  We consider networks of small, autonomous devices that communicate with each
other wirelessly. Minimizing energy usage is an important consideration in
designing algorithms for such networks, as battery life is a crucial and
limited resource. Working in a model where both sending and listening for
messages deplete energy, we consider the problem of finding a maximal matching
of the nodes in a radio network of arbitrary and unknown topology.
  We present a distributed randomized algorithm that produces, with high
probability, a maximal matching. The maximum energy cost per node is $O(\log^2
n)$, where $n$ is the size of the network. The total latency of our algorithm
is $O(n \log n)$ time steps. We observe that there exist families of network
topologies for which both of these bounds are simultaneously optimal up to
polylog factors, so any significant improvement will require additional
assumptions about the network topology.
  We also consider the related problem of assigning, for each node in the
network, a neighbor to back up its data in case of node failure. Here, a key
goal is to minimize the maximum load, defined as the number of nodes assigned
to a single node. We present a decentralized low-energy algorithm that finds a
neighbor assignment whose maximum load is at most a polylog($n$) factor bigger
that the optimum.
