  A customary solution to reduce the energy consumption of wireless
communication devices is to periodically put the radio into low-power sleep
mode. A relevant problem is to schedule the wake-up of nodes in such a way as
to ensure proper coordination among devices, respecting delay constraints while
still saving energy. In this paper, we introduce a simple algebraic
characterization of the problem of periodic wake-up scheduling under both
energy consumption and delay constraints. We demonstrate that the general
problem of wake-up times coordination is equivalent to integer factorization
and discuss the implications on the design of efficient scheduling algorithms.
We then propose simple polynomial time heuristic algorithms that can be
implemented in a distributed fashion and present a message complexity of the
order of the number of links in the network. Numerical results are provided in
order to assess the performance of the proposed techniques when applied to
wireless sensor networks.
