  Distributed consensus has been widely studied for sensor network
applications. Whereas the asymptotic convergence rate has been extensively
explored in prior work, other important and practical issues, including energy
efficiency and link reliability, have received relatively little attention. In
this paper, we present a distributed consensus approach that can achieve a good
balance between convergence rate and energy efficiency.
  The approach selects a subset of links that significantly contribute to the
formation of consensus at each iteration, thus adapting the network's topology
dynamically to the changes of the sensor states. A global optimization problem
is formulated for optimal link selection, which is subsequently factorized into
sub-problems that can be solved locally, and practically via approximation. An
algorithm is derived to solve the approximation efficiently, using quadratic
programming (QP) relaxation and random sampling. Simulations on networks of
different types demonstrate that the proposed method reduces the communication
energy costs without significantly impacting the convergence rate and that the
approach is robust to link failures.
