  In this work, a heterogeneous set of wireless devices sharing a common access
point collaborates to perform a set of tasks. Using the Map-Reduce distributed
computing framework, the tasks are optimally distributed amongst the nodes with
the objective of minimizing the total energy consumption of the nodes while
satisfying a latency constraint. The derived optimal collaborative-computing
scheme takes into account both the computing capabilities of the nodes and the
strength of their communication links. Numerical simulations illustrate the
benefits of the proposed optimal collaborative-computing scheme over a blind
collaborative-computing scheme and the non-collaborative scenario, both in term
of energy savings and achievable latency. The proposed optimal scheme also
exhibits the interesting feature of allowing to trade energy for latency, and
vice versa.
