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 was primarily studied in always-active wireless ad hoc networks. In this paper, we study the duty-cycle-aware MEM problem in wireless sensor networks both for one-to-many multicasting and for all-to-all multicasting. In the case of one-to-many multicasting, we present a formalization 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 - 0(1)) ln Δ, where Δ is the maximum node degree in a network. We propose a polynomial-time approximation algorithm for the MEMTCS problem with a performance ratio of O (H(Δ + 1)), where H(·) is the harmonic number. In the case of all-to-all multicasting, we prove that the Minimum-Energy Multicast Backbone Construction and Scheduling (MEMBCS) problem is also NP-hard and present an approximation algorithm for it, which has the same approximation ratio as that of the proposed algorithm for the MEMTCS problem. We also provide a distributed implementation of our algorithms, as well as a simple but efficient collision-free scheduling scheme to avoid packet loss. Finally, we perform extensive simulations, and the results demonstrate that our algorithms significantly outperform other known algorithms in terms of the total transmission energy cost, without sacrificing much of the delay performance.