Parallel Batch Dynamic Vertex Coloring in $O(\log \Delta)$ Amortized Update Time

Abstract

We present the first parallel batch-dynamic algorithm for maintaining a proper $(\Delta + 1)$-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 $O(\log \Delta)$ expected amortized update time and, for any batch of $b$ updates, has parallel span $O(\operatorname{polylog} b + \operatorname{polylog} n)$ with high probability.