In this paper we provide an\u00a0\\(O_~(nd+d_3)\\)\u00a0time randomized algorithm for solving linear programs with\u00a0\\(d\\)\u00a0variables and\u00a0\\(n\\)\u00a0constraints with high probability. To obtain this result we provide a robust, primal-dual\u00a0\\(O_~(\\sqrt{d–\u221a})\\)-iteration interior point method inspired by the methods of Lee and Sidford (2014, 2019) and show how to efficiently implement this method using new data-structures based on heavy-hitters, the Johnson-Lindenstrauss lemma, and inverse maintenance. Interestingly, we obtain this running time without using fast matrix multiplication and consequently, barring a major advance in linear system solving, our running time is near optimal for solving dense linear programs among algorithms that do not use fast matrix multiplication.<\/p>\n","protected":false},"excerpt":{"rendered":"
In this paper we provide an\u00a0\u00a0time randomized algorithm for solving linear programs with\u00a0\u00a0variables and\u00a0\u00a0constraints with high probability. To obtain this result we provide a robust, primal-dual\u00a0-iteration interior point method inspired by the methods of Lee and Sidford (2014, 2019) and show how to efficiently implement this method using new data-structures based on heavy-hitters, the Johnson-Lindenstrauss […]<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","msr-author-ordering":[{"type":"text","value":"Jan van den Brand","user_id":0},{"type":"text","value":"Yin Tat Lee","user_id":0},{"type":"user_nicename","value":"Aaron Sidford","user_id":"31120"},{"type":"user_nicename","value":"Zhao 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