Graph coloring problems are among the most fundamental problems in parallel and distributed computing, and have been studied extensively in both settings. In this context, designing efficient deterministic algorithms for these problems has been found particularly challenging. In this work we consider this challenge, and design a novel framework for derandomizing algorithms for coloring-type problems in the Massively Parallel Computation (MPC) model with sublinear space. We give an application of this framework by showing that a recent $(degree+1)$-list coloring algorithm by Halldorsson et al. (STOC'22) in the LOCAL model of distributed computation can be translated to the MPC model and efficiently derandomized. Our algorithm runs in $O(\log \log \log n)$ rounds, which matches the complexity of the state of the art algorithm for the $(\Delta + 1)$-coloring problem.

翻译：图着色问题是并行与分布式计算中最基本的问题之一，在这两种场景下都得到了广泛研究。在此背景下，为这些问题设计高效的确定性算法被证明极具挑战性。本研究聚焦于这一挑战，针对亚线性空间的大规模并行计算（MPC）模型中的着色类问题，设计了一种新颖的去随机化框架。通过展示Halldorsson等人（STOC'22）在分布式计算LOCAL模型中提出的近期(degree+1)-列表着色算法可被迁移到MPC模型并高效地实现去随机化，我们给出了该框架的一个应用实例。我们的算法在$O(\log \log \log n)$轮内运行，这与(Δ+1)-着色问题当前最优算法的复杂度相匹配。