{"id":"https://openalex.org/W3034220602","doi":"https://doi.org/10.1145/3357713.3384309","title":"Solving tall dense linear programs in nearly linear time","display_name":"Solving tall dense linear programs in nearly linear time","publication_year":2020,"publication_date":"2020-06-07","ids":{"openalex":"https://openalex.org/W3034220602","doi":"https://doi.org/10.1145/3357713.3384309","mag":"3034220602"},"language":"en","primary_location":{"id":"doi:10.1145/3357713.3384309","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3357713.3384309","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 52nd Annual ACM SIGACT Symposium on Theory of Computing","raw_type":"proceedings-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/A5054956160","display_name":"Jan van den Brand","orcid":"https://orcid.org/0000-0001-8611-6896"},"institutions":[{"id":"https://openalex.org/I86987016","display_name":"KTH Royal Institute of Technology","ror":"https://ror.org/026vcq606","country_code":"SE","type":"education","lineage":["https://openalex.org/I86987016"]}],"countries":["SE"],"is_corresponding":true,"raw_author_name":"Jan van den Brand","raw_affiliation_strings":["KTH, Sweden"],"affiliations":[{"raw_affiliation_string":"KTH, Sweden","institution_ids":["https://openalex.org/I86987016"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5024980585","display_name":"Yin Tat Lee","orcid":null},"institutions":[{"id":"https://openalex.org/I1290206253","display_name":"Microsoft (United States)","ror":"https://ror.org/00d0nc645","country_code":"US","type":"company","lineage":["https://openalex.org/I1290206253"]},{"id":"https://openalex.org/I201448701","display_name":"University of Washington","ror":"https://ror.org/00cvxb145","country_code":"US","type":"education","lineage":["https://openalex.org/I201448701"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Yin Tat Lee","raw_affiliation_strings":["University of Washington, USA / Microsoft Research, USA"],"affiliations":[{"raw_affiliation_string":"University of Washington, USA / Microsoft Research, USA","institution_ids":["https://openalex.org/I1290206253","https://openalex.org/I201448701"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5086787265","display_name":"Aaron Sidford","orcid":"https://orcid.org/0000-0003-2675-7610"},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Aaron Sidford","raw_affiliation_strings":["Stanford University, USA"],"affiliations":[{"raw_affiliation_string":"Stanford University, USA","institution_ids":["https://openalex.org/I97018004"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5103280080","display_name":"Zhao Song","orcid":"https://orcid.org/0000-0003-4589-5234"},"institutions":[{"id":"https://openalex.org/I20089843","display_name":"Princeton University","ror":"https://ror.org/00hx57361","country_code":"US","type":"education","lineage":["https://openalex.org/I20089843"]},{"id":"https://openalex.org/I40036882","display_name":"Institute for Advanced Study","ror":"https://ror.org/00f809463","country_code":"US","type":"facility","lineage":["https://openalex.org/I40036882"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Zhao Song","raw_affiliation_strings":["Institute for Advanced Study at Princeton, USA / Princeton University, USA"],"affiliations":[{"raw_affiliation_string":"Institute for Advanced Study at Princeton, USA / Princeton University, USA","institution_ids":["https://openalex.org/I40036882","https://openalex.org/I20089843"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5054956160"],"corresponding_institution_ids":["https://openalex.org/I86987016"],"apc_list":null,"apc_paid":null,"fwci":8.6034,"has_fulltext":false,"cited_by_count":58,"citation_normalized_percentile":{"value":0.9899281,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"775","last_page":"788"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9998000264167786,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/matrix-multiplication","display_name":"Matrix multiplication","score":0.6288228034973145},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.5885741710662842},{"id":"https://openalex.org/keywords/interior-point-method","display_name":"Interior point method","score":0.5833901762962341},{"id":"https://openalex.org/keywords/multiplication","display_name":"Multiplication (music)","score":0.5478309988975525},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.542437732219696},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.5366963744163513},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5171663165092468},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5088322758674622},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.5032727122306824},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.46371057629585266},{"id":"https://openalex.org/keywords/dual","display_name":"Dual (grammatical number)","score":0.44800737500190735},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.4220130443572998},{"id":"https://openalex.org/keywords/running-time","display_name":"Running time","score":0.42039021849632263},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3682308793067932},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.34556475281715393},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.1745888590812683}],"concepts":[{"id":"https://openalex.org/C17349429","wikidata":"https://www.wikidata.org/wiki/Q1049914","display_name":"Matrix multiplication","level":3,"score":0.6288228034973145},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.5885741710662842},{"id":"https://openalex.org/C155253501","wikidata":"https://www.wikidata.org/wiki/Q461992","display_name":"Interior point method","level":2,"score":0.5833901762962341},{"id":"https://openalex.org/C2780595030","wikidata":"https://www.wikidata.org/wiki/Q3860309","display_name":"Multiplication (music)","level":2,"score":0.5478309988975525},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.542437732219696},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.5366963744163513},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5171663165092468},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5088322758674622},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.5032727122306824},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.46371057629585266},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.44800737500190735},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.4220130443572998},{"id":"https://openalex.org/C3017489831","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Running time","level":2,"score":0.42039021849632263},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3682308793067932},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.34556475281715393},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.1745888590812683},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"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/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","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},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"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/C124952713","wikidata":"https://www.wikidata.org/wiki/Q8242","display_name":"Literature","level":1,"score":0.0},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/3357713.3384309","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3357713.3384309","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 52nd Annual ACM SIGACT Symposium on Theory of Computing","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2619213748","display_name":null,"funder_award_id":"CCF-1749609, CCF-1740551, DMS-1839116, CCF-1844855","funder_id":"https://openalex.org/F4320315254","funder_display_name":"Innovative Research Group Project of the National Natural Science Foundation of China"},{"id":"https://openalex.org/G8727312542","display_name":null,"funder_award_id":"715672","funder_id":"https://openalex.org/F4320338352","funder_display_name":"FP7 Ideas: European Research Council"}],"funders":[{"id":"https://openalex.org/F4320308943","display_name":"Microsoft Research","ror":"https://ror.org/00d0nc645"},{"id":"https://openalex.org/F4320315254","display_name":"Innovative Research Group Project of the National Natural Science Foundation of China","ror":null},{"id":"https://openalex.org/F4320338352","display_name":"FP7 Ideas: European Research Council","ror":"https://ror.org/0472cxd90"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":50,"referenced_works":["https://openalex.org/W1493892051","https://openalex.org/W1516099340","https://openalex.org/W1540625694","https://openalex.org/W1632601927","https://openalex.org/W1865797552","https://openalex.org/W1972332180","https://openalex.org/W1972525637","https://openalex.org/W1973117121","https://openalex.org/W1979740015","https://openalex.org/W1981914220","https://openalex.org/W1983193888","https://openalex.org/W1997901185","https://openalex.org/W2016425264","https://openalex.org/W2020301027","https://openalex.org/W2022004439","https://openalex.org/W2033040247","https://openalex.org/W2035144082","https://openalex.org/W2038073775","https://openalex.org/W2047782012","https://openalex.org/W2058790613","https://openalex.org/W2069291005","https://openalex.org/W2076680677","https://openalex.org/W2084990336","https://openalex.org/W2086867325","https://openalex.org/W2097796125","https://openalex.org/W2099450374","https://openalex.org/W2101043704","https://openalex.org/W2113623631","https://openalex.org/W2120248756","https://openalex.org/W2121689290","https://openalex.org/W2134342155","https://openalex.org/W2201600774","https://openalex.org/W2295512376","https://openalex.org/W2479585433","https://openalex.org/W2591972614","https://openalex.org/W2609713339","https://openalex.org/W2912973156","https://openalex.org/W2919126668","https://openalex.org/W2962877742","https://openalex.org/W2962921664","https://openalex.org/W2963098024","https://openalex.org/W2963464974","https://openalex.org/W2964122023","https://openalex.org/W2964343692","https://openalex.org/W3002603762","https://openalex.org/W3112410551","https://openalex.org/W4233058511","https://openalex.org/W4244670803","https://openalex.org/W4249843299","https://openalex.org/W4250955649"],"related_works":["https://openalex.org/W3099313426","https://openalex.org/W4287593139","https://openalex.org/W752783541","https://openalex.org/W1506547947","https://openalex.org/W2995605830","https://openalex.org/W4206811032","https://openalex.org/W2086123442","https://openalex.org/W2596457687","https://openalex.org/W3212757063","https://openalex.org/W2093666864"],"abstract_inverted_index":{"In":[0],"this":[1,26,53,70],"paper":[2],"we":[3,28,68],"provide":[4,29],"an":[5],"O(nd+d":[6],"3)":[7],"time":[8,72,90],"randomized":[9],"algorithm":[10],"for":[11,94],"solving":[12,95],"linear":[13,85,97],"programs":[14,98],"with":[15,21],"d":[16],"variables":[17],"and":[18,43,47,64,78],"n":[19],"constraints":[20],"high":[22],"probability.":[23],"To":[24],"obtain":[25,69],"result":[27],"a":[30,81],"robust,":[31],"primal-dual":[32],"O(\u221ad)-iteration":[33],"interior":[34],"point":[35],"method":[36,54],"inspired":[37],"by":[38],"the":[39,61],"methods":[40],"of":[41],"Lee":[42],"Sidford":[44],"(2014,":[45],"2019)":[46],"show":[48],"how":[49],"to":[50],"efficiently":[51],"implement":[52],"using":[55,74],"new":[56],"data-structures":[57],"based":[58],"on":[59],"heavy-hitters,":[60],"Johnson\u2013Lindenstrauss":[62],"lemma,":[63],"inverse":[65],"maintenance.":[66],"Interestingly,":[67],"running":[71,89],"without":[73],"fast":[75,105],"matrix":[76,106],"multiplication":[77],"consequently,":[79],"barring":[80],"major":[82],"advance":[83],"in":[84],"system":[86],"solving,":[87],"our":[88],"is":[91],"near":[92],"optimal":[93],"dense":[96],"among":[99],"algorithms":[100],"that":[101],"do":[102],"not":[103],"use":[104],"multiplication.":[107]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":14},{"year":2021,"cited_by_count":12},{"year":2020,"cited_by_count":15}],"updated_date":"2026-03-09T08:58:05.943551","created_date":"2025-10-10T00:00:00"}
