Beyond Averaging in John Ellipsoid Approximation: High-Accuracy Algorithms in the Leverage-Score Model
arXiv:2606.20082v1 Announce Type: cross Abstract: The John ellipsoid of a symmetric polytope $P=\{\mathbf{x}\in\mathbb{R}^d:\|\mathbf{A}\mathbf{x}\|_\infty\le1\}$, $\mathbf{A}\in\mathbb{R}^{n\times d}$, is computed by a long line of leverage-score algorithms, from Cohen, Cousins, Lee and Yang (COLT 2019) to its successors [WY24, CLS+25], all reaching a $(1+\varepsilon)$-approximation in $\Theta(\varepsilon^{-1}\log(n/d))$ iterations. We separate this complexity into three costs the modern line conflates (certification, identification, and accuracy) and locate the historical $\varepsilon^{-1}$
This is a theoretical computer science paper published on arXiv, representing ongoing academic research in algorithmic efficiency.
This paper refines algorithms for a specific mathematical problem, relevant primarily to researchers in computational mathematics and theoretical computer science, not directly impacting broader strategic concerns.
This paper improves the understanding and efficiency of calculating John ellipsoid approximations, which is a niche area of algorithmic research.
Increased efficiency in a specific mathematical computation.
Potential for marginal improvements in related computational geometry or optimization problems.
Very long-term, highly indirect contributions to broader AI or optimization landscapes are conceivable but extremely tenuous.
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