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arXiv · 2610.17133

LOCAL LLL in $\operatorname{poly}(\log\log n)$ Rounds

Maxime Flin·Mohsen Ghaffari·Magnús M. Halldórsson·Yannic Maus·Alexandre Nolin
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Abstract

We provide a $\operatorname{poly}(\log\log n)$-round randomized LOCAL algorithm for the constructive Lovász Local Lemma with polynomial criterion $pd^{c} < 1$, for a sufficiently large constant $c$. The best previous general round complexity was $\widetilde O(\log n)$. The key ingredient is a local reduction that amplifies the LLL probability exponent quadratically, while increasing the dependency radius only by a constant factor.

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Maxime Flin, Mohsen Ghaffari, Magnús M. Halldórsson, Yannic Maus, Alexandre Nolin. 2026-10-12. LOCAL LLL in $\operatorname{poly}(\log\log n)$ Rounds. https://arxiv.org/abs/2610.17133

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