  Recent work has shown that it is sometimes feasible to significantly reduce
the energy usage of some radio-network algorithms by adaptively powering down
the radio receiver when it is not needed. Although past work has focused on
modifying specific network algorithms in this way, we now ask the question of
whether this problem can be solved in a generic way, treating the algorithm as
a kind of black box.
  We are able to answer this question in the affirmative, presenting a new
general way to modify arbitrary radio-network algorithms in an attempt to save
energy. At the expense of a small increase in the time complexity, we can
provably reduce the energy usage to an extent that is provably nearly optimal
within a certain class of general-purpose algorithms.
  As an application, we show that our algorithm reduces the energy cost of
breadth-first search in radio networks from the previous best bound of
$2^{O(\sqrt{\log n})}$ to $\mathrm{polylog}(n)$, where $n$ is the number of
nodes in the network
  A key ingredient in our algorithm is hierarchical clustering based on
additive Voronoi decomposition done at multiple scales. Similar clustering
algorithms have been used in other recent work on energy-aware computation in
radio networks, but we believe the specific approach presented here may be of
independent interest.
