Low-Complexity Energy-Efficient Broadcasting in One-Dimensional Wireless Networks

In this paper, we investigate the transmission range assignment for
N
wireless nodes located on a line (a linear wireless network) for broadcasting data from one specific node to all the nodes in the network with minimum energy. Our goal is to find a solution that has low complexity and yet performs close to optimal. We propose an algorithm for finding the optimal assignment (which results in the minimum energy consumption) with complexity
O
(
N
²
) . An approximation algorithm with complexity
O
(
N
) is also proposed. It is shown that, for networks with uniformly distributed nodes, the linear-time approximate solution obtained by this algorithm, on average, performs practically identical to the optimal assignment. Both the optimal and the suboptimal algorithms require full knowledge of the network topology and are thus centralized. We also propose a distributed algorithm of negligible complexity, i.e., with complexity
O
(1), which only requires knowledge of the adjacent neighbors at each wireless node. Our simulations demonstrate that the distributed solution, on average, performs almost as good as the optimal solution for networks with uniformly distributed nodes.