We investigate local computation algorithms (LCA) for two-coloring of $k$-uniform hypergraphs. We focus on hypergraph instances that satisfy strengthened assumption of the Lov\'{a}sz Local Lemma of the form $2^{1-\alpha k} (\Delta+1) \mathrm{e} < 1$, where $\Delta$ is the bound on the maximum edge degree. The main question which arises here is for how large $\alpha$ there exists an LCA that is able to properly color such hypergraphs in polylogarithmic time per query. We describe briefly how upgrading the classical sequential procedure of Beck from 1991 with Moser and Tardos' RESAMPLE yields polylogarithmic LCA that works for $\alpha$ up to $1/4$. Then, we present an improved procedure that solves wider range of instances by allowing $\alpha$ up to $1/3$.

翻译：我们研究k-一致超图二着色的局部计算算法（LCA）。重点关注满足Lovász局部引理加强假设的超图实例，该假设形式为$2^{1-\alpha k} (\Delta+1) \mathrm{e} < 1$，其中$\Delta$为最大边度约束。这里提出的核心问题是：对于多大的$\alpha$值，存在可在每次查询时以多对数时间正确着色此类超图的LCA。我们简要描述了如何将Beck（1991）的经典顺序算法与Moser和Tardos的RESAMPLE相结合，从而得到在$\alpha$高达$1/4$时有效的多对数时间LCA。随后，我们提出了一种改进算法，通过允许$\alpha$值达到$1/3$，能够求解更广泛的实例范围。