We present the first parallel batch-dynamic algorithm for maintaining a proper $(Δ+ 1)$-vertex coloring. Our approach builds on a new sequential dynamic algorithm inspired by the work of Bhattacharya et al. (SODA'18). The resulting randomized algorithm achieves $O(\log Δ)$ expected amortized update time and, for any batch of $b$ updates, has parallel span $O(\operatorname{polylog} b + \operatorname{polylog} n)$ with high probability.

翻译：我们提出了首个用于维护正确 $(Δ+1)$-顶点着色的并行批量动态算法。该方法基于受 Bhattacharya 等人（SODA'18）工作启发的新顺序动态算法。所得随机化算法实现了 $O(\\log Δ)$ 的期望摊销更新时间，且对于任意包含 $b$ 个更新的批次，在高概率下具有 $O(\\operatorname{polylog} b + \\operatorname{polylog} n)$ 的并行跨度。