  We present new randomized algorithms that improve the complexity of the
classic $(\Delta+1)$-coloring problem, and its generalization
$(\Delta+1)$-list-coloring, in three well-studied models of distributed,
parallel, and centralized computation:
  Distributed Congested Clique: We present an $O(1)$-round randomized algorithm
for $(\Delta+1)$-list coloring in the congested clique model of distributed
computing. This settles the asymptotic complexity of this problem. It moreover
improves upon the $O(\log^\ast \Delta)$-round randomized algorithms of Parter
and Su [DISC'18] and $O((\log\log \Delta)\cdot \log^\ast \Delta)$-round
randomized algorithm of Parter [ICALP'18].
  Massively Parallel Computation: We present a $(\Delta+1)$-list coloring
algorithm with round complexity $O(\sqrt{\log\log n})$ in the Massively
Parallel Computation (MPC) model with strongly sublinear memory per machine.
This algorithm uses a memory of $O(n^{\alpha})$ per machine, for any desirable
constant $\alpha>0$, and a total memory of $\widetilde{O}(m)$, where $m$ is the
size of the graph. Notably, this is the first coloring algorithm with
sublogarithmic round complexity, in the sublinear memory regime of MPC. For the
quasilinear memory regime of MPC, an $O(1)$-round algorithm was given very
recently by Assadi et al. [SODA'19].
  Centralized Local Computation: We show that $(\Delta+1)$-list coloring can be
solved with $\Delta^{O(1)} \cdot O(\log n)$ query complexity, in the
centralized local computation model. The previous state-of-the-art for
$(\Delta+1)$-list coloring in the centralized local computation model are based
on simulation of known LOCAL algorithms.

Data Structures and Algorithms