{"id":"https://openalex.org/W2488992236","doi":"https://doi.org/10.1080/10556788.2016.1208748","title":"The simplex method using Tardos' basic algorithm is strongly polynomial for totally unimodular LP under nondegeneracy assumption","display_name":"The simplex method using Tardos' basic algorithm is strongly polynomial for totally unimodular LP under nondegeneracy assumption","publication_year":2016,"publication_date":"2016-07-19","ids":{"openalex":"https://openalex.org/W2488992236","doi":"https://doi.org/10.1080/10556788.2016.1208748","mag":"2488992236"},"language":"en","primary_location":{"id":"doi:10.1080/10556788.2016.1208748","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10556788.2016.1208748","pdf_url":null,"source":{"id":"https://openalex.org/S103047102","display_name":"Optimization methods & software","issn_l":"1026-7670","issn":["1026-7670","1029-4937","1055-6788"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Optimization Methods and Software","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/A5084749482","display_name":"Shinji Mizuno","orcid":"https://orcid.org/0000-0001-6472-8891"},"institutions":[{"id":"https://openalex.org/I114531698","display_name":"Tokyo Institute of Technology","ror":"https://ror.org/0112mx960","country_code":"JP","type":"education","lineage":["https://openalex.org/I114531698"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"S. Mizuno","raw_affiliation_strings":["Tokyo Institute of Technology, 2-12-1-W9-58, Oo-Okayama, Meguro-ku, Tokyo 152-8552, Japan"],"affiliations":[{"raw_affiliation_string":"Tokyo Institute of Technology, 2-12-1-W9-58, Oo-Okayama, Meguro-ku, Tokyo 152-8552, Japan","institution_ids":["https://openalex.org/I114531698"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5084749482"],"corresponding_institution_ids":["https://openalex.org/I114531698"],"apc_list":null,"apc_paid":null,"fwci":0.29952177,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.71165043,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"31","issue":"6","first_page":"1298","last_page":"1304"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9970999956130981,"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":0.9970999956130981,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9940999746322632,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.993399977684021,"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/unimodular-matrix","display_name":"Unimodular matrix","score":0.9692872762680054},{"id":"https://openalex.org/keywords/simplex-algorithm","display_name":"Simplex algorithm","score":0.7294746041297913},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6801730394363403},{"id":"https://openalex.org/keywords/simplex","display_name":"Simplex","score":0.6620387434959412},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5116972923278809},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.49836111068725586},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4873436391353607},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4375610947608948},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.436884343624115},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.3494221568107605},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.13390234112739563},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.05917465686798096}],"concepts":[{"id":"https://openalex.org/C201958917","wikidata":"https://www.wikidata.org/wiki/Q1367055","display_name":"Unimodular matrix","level":2,"score":0.9692872762680054},{"id":"https://openalex.org/C144521790","wikidata":"https://www.wikidata.org/wiki/Q134164","display_name":"Simplex algorithm","level":3,"score":0.7294746041297913},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6801730394363403},{"id":"https://openalex.org/C62438384","wikidata":"https://www.wikidata.org/wiki/Q331350","display_name":"Simplex","level":2,"score":0.6620387434959412},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5116972923278809},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.49836111068725586},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4873436391353607},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4375610947608948},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.436884343624115},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.3494221568107605},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.13390234112739563},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.05917465686798096},{"id":"https://openalex.org/C43617362","wikidata":"https://www.wikidata.org/wiki/Q170050","display_name":"Chromatography","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/10556788.2016.1208748","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10556788.2016.1208748","pdf_url":null,"source":{"id":"https://openalex.org/S103047102","display_name":"Optimization methods & software","issn_l":"1026-7670","issn":["1026-7670","1029-4937","1055-6788"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Optimization Methods and Software","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G697129806","display_name":null,"funder_award_id":"Grant-in-Aid for Science Research (A) 26242027","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"}],"funders":[{"id":"https://openalex.org/F4320334764","display_name":"Japan Society for the Promotion of Science","ror":"https://ror.org/00hhkn466"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W1964500497","https://openalex.org/W1984901446","https://openalex.org/W2003327511","https://openalex.org/W2011545080","https://openalex.org/W2033040247","https://openalex.org/W2082824470","https://openalex.org/W2103985627","https://openalex.org/W2133159317","https://openalex.org/W2328172603","https://openalex.org/W2611147814"],"related_works":["https://openalex.org/W2133667137","https://openalex.org/W2575520949","https://openalex.org/W2384679317","https://openalex.org/W2477407501","https://openalex.org/W1570109187","https://openalex.org/W2366013513","https://openalex.org/W3125083766","https://openalex.org/W4244786412","https://openalex.org/W2028887049","https://openalex.org/W3143155029"],"abstract_inverted_index":{"In":[0,85],"this":[1],"paper,":[2],"we":[3,91],"show":[4],"that":[5],"the":[6,15,26,30,35,64,72,78,86,89,93],"total":[7],"number":[8,27,31],"of":[9,28,32,40,42,88],"distinct":[10],"basic":[11,20,47],"solutions":[12],"generated":[13],"by":[14,96],"simplex":[16,80],"method":[17,81],"using":[18],"Tardos'":[19,46],"algorithm":[21,48],"is":[22,67,82],"polynomially":[23],"bounded":[24],"in":[25],"constraints,":[29],"variables,":[33],"and":[34,59,70,98],"maximum":[36],"absolute":[37],"value":[38],"determinant":[39],"submatrices":[41],"a":[43],"coefficient":[44,65],"matrix.":[45],"generates":[49],"auxiliary":[50,73],"LP":[51],"problems":[52,74],"whose":[53],"right-hand":[54],"side":[55],"vectors":[56],"are":[57,75],"scaled":[58],"rounded":[60],"to":[61],"integers.":[62],"If":[63],"matrix":[66],"totally":[68],"unimodular":[69],"all":[71],"nondegenerate,":[76],"then":[77],"proposed":[79],"strongly":[83],"polynomial.":[84],"analysis":[87],"algorithm,":[90],"use":[92],"recent":[94],"results":[95],"Kitahara":[97],"Mizuno.":[99]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2018,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
