Duty-Cycle-Aware Minimum-Energy Multicasting in Wireless Sensor Networks

In duty-cycled wireless sensor networks, the nodes switch between active and dormant states, and each node may determine its active/dormant schedule independently. This complicates the Minimum-Energy Multicasting (MEM) problem, which has been primarily studied in always-active wireless ad-hoc networks. In this paper, we study the duty-cycle-aware MEM problem in wireless sensor networks, and we present a formulation of the Minimum-Energy Multicast Tree Construction and Scheduling (MEMTCS) problem. We prove that the MEMTCS problem is NP-hard, and it is unlikely to have an approximation algorithm with a performance ratio of $(1-o(1))\ln\Delta$, where $\Delta$ is the maximum node degree in a network. We propose a polynomial-time approximation algorithm for the MEMTCS problem with a performance ratio of $\mathcal{O}(H(\Delta+1))$, where $H(\cdot)$ is the harmonic number. We also provide a distributed implementation of our algorithm. Finally, we perform extensive simulations and the results demonstrate that our algorithm significantly outperform other known algorithms in terms of both the total energy cost and the transmission redundancy.