{"id":"https://openalex.org/W4378977931","doi":"https://doi.org/10.1137/22m1482044","title":"Discrete Optimal Transport with Independent Marginals is #P-Hard","display_name":"Discrete Optimal Transport with Independent Marginals is #P-Hard","publication_year":2023,"publication_date":"2023-06-01","ids":{"openalex":"https://openalex.org/W4378977931","doi":"https://doi.org/10.1137/22m1482044"},"language":"en","primary_location":{"id":"doi:10.1137/22m1482044","is_oa":false,"landing_page_url":"https://doi.org/10.1137/22m1482044","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"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 Optimization","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://infoscience.epfl.ch/handle/20.500.14299/185983","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5003265461","display_name":"Bahar Ta\u015fkesen","orcid":"https://orcid.org/0000-0002-7767-5108"},"institutions":[{"id":"https://openalex.org/I5124864","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I5124864"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Bahar Ta\u015fkesen","raw_affiliation_strings":["Risk Analytics and Optimization Chair, EPFL Lausanne, 1015 Lausanne, Switzerland"],"raw_orcid":"https://orcid.org/0000-0002-7767-5108","affiliations":[{"raw_affiliation_string":"Risk Analytics and Optimization Chair, EPFL Lausanne, 1015 Lausanne, Switzerland","institution_ids":["https://openalex.org/I5124864"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5030361767","display_name":"Soroosh Shafieezadeh-Abadeh","orcid":"https://orcid.org/0000-0001-9095-2686"},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Soroosh Shafieezadeh-Abadeh","raw_affiliation_strings":["Tepper School of Business, Carnegie Mellon University, Pittsburgh, PA 15213 USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Tepper School of Business, Carnegie Mellon University, Pittsburgh, PA 15213 USA","institution_ids":["https://openalex.org/I74973139"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065780980","display_name":"Daniel K\u00fchn","orcid":"https://orcid.org/0000-0003-2697-8886"},"institutions":[{"id":"https://openalex.org/I5124864","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I5124864"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Daniel Kuhn","raw_affiliation_strings":["Risk Analytics and Optimization Chair, EPFL Lausanne, 1015 Lausanne, Switzerland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Risk Analytics and Optimization Chair, EPFL Lausanne, 1015 Lausanne, Switzerland","institution_ids":["https://openalex.org/I5124864"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5019311010","display_name":"Karthik Natarajan","orcid":"https://orcid.org/0000-0002-3868-7587"},"institutions":[{"id":"https://openalex.org/I152815399","display_name":"Singapore University of Technology and Design","ror":"https://ror.org/05j6fvn87","country_code":"SG","type":"education","lineage":["https://openalex.org/I152815399"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"Karthik Natarajan","raw_affiliation_strings":["Engineering Systems and Design, Singapore University of Technology and Design, Singapore"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Engineering Systems and Design, Singapore University of Technology and Design, Singapore","institution_ids":["https://openalex.org/I152815399"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.3901,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.62528388,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"33","issue":"2","first_page":"589","last_page":"614"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11413","display_name":"Risk and Portfolio Optimization","score":0.9833999872207642,"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"}},"topics":[{"id":"https://openalex.org/T11413","display_name":"Risk and Portfolio Optimization","score":0.9833999872207642,"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9782000184059143,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T11830","display_name":"Point processes and geometric inequalities","score":0.9667999744415283,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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":0.8176348209381104},{"id":"https://openalex.org/keywords/multivariate-random-variable","display_name":"Multivariate random variable","score":0.726132869720459},{"id":"https://openalex.org/keywords/bernoullis-principle","display_name":"Bernoulli's principle","score":0.6720908880233765},{"id":"https://openalex.org/keywords/random-variable","display_name":"Random variable","score":0.5697401762008667},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4962967038154602},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.48661503195762634},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.44570034742355347},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4293774962425232},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.4289870858192444},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.34870991110801697},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3337171673774719},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.15370133519172668}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8176348209381104},{"id":"https://openalex.org/C138405894","wikidata":"https://www.wikidata.org/wiki/Q3179949","display_name":"Multivariate random variable","level":3,"score":0.726132869720459},{"id":"https://openalex.org/C152361515","wikidata":"https://www.wikidata.org/wiki/Q181328","display_name":"Bernoulli's principle","level":2,"score":0.6720908880233765},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.5697401762008667},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4962967038154602},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.48661503195762634},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.44570034742355347},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4293774962425232},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.4289870858192444},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.34870991110801697},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3337171673774719},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.15370133519172668},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/22m1482044","is_oa":false,"landing_page_url":"https://doi.org/10.1137/22m1482044","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"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 Optimization","raw_type":"journal-article"},{"id":"pmh:oai:infoscience.epfl.ch:292507","is_oa":true,"landing_page_url":"https://infoscience.epfl.ch/handle/20.500.14299/185983","pdf_url":null,"source":{"id":"https://openalex.org/S4306400487","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"research article"}],"best_oa_location":{"id":"pmh:oai:infoscience.epfl.ch:292507","is_oa":true,"landing_page_url":"https://infoscience.epfl.ch/handle/20.500.14299/185983","pdf_url":null,"source":{"id":"https://openalex.org/S4306400487","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"research article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1261493697","display_name":null,"funder_award_id":"T2MOE1906","funder_id":"https://openalex.org/F4320320751","funder_display_name":"Ministry of Education - Singapore"},{"id":"https://openalex.org/G1294180184","display_name":"NCCR Automation: Dependable Ubiquitous Automation","funder_award_id":"51 NF40_1 80545","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"},{"id":"https://openalex.org/G6713008056","display_name":"Dynamic Data-Driven Optimization: Scalability and Performance Guarantees","funder_award_id":"195149","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"}],"funders":[{"id":"https://openalex.org/F4320320751","display_name":"Ministry of Education - Singapore","ror":"https://ror.org/01kcva023"},{"id":"https://openalex.org/F4320320924","display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung","ror":"https://ror.org/00yjd3n13"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":51,"referenced_works":["https://openalex.org/W385466589","https://openalex.org/W1594039573","https://openalex.org/W1632601927","https://openalex.org/W1762430620","https://openalex.org/W1985506636","https://openalex.org/W1985985425","https://openalex.org/W1989921461","https://openalex.org/W2005107874","https://openalex.org/W2006912660","https://openalex.org/W2009172320","https://openalex.org/W2011039300","https://openalex.org/W2036996178","https://openalex.org/W2057869046","https://openalex.org/W2069737635","https://openalex.org/W2115826669","https://openalex.org/W2116509768","https://openalex.org/W2117371776","https://openalex.org/W2123961099","https://openalex.org/W2132883347","https://openalex.org/W2135756775","https://openalex.org/W2143668817","https://openalex.org/W2161086299","https://openalex.org/W2164260102","https://openalex.org/W2222512263","https://openalex.org/W2312355711","https://openalex.org/W2528351259","https://openalex.org/W2543484873","https://openalex.org/W2559655401","https://openalex.org/W2604272474","https://openalex.org/W2612690371","https://openalex.org/W2735418187","https://openalex.org/W2962792820","https://openalex.org/W2963450292","https://openalex.org/W3016365586","https://openalex.org/W3042316919","https://openalex.org/W3094491077","https://openalex.org/W3111414186","https://openalex.org/W3124187518","https://openalex.org/W3124407081","https://openalex.org/W3139172074","https://openalex.org/W3141207716","https://openalex.org/W4206471589","https://openalex.org/W4211206129","https://openalex.org/W4212774754","https://openalex.org/W4212998659","https://openalex.org/W4245577611","https://openalex.org/W4246219036","https://openalex.org/W4252698487","https://openalex.org/W4299648429","https://openalex.org/W4300645277","https://openalex.org/W4308018161"],"related_works":["https://openalex.org/W170825502","https://openalex.org/W2052718200","https://openalex.org/W1498343739","https://openalex.org/W2538141928","https://openalex.org/W3195391652","https://openalex.org/W3022473826","https://openalex.org/W4238695833","https://openalex.org/W2365690901","https://openalex.org/W4236621564","https://openalex.org/W4231762030"],"abstract_inverted_index":{"We":[0,78,120],"study":[1],"the":[2,6,12,17,37,40,45,50,68,71,81,93,104,129,136,139],"computational":[3],"complexity":[4],"of":[5,19,39,42,44,52,70,92,138],"optimal":[7,83],"transport":[8,84],"problem":[9,31,72,85,152],"that":[10,80,127,154],"evaluates":[11],"Wasser-":[13],"stein":[14],"distance":[15,131],"between":[16],"distributions":[18],"two":[20,46,110],"K-dimensional":[21],"discrete":[22,146],"random":[23,54,95,101,106,141],"vectors.":[24],"The":[25],"best":[26],"known":[27],"algorithms":[28],"for":[29],"this":[30,59],"run":[32],"in":[33,36,64,132,159],"polynomial":[34,161],"time":[35,134],"maximum":[38],"number":[41,60],"atoms":[43],"distributions.":[47],"However,":[48],"if":[49,89,114],"components":[51,91,137],"either":[53],"vector":[55,96,107,142],"are":[56,97,118],"independent,":[57],"then":[58],"can":[61,155],"be":[62,156],"exponential":[63],"K":[65],"even":[66,88,113],"though":[67],"size":[69],"description":[73],"scales":[74],"linearly":[75],"with":[76],"K.":[77],"prove":[79],"described":[82],"is":[86],"#P-hard":[87],"all":[90],"first":[94,140],"independent":[98,145],"uniform":[99],"Bernoulli":[100],"variables,":[102],"while":[103],"second":[105],"has":[108],"merely":[109],"atoms,":[111],"and":[112,148],"only":[115],"approximate":[116],"solutions":[117],"sought.":[119],"also":[121],"develop":[122],"a":[123],"dynamic":[124],"programming-type":[125],"algorithm":[126],"approximates":[128],"Wasserstein":[130],"pseudo-polynomial":[133],"when":[135],"follow":[143],"arbitrary":[144],"distributions,":[147],"we":[149],"identify":[150],"special":[151],"instances":[153],"solved":[157],"exactly":[158],"strongly":[160],"time.":[162]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1}],"updated_date":"2026-08-06T08:24:18.245995","created_date":"2025-10-10T00:00:00"}