Optimal (degree+1)-Coloring in Congested Clique
This solves a benchmark problem in distributed and parallel computing, with implications for algorithm design in network settings.
The paper tackled the (degree+1)-list coloring problem in the Congested Clique model by showing it can be solved deterministically in a constant number of rounds, settling its complexity.
We consider the distributed complexity of the (degree+1)-list coloring problem, in which each node $u$ of degree $d(u)$ is assigned a palette of $d(u)+1$ colors, and the goal is to find a proper coloring using these color palettes. The (degree+1)-list coloring problem is a natural generalization of the classical $(Î+1)$-coloring and $(Î+1)$-list coloring problems, both being benchmark problems extensively studied in distributed and parallel computing. In this paper we settle the complexity of the (degree+1)-list coloring problem in the Congested Clique model by showing that it can be solved deterministically in a constant number of rounds.