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arXiv:2611.07980 · v1

Solving Linear Programs in the Matrix Multiplication Time

Zhao Song
cs.DS
首次提交 2026-11-05 21:10
版本更新 2026-11-05 21:10
雷达观测 2026-11-06 11:06
arXiv ↗PDF ↗

摘要

We give a randomized algorithm for feasible bounded-box linear programs with $n$ variables and $d\le n=O(d)$ linearly independent equality constraints. For additive accuracy $ε$, its expected running time is $O((n^ω+n^2\log n)\log(1/ε))$, where $ω$ is the matrix multiplication exponent. This answers the matrix-multiplication-time open question posted in Song's Ph.D. thesis [Son19] in this setting.

作者备注：124 pages, 5 figures

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v1 · 2026-11-05 21:10 · 最新观测版本

Solving Linear Programs in the Matrix Multiplication Time

We give a randomized algorithm for feasible bounded-box linear programs with $n$ variables and $d\le n=O(d)$ linearly independent equality constraints. For additive accuracy $ε$, its expected running time is $O((n^ω+n^2\log n)\log(1/ε))$, where $ω$ is the matrix multiplication exponent. This answers the matrix-multiplication-time open question posted in Song's Ph.D. thesis [Son19] in this setting.

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