[18,73],"problems.":[19],"In":[20],"particular,":[21],"we":[22,52],"set":[23],"up":[24],"an":[25],"equivalence":[26],"between":[27],"the":[28,55,63,77,80,88,96,106,114,121],"external":[29],"representation":[30],"of":[31,76,83,91,109,113],"convex":[33],"sets":[34],"and":[35],"stochastic":[37],"games,":[38],"in":[39,120],"which":[40,95,116],"polyhedra":[42],"correspond":[43],"deterministic":[45],"games":[46],"with":[47,105],"finite":[48],"action":[49],"spaces.":[50],"Then,":[51],"winning":[56],"initial":[57],"positions":[58],"can":[59],"be":[60],"determined":[61],"associated":[64],"polyhedron.":[66],"obtain":[68],"as":[69,87],"a":[70,72,84,92,101],"corollary":[71],"theoretical":[74],"proof":[75],"fact":[78],"rank":[82],"matrix,":[85],"defined":[86],"maximal":[89,107],"size":[90],"submatrix":[93],"for":[94],"optimal":[97],"assignment":[98],"problem":[99],"has":[100],"unique":[102],"solution,":[103],"coincides":[104],"number":[108],"rows":[110],"(or":[111],"columns)":[112],"matrix":[115],"linearly":[118],"independent":[119],"sense.":[123],"Our":[124],"proofs":[125],"rely":[126],"on":[127],"techniques":[128],"non-linear":[130],"Perron\u2013Frobenius":[131],"theory.":[132]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":7},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":9},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":9},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":8},{"year":2015,"cited_by_count":9},{"year":2014,"cited_by_count":10},{"year":2013,"cited_by_count":7},{"year":2012,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2016-06-24T00:00:00"}
