{"id":"https://openalex.org/W3188012373","doi":"https://doi.org/10.1137/20m138836x","title":"Computing the nc-Rank via Discrete Convex Optimization on CAT(0) Spaces","display_name":"Computing the nc-Rank via Discrete Convex Optimization on CAT(0) Spaces","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3188012373","doi":"https://doi.org/10.1137/20m138836x","mag":"3188012373"},"language":"en","primary_location":{"id":"doi:10.1137/20m138836x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m138836x","pdf_url":null,"source":{"id":"https://openalex.org/S2996807011","display_name":"SIAM Journal on Applied Algebra and Geometry","issn_l":"2470-6566","issn":["2470-6566"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Algebra and Geometry","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/A5012127006","display_name":"Masaki Hamada","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Masaki Hamada","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5090989020","display_name":"Hiroshi Hirai","orcid":"https://orcid.org/0000-0002-4784-5110"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hiroshi Hirai","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5012127006"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.1074,"has_fulltext":false,"cited_by_count":27,"citation_normalized_percentile":{"value":0.92567061,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"5","issue":"3","first_page":"455","last_page":"478"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9987999796867371,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9987999796867371,"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":0.9987000226974487,"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/T10287","display_name":"Algebraic structures and combinatorial models","score":0.9980999827384949,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7458302974700928},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.7050327062606812},{"id":"https://openalex.org/keywords/noncommutative-geometry","display_name":"Noncommutative geometry","score":0.6255102753639221},{"id":"https://openalex.org/keywords/submodular-set-function","display_name":"Submodular set function","score":0.5221545696258545},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.479618638753891},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.4345465898513794},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.4280428886413574},{"id":"https://openalex.org/keywords/gaussian-elimination","display_name":"Gaussian elimination","score":0.4166531562805176},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.37964048981666565},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3788573741912842},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3381693363189697},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3089945912361145},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.17273956537246704}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7458302974700928},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.7050327062606812},{"id":"https://openalex.org/C68797384","wikidata":"https://www.wikidata.org/wiki/Q2746792","display_name":"Noncommutative geometry","level":2,"score":0.6255102753639221},{"id":"https://openalex.org/C178621042","wikidata":"https://www.wikidata.org/wiki/Q7631710","display_name":"Submodular set function","level":2,"score":0.5221545696258545},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.479618638753891},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.4345465898513794},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.4280428886413574},{"id":"https://openalex.org/C126312332","wikidata":"https://www.wikidata.org/wiki/Q2658","display_name":"Gaussian elimination","level":3,"score":0.4166531562805176},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.37964048981666565},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3788573741912842},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3381693363189697},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3089945912361145},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.17273956537246704},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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:10.1137/20m138836x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m138836x","pdf_url":null,"source":{"id":"https://openalex.org/S2996807011","display_name":"SIAM Journal on Applied Algebra and Geometry","issn_l":"2470-6566","issn":["2470-6566"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Algebra and Geometry","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2765942736","display_name":null,"funder_award_id":"JPMJPR192A","funder_id":"https://openalex.org/F4320338111","funder_display_name":"Precursory Research for Embryonic Science and Technology"},{"id":"https://openalex.org/G3104865560","display_name":null,"funder_award_id":"17K00029","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G3238366090","display_name":null,"funder_award_id":"25280004","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G3812730929","display_name":null,"funder_award_id":"26280004","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G5125385199","display_name":null,"funder_award_id":"26330023","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"},{"id":"https://openalex.org/F4320338111","display_name":"Precursory Research for Embryonic Science and Technology","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W1966991151","https://openalex.org/W1973005928","https://openalex.org/W1990283121","https://openalex.org/W1996970275","https://openalex.org/W2019557076","https://openalex.org/W2026036943","https://openalex.org/W2046344295","https://openalex.org/W2050735826","https://openalex.org/W2060262514","https://openalex.org/W2062185175","https://openalex.org/W2076187197","https://openalex.org/W2121388476","https://openalex.org/W2139834426","https://openalex.org/W2142920747","https://openalex.org/W2396964413","https://openalex.org/W2962745033","https://openalex.org/W2962787199","https://openalex.org/W2962789909","https://openalex.org/W2962817959","https://openalex.org/W2963059622","https://openalex.org/W2964029293","https://openalex.org/W2964051254","https://openalex.org/W2964075524","https://openalex.org/W2975794839","https://openalex.org/W2990372584","https://openalex.org/W3102768503","https://openalex.org/W3103545055","https://openalex.org/W4210681352"],"related_works":["https://openalex.org/W3111851529","https://openalex.org/W1657799247","https://openalex.org/W1661873676","https://openalex.org/W2949772116","https://openalex.org/W1595919516","https://openalex.org/W2034563384","https://openalex.org/W4297663571","https://openalex.org/W3121296545","https://openalex.org/W2080153006","https://openalex.org/W4287599015"],"abstract_inverted_index":{"We":[0,46],"study":[1],"the":[2,34],"noncommutative":[3,17],"rank":[4],"(nc-rank)":[5],"computation":[6],"of":[7,66],"a":[8,48,64],"symbolic":[9],"matrix":[10],"whose":[11],"entries":[12],"are":[13],"linear":[14],"forms":[15],"in":[16],"variables.":[18],"For":[19],"this":[20],"problem,":[21],"polynomial":[22,51],"time":[23,52],"algorithms":[24],"were":[25],"given":[26],"by":[27,38],"Garg,":[28],"Gurvits,":[29],"Oliveira,":[30],"and":[31,37,41,72],"Wigderson":[32],"over":[33,43],"rational":[35],"numbers,":[36],"Ivanyos,":[39],"Qiao,":[40],"Subrahmanyam":[42],"arbitrary":[44],"fields.":[45],"present":[47],"significantly":[49],"different":[50],"algorithm":[53,60],"that":[54],"works":[55],"for":[56],"any":[57],"field.":[58],"Our":[59],"is":[61],"based":[62],"on":[63,69,75],"combination":[65],"submodular":[67],"optimization":[68,74],"modular":[70],"lattices":[71],"convex":[73],"CAT(0)":[76],"spaces.":[77]},"counts_by_year":[{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":8},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
