We address the fundamental network design problem of constructing approximate minimum spanners. Our contributions are for distributed setting, providing both algorithmic and hardness results. main result shows that an $\alpha$-approximation directed $k$-spanner $k \geq 5$ requires $\Omega(n /\sqrt{\alpha}\log{n})$ rounds using deterministic algorithms or $\Omega(\sqrt{n }/\sqrt{\alpha}\log{n})$...

Abstract We consider a scenario where server is wirelessly connected to countless sensor nodes that continuously measure data. The task of the monitor sensors’ More precisely, at each time step calculates function defined over current measurements sensors. Since sensors only have small computational power and tight battery constraints, communication between should be as possible, i.e., we aim m...