  Linial's famous color reduction algorithm reduces a given $m$-coloring of a
graph with maximum degree $\Delta$ to a $O(\Delta^2\log m)$-coloring, in a
single round in the LOCAL model. We show a similar result when nodes are
restricted to choose their color from a list of allowed colors: given an
$m$-coloring in a directed graph of maximum outdegree $\beta$, if every node
has a list of size $\Omega(\beta^2 (\log \beta+\log\log m + \log \log
|\mathcal{C}|))$ from a color space $\mathcal{C}$ then they can select a color
in two rounds in the LOCAL model. Moreover, the communication of a node
essentially consists of sending its list to the neighbors. This is obtained as
part of a framework that also contains Linial's color reduction (with an
alternative proof) as a special case. Our result also leads to a defective list
coloring algorithm. As a corollary, we improve the state-of-the-art truly local
$(deg+1)$-list coloring algorithm from Barenboim et al. [PODC'18] by slightly
reducing the runtime to $O(\sqrt{\Delta\log\Delta})+\log^* n$ and significantly
reducing the message size (from huge to roughly $\Delta$). Our techniques are
inspired by the local conflict coloring framework of Fraigniaud et al.
[FOCS'16].

Data Structures and Algorithms;Distributed, Parallel, and Cluster Computing