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- W3005337135 abstract "In this paper we provide an $tilde{O}(nd+d^{3})$ time randomized algorithm for solving linear programs with $d$ variables and $n$ constraints with high probability. To obtain this result we provide a robust, primal-dual $tilde{O}(sqrt{d})$-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." @default.
- W3005337135 created "2020-02-14" @default.
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- W3005337135 date "2020-02-06" @default.
- W3005337135 modified "2023-10-03" @default.
- W3005337135 title "Solving Tall Dense Linear Programs in Nearly Linear Time" @default.
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- W3005337135 doi "https://doi.org/10.48550/arxiv.2002.02304" @default.
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