Author

Dylan J. Altschuler

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Preprint Jul 2026

Online Beck--Fiala Down to Logarithmic Sparsity

The main thrust of the result is that it is actually obtained by an efficient \textit{online} algorithm that minimizes prefix discrepancy, and is also essentially optimal, since online prefix discrepancy is known to scale as $\omega(\sqrt{d})$ for $d =o(\log T)$.

Dylan J. Altschuler, Konstantin E. Tikhomirov · 1 citation