Topology control is a well-known strategy to save energy and extend the lifetime of wireless sensor networks. This paper introduces the A3 (a tree) algorithm, a simple, distributed, and energy-efficient topology construction mechanism that finds a sub-optimal Connected Dominating Set (CDS) to turn unnecessary nodes off while keeping the network connected and providing complete communication coverage. A3 utilizes a weighted distance-energy-based metric that permits the network operator to trade off the lengths of the branches (distance) for the robustness and durability of the tree (energy). Comparisons with other well-known topology construction mechanisms show the superiority of the proposed scheme in terms of the number of active nodes and energy efficiency. Simulation experiments show that to achieve complete communication coverage, A3 needs only 6% and 41% of the nodes active in dense and sparse scenarios, versus 8% and 43% and 5% and 43% of the EECDS and CDS- Rule-K algorithms, respectively. More importantly, the proposed protocol presents a low linearly bounded worst-case amount of messages per node that limits the overhead and the energy usage compared to a non-linear increase of the EECDS and CDS-Rule- K algorithms.
