  In distributed network computing, a variant of the LOCAL model has been
recently introduced, referred to as the SLEEPING model. In this model, nodes
have the ability to decide on which round they are awake, and on which round
they are sleeping. Two (adjacent) nodes can exchange messages in a round only
if both of them are awake in that round. The SLEEPING model captures the
ability of nodes to save energy when they are sleeping. In this framework, a
major question is the following: is it possible to design algorithms that are
energy efficient, i.e., where each node is awake for a few number of rounds
only, without losing too much on the time efficiency, i.e., on the total number
of rounds? This paper answers positively to this question, for one of the most
fundamental problems in distributed network computing, namely
$(\Delta+1)$-coloring networks of maximum degree $\Delta$. We provide a
randomized algorithm with average awake-complexity constant, maximum
awake-complexity $O(\log\log n)$ in $n$-node networks, and round-complexity
$poly\!\log n$.
