Max-Life Power Schedule for Connectivity and Biconnectivity in Wireless Ad Hoc Networks

Abstract

Given the initial energy supplies and the maximal transmission power of the individual nodes in a wireless ad hoc network, a power schedule of duration t for a specified topological property $\mathcal{P}$ is a scheduling of the transmission powers of the individual nodes over the period [0, t] such that (1) the total amount of energy consumed by each node during the period [0, t] does not exceed its initial energy supply, (2) the transmission power of each node at any moment in the period [0, t] does not exceed its maximal transmission power, and (3) the produced network topology at any moment in the period [0, t] satisfies the property $\mathcal{P}$. The problem Max-Life Power Schedule for $\mathcal{P}$ seeks a power schedule of the maximal duration for $\mathcal{P}$. Let g be the golden ratio $(1+\sqrt{5}) /2$, and ε be an arbitrarily positive constant less than one. In this paper, we present a $9g/\left(1-\varepsilon\right)^{2}$-approximation algorithm for Max-Life Power Schedule for Connectivity, a $36g/\!\left(1-\varepsilon\right)^{2}$-approximation algorithm for Max-Life Power Schedule for 2-Node-Connectivity, and a $36g/\!\left(1-\varepsilon\right)^{2}$-approximation algorithm for Max-Life Power Schedule for 2-Edge-Connectivity.