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For the current value of \u03c9 \u03b4 2.37 and \u03b1 \u03b4 0.31, our algorithm takes\n            <jats:italic>O<\/jats:italic>\n            <jats:sup>*<\/jats:sup>\n            (\n            <jats:italic>n<\/jats:italic>\n            <jats:sup>\u03c9<\/jats:sup>\n            log (\n            <jats:italic>n<\/jats:italic>\n            \/\u03b4)) time. When \u03c9 = 2, our algorithm takes\n            <jats:italic>O<\/jats:italic>\n            <jats:sup>*<\/jats:sup>\n            (\n            <jats:italic>n<\/jats:italic>\n            <jats:sup>2+1\/6<\/jats:sup>\n            log (\n            <jats:italic>n<\/jats:italic>\n            \/\u03b4)) time.\n          <\/jats:p>\n          <jats:p>Our algorithm utilizes several new concepts that we believe may be of independent interest:<\/jats:p>\n          <jats:p>\u2022 We define a stochastic central path method.<\/jats:p>\n          <jats:p>\n            \u2022 We show how to maintain a projection matrix \u221a\n            <jats:italic>W<\/jats:italic>\n            <jats:italic>A<\/jats:italic>\n            <jats:sup>\u22a4<\/jats:sup>\n            (\n            <jats:italic>AWA<\/jats:italic>\n            <jats:sup>\u22a4<\/jats:sup>\n            )\n            <jats:sup>\u22121<\/jats:sup>\n            <jats:italic>A<\/jats:italic>\n            \u221a\n            <jats:italic>W<\/jats:italic>\n            in sub-quadratic time under \\ell\n            <jats:sub>2<\/jats:sub>\n            multiplicative changes in the diagonal matrix\n            <jats:italic>W<\/jats:italic>\n            .\n          <\/jats:p>","DOI":"10.1145\/3424305","type":"journal-article","created":{"date-parts":[[2021,1,5]],"date-time":"2021-01-05T17:04:35Z","timestamp":1609866275000},"page":"1-39","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":114,"title":["Solving Linear Programs in the Current Matrix Multiplication Time"],"prefix":"10.1145","volume":"68","author":[{"given":"Michael B.","family":"Cohen","sequence":"first","affiliation":[{"name":"Massachusetts Institute of Technology, Cambridge, Massachusetts"}]},{"given":"Yin Tat","family":"Lee","sequence":"additional","affiliation":[{"name":"The University of Washington 8 MSR Redmond, Seattle, WA, USA"}]},{"given":"Zhao","family":"Song","sequence":"additional","affiliation":[{"name":"The University of Texas at Austin, Princeton, NJ, USA"}]}],"member":"320","published-online":{"date-parts":[[2021,1,5]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.4230\/LIPIcs.CCC.2019.12"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1109\/FOCS.2018.00061"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1145\/2746539.2746554"},{"key":"e_1_2_1_4_1","unstructured":"Jan van den Brand Binghui Peng Zhao Song and Omri Weinstein. 2020. 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