Deterministic Distributed Vertex Coloring: Simpler, Faster, and without Network Decomposition

We present a simple deterministic distributed algorithm that computes a ($\Delta+1$)-vertex coloring in $O(\text{log}^{2}\Delta. \text{log}\ n)$ rounds. The algorithm can be implemented with $O(\text{log}\ n)$-bit messages. The algorithm can also be extended to the more general ($degree+1$)-list coloring problem. Obtaining a polylogarithmic-time determin...